A bicycle odometer (whica s)5(r3:svli 7pqp uwh measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you u:ulavp5q ()p7w i3ss rse it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocir z4depb+ adtggm61m7 imgr5h9(jt0 4ty. Does a point on the rim have a1 9gi(d7dtz65 0m+mrprhgm e j4gb4tradial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular ve3r; u(wx6 , 7u* apuijcs0lemolocity $\omega$ Explain.

Can a small force ever exert a greater torque thanoi,cx ywq*snyw e1ud*9,a7z 0 a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behind your head thaoyjoqfjp lkyt p, );u 0x3-8k/n when your arms are stretched out in front of you? A diagramjtuxop ;/lkjq yk p8,y)o-f 03 may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear whecoly0hp:2 i.x el and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small frontx0:l cypo.h i2 sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with fles*d y3amm,bqe0eg*9ro h and muscle concentrat *ae,yo 0 rg*mqmebd93ed high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–3l1w gxk/2e:k c5) carry a long, narrow beam?

If the net force on a system is zero, is the net tr n1ch rpr,).v m2pvn+orque also zero? If the net torque on a system is zero, is the net fv+v2pr1 )rrh,n c pnm.orce zero?

Two inclines have the same hehb 3(*2j kfn:totrvz0ight but make different angles with the horizontal. The same steel ball is rolled doj3ot2f :k*vb zt(hn 0rwn each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inclmz;a-wvbvjo26q6 l)4 s1 c pyaine. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Wy2a 16 4vmwj qszvp-aclb6 ;)ohich has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start 6;g-t .l8/ tagjsop rwfrom rest at the top of an incline. Which reaches the bottom first? Which has the gr.-pglot /sjt8;r g 6waeater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular eb*v,tb-z)l smomentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Expl*bl)bte-svz ,ain.

If there were a great migration o5qq mrp(hxr1 z o6o/ oc6ah99qf people toward the Earth’s equator, how would this affect q a1c9rqoh/6xo96o zm qr(5hpthe length of the day?

Can the diver of Fig. 8–22jcl6n0/ sbz jbi8criian r.,6vv(2o9 do a somersault without having any initial rotation when she leave cslan/.,c jrojb v n0iv(86zii2br26s the board?

The moment of inertia of a rotating solid disk about an axis th1yql ts1s4y6i rough its center of mais 1ylt6syq14ss is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotatiif(s3u:+ r7v go-ooob7) iemoyy,a+ q ng stool holding a 2-kg mass in each outstretched hand. If you 3oiyb)+(vu7a m:-rgoo+ ,f 7q eoiyossuddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, on064l:wimygynm b e8 (u7hg h)ke is hollow and the other is solid. Describe an ex7h8gwy)4gn hiykm : b6 eul0(mperiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal a6vygu5d vxyp ;y i;+h6x* y5osxle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Idhs;x5;vv6yi6* gy+yo uy5xp s the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntgprl2x9q/kd; m l5 +aq kis,(pable. What ha5 mg, lkxs9pl 2/qrd;+(aipqkppens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickx.-8 qc(f pk3hcjmcx- q/ fl8fly. As he throws the ball, the upper part of his body rotatex3c--c fq8 kfqfx hlj/m.cp(8s. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation,aatrn0cq ukew8r9 2lzx7 b ,3 of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helic a,9qbk3l, zen a7xuw 2rt80rcopter stable.

  Express the following angles in ra zl )h7 yv1-4-hchgkineyx,c, dians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amaznx-d8(-co0 h3tjy :ar )v hsveing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as se-3-dx:8 oj)cntrhh(esav 0v yen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,0k-*vt o+3mue)f ypv;m 00 km from Earth. The beam diverges at an anvm;-o*+v3ymp)uetfk gle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. Whenm ,a4s:ana-j rfew69l the motor is turned off during operation, the blad ar9nefwa4jml sa -,6:es slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m 3j wou 3zaoj--iwak9)to another child. If the ball makes 15.0 revolutions, what is aj393 z)iakow -wjuo -its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many r*eb-8ev gtsifv 1kay6t,m/8bevolutions do the wheels,betg*88 bv6i fmtavy1 s/ ke- make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angx* gghd8pm/)ba1:eriular velog d1 bh*/e8m:gar)xpicity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revoluti (m,wxr1 yp co64jc r,slgj k60:ftlc+on in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the centp,0y ,+4 kctjj6xrwcm 6:rgf(1cls oler?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a)nr 3hg0cm23cpi 0m) 2 epix*me in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spur- c7b rwq6w8eed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from t4 z3m *eybgpsltw; 8-u do*;zl+pgvc9 he axis of rotation is to experience an acceleratgptbdsvl4*;c ;z* ye-w38 go mzp +ul9ion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheelq9 l;fz )x)p9o5 utknozlpo;* accelerates uniformly about its center from 130 rpm to 280 o5;* )oxtozqk ; z9)plpu9 flnrpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius 8 9shg/ mj+:y lnyd8mg$R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronautszs)x.e7tef4l5ab q ew 4ab88*b;huo e aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The sq;t)he5esezax7b4 eflo8wb 84b.ua* pacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelera-/vs aujsj)q c+ow64v,c dk 5ztes uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions dsca duv5vs4ozj)/6 w+j-, ckqid it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm t(0-3c cvjt 6tafak3 aoo 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the rxd1vjkd0+ 2 tstresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final s2tv jddxr+10 kpeed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6.oog9l+m6i d) 8b g; inh8gr,dw5 s. How far will a point on the edge of the wheel haved,l8rbw g)ni +9o6;dhmgo8gi traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min Itj3 :m v cw(;h qxbf3hyhkds /z2xi)t2+ turns 1500 revolutions before2qvy hd )3:cfz2 xms (ibtw3;jhx/+hk it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 rm87 6qk9u*lkz zsdyp0 chd)-revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires hsy70zkc6 prlduq 8z kdh*m9-) ave a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces iz2-qyx*m7x- e 7wgfgq dxg8j 7ts speed uniformly from 95km/h to 45km/h The tires have a diam mx8z7dx-gfjg7q7w 2*gq-ye xeter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pxbzf)4h,0 lnw/4u bmtedal when climbing a hill. The pedals rotate i40uz 4bwm t)lhnf ,bx/n a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm b8+ ya*pspics/ ud8/uuk. ejp3ujg 44wide. What is the magnitude of the torque if 8+bs83*jsupj ayu gi . 4 pc/kdupu4e/the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque aboum,:+qetram dm0q e,w,t the axle of the wheel shown in Fig. 8–39. Assume that a friction mrq:,,mamd w 0,t+qe etorque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless 0cy de4jn q(u-x -ptp1rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calcx 4-y1jce( uqptd0n-p ulate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require p *l3l+jk;jr,1 i rr-lzr ifxxda(,.g tightening to a torque of 38 ,ri ;r rdf*lkilz(-pa,gj.+ ljr1x3x$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-(se +2qzr* d0qeg5p6ky2wwp xkg sphere of radius 0.648 m when the axis of rotation is theg* dqq2re+ys( k06pxz2pw 5wrough its center.    $kg \cdot m^2$

  Calculate the moment of inertpsobf/k) 3.g 9ouq5oyia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (whysqf3 )5goouy.o 9k /bp?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, lighug l(ycrl99se whb.* :;fui.ut rod is rotated in a horizontal circf*(u ycw.s;lug9e.rlb:iu9 h le of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a w95h1k -gtgg; lz2ikf-opgqr yi8 2 8ybowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her handg9itpz2gwg8 i-y - o1gkfk8yh2r5q l;s and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of poih6eu3qnidp; 8g7 i7rhq p2rj 9nt objects shown in Fig. 8–43 aboutd igerq7j 7hh; i3u 6nr2qp98p
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total33 rprgxwh00gspv, 3hl(g*n a mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, engi gm97uy,dzhype; 0 cb;neers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min?yhm9;bcy p zg,;u 7ed0 $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylin1 3anwh 6e2kupder with a radius of 8.50 cm and a mass of 0.580 kg. kp32e u1w6hna Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, acceleratislkbu y;3*;dnh hf/x/ng it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and is a2jjz;x2 yt2lo)x :wmoar. kyna4o 4cf rv2i 8:ble to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (e)a::co z vwxjf .my2k nxo4a jrr oly;t224i82ach with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating atyqdho2r-cys9g8 4d+g 10,300 rpm is shut off and is eventually brought uniformly to rest by d-9os q+y 84grc y2hdga frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelrxjbixv;/,xxy/a a99 n : o-egerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forear.l swu2 wvbc.7g n1.5fpfji n)m, which rotates about the elbow join.pfunjs72f.b wi l5.wc )g1vnt under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig. 8yhh,0odjv0 :ncisqy b q l-f *gkjex:/,yo 9,7–46.xby jj -qqh9h,7s,g/*,dn ofyy0clkivo :0:e
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine con8+mfmr b y(7ipfh 1;smsists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates gze1ee*d;52(r rs reh -l7xyuthe hammer from rest within four full turns (revolutions) and releases it at-eu51(z7dg2; r ere*xyshrle a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia /up ypig4;(yo of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 280ak)dp54(j0 zfmd)), fl *btr5 d nojiz $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and-r*bz 6y meafc) -por( radius 9.0 cm rolls without slipping down a lane at 3.3 *a)cyerro-b m( fpz6- $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic enerah /u3 y5v- jgc7m,pxxgy of the Earth with respect to the Sun as the sum of two ter- vpyhcj,u/x 537mgax ms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius ofo 2kksx6 n5ow7 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assumes6oon75kkxw 2 it is a solid cylinder.    J

  A sphere of radius 20.0 (n :51)r wb,1o sozjca fx-nqv a,e8nocm and mass 1.80 kg starts from rest and rolls without slippi vcq,oo-b,1s( ) rafenanx1zowjn:58ng down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its 2w60n5lz,u cssx n e ixv)6,vltip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just6w xx c2,) 6sv,i nunlslve0z5 before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of1vh yeqn.d5qrmi rjq af+ n.;199u2u p a 0.210-kg ball rotating on the end of a thin stri 9ymq2. a9+qn du1r qh5 ife;vrup1.njng in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cy(aw.od r uff -rpg9xxcul7z).9j7b r /lindrical grinding wheel of r.pj(-a.for f7cx g9xuul) dbr7w 9z/ radius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is r-d il;zthj ;)aotating at a rate of 1.3rev/s If he-zhtd)a; ;i lj raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of inertlh+4mkvlj 5tds) 3m l-ia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is herd lv)l j34h5+-smmtk l angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotationfbwjt :6vs+v+mzy b0r,-zj 1 j rate from an initial rate of 1.0 rev every 2.0 s to a final wtjvmz+01fb+sbvrz-6:j j, y rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around awv.h4;u4 a0/ltfp nkk vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk a0t/kv .;klw4h 4 nfpuof mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of c7lo fh;;kn .ve7+43f zloahg a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Ezytri;sp8) gc fh27w9v( b 5duarth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an idbii (.jb7advn /v / -lgk/or7rnw :.ryx5tcv4entical disk rotating at angular speea rk7 /crnrw4/vb.:tl 5bj-.vnd/ x g(yii 7vod $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2i,ix0n+ hkoj,0jr8n uai m)c4.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round m:3 ;:.cqqg*6elfvb mll1ljqplatform .l qm:*e m l;f3qj1lqgcbvl:6of radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-rbjtd9vs b1qnw-phm1 ,i3t2y. ound is rotating freely with an angular velocity of 0.8h3,dvnpm 1-qt jyi b9w12b.st $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun event 3z8tzxak 0d3hually collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the 03atz z3k8xdhlost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winw,2 h yc4p;yi;pby fr2ds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass 2i tv)o mmu6dmetj4bn-lvzo w5.31.psmk.e0$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely withundpoyt lq 5( 9 5srk+zh:)9nxout friction. The moment of inertia of the person plus the platfo lndyrt5)uz:(phk+n 5oq99sx rm is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-roun-rdujo:j6-ojs6ad )t7jdhj 6 d turntable that is mounted on frictionlessju: 6sjj6 hojjd)d-r a-dt 7o6 bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope ror u(qfvc6 km)-lls on the ground with the end of the rope lying on the top edge of the s6km uqv)rcf (-pool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that t8x2fc -mlw5i pqmy l* w,qv/6xhe same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about *qf w/86ximx, w2 yvq5l-mcp lits own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rrkh0rzs pc7:kv 1:2pq est at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a unifhzc5uolc ,ko;4q)d q1; xm:pinn co*) 3jyx9gorm cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the1oxjc*:zopoc xkm ; 9n,;4q i lu3)hdyqc5ng) motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg and dtj6 s9gqaa88grm2*q fiameter 0.075 m, joined by a (concentric) thin solid cylindrical hub o6 9rm8t2*qja fgq 8asgf mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angulaml rb3d*u5t3 jr speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Su;ykpg qolynbd8-+uqu5 ez5/-n, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass inuqk-z /o8q;u-d lb+5 gy enpy5 the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy store 25inekz5o lrw1i,cmg4,-vrzk bn:u.d in a heavy rotating flywheel. :,k l4rmekz5bwc2. uoz v ,ni1gr5ni- Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustra d nt7gy/3q e+hv3*fomtes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a vk-h,k8 c t25vcy9msu+21i slhd w e,dhorizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivu4j2a 5- d ax74szcwhh 2o8wifot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The dsoa2 7 xh-a48 wh524zcfwuij rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is stand8mf* yu -hijty8zor v/; jpe5*ing vertically on the floor, and we want to exert a horizontal force F at its v* jeyj-;f u 5him/8rpto*yz 8axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a -i7j+ww f*ajdzji g11turn with a radius The forces acting on the cyclist and cycle w7*i jjdz-1 a1 +fjgwiare the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begins whebbxe -ypi5,nn:(2a*2w udu virling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this fe n 5evawx e22*b y,(bu-:nudpiat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as y1q wh,eg 76i407k+vt t cisuea solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angules iq707 ktew u+c1gtv46, yihar speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrican/0;e6r (14w kk 2uub shv8bmh*ishxdl plates, of ma mbbv u*8 2rx6;h(sn1 ei40/whkkhdsuss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radi3)z gy+r 0i jto5cqke7us r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of theoti3z+e jrqy7g k c)50 loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do3,mwqzk;9c ( jrzm 3xv not assume $r\ll R$ h =    (R-r)

  The tires of a car mak*pa,q0v qvz2we 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular p a*v z2,q0vwqacceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s