A bicycle odometer (whichfz.vj1b -afp(eg6shk9pi * ; h measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wvp* h6ik9(-zgf jfbha;p 1e s.heels?

Suppose a disk rotates at constant anvq3xsbt k) (m;(6;o vmepu y2qgular velocity. Does a point on the rim have radial and/or tangential acceleration? If ybpvq6e(q 2u 3x (mm;kov;ts)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 veloc8.uu m 6xqr*zxejl7 i7ity $\omega$ Explain.

Can a small force ever exert a greater torqu 0bqi 4lbxomif7hj. 9(e than 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 bq g-r ; 06,byv4al+fxllfd 1gpehind your head than when your arms a+bl;lg-v0,g d xr 6 4pf1qlfyare stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rearq1mq,y6f*ye.c- wsxq dc0- xzr.x +qs wheel 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-xq*ecxzfc 0ys .-+ qxqy1w mr6s.d,q gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legsye6tzr6g(k f,v9ph 4js z*ii4 with flesh t e,9pz hg*f6kjrsvi6z4 4(y iand muscle concentrated 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–iu((eujgq.cw u :;fx)t a0b.x35) carry a long, narrow beam?

If the net force on a system is zero, is the net torqc0pg0;gr :: pai p*lgrue also zero? If the net torque on a system is zero, is the net forceg;l* a:p0i :cppg0g rr zero?

Two inclines have the same height but make different angles with the horizontal.bd0lfgua6 vn8s ::kb9 The same steel ball is rolled down each incline. On which incline will the speed of the ballb:v 9n 6dlb80gfk :asu at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down *vauv;2g-mr mx zh 6r/an incline. 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 sperahug *z/m-v;6 2vrx med there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder vna5i7n+ g)de8 jc8knhave the same radius and the same mass. They start from rest at the top of an incline. Whi8+5gvi kda nn7ec)n8jch reaches the bottom first? Which has the greater 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 lbu 16bu ijpxjg03-k/angular momentum are conserved. Yet most moving or rotating objects event 3ug ukxb6j-1pij b/l0ually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wouleq80+b 1 w/do+p eheftd this affect the lene10/hb8t qd+ewop ef+ gth of the day?

Can the diver of Fig. 8–29 do a somersault without havh+b6 2enk b:lmbt6iz;ing any initial rotation when she leaves the board?2z6ik:t bhbl; 6nmb +e

The moment of inertia of a rotating solid disk about an axis tx;1:aq bq,vqthrough its center of m,vxtbq ; 1q:aqass 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 sittid s+bfo3run3j 48adc*ng on a rotating stool holding a 2-kg mass in each outstretched ha8c+judornsf 3*ba d34nd. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howevers+zyl9,gm n7x , one is hollow and the other is solid. Describe an experiment to determine +s9yxmg,nlz 7which is which.

The angular velocity of a bewvt3b y5kj+dvaboo9 .)j.qj 43i s,wheel rotating on a horizontal axle 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. Is the angular speed increasing or decreasinjjt+b3 boq i5,34 vo.kd9v jybs.a)weg?

Suppose you are standing on the edg)-egaq dwexe8vj.2hi -4u iu2 e of a large freely rotating turntable. What happens if you walk toward thx au- qi4u h2dee28w )ivj.ge-e center?

A shortstop may leap ivmkjy(-epu5 z0p/n *jnto the air to catch a ball and throw it quickly. As he throws the ball, the upper nj0u/pz-pyk(*5v e mj part of his body rotates. 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 conservab,)n ; 5oqu3rr jj 7jdwyr*62gqrm1kption of angular momentum, discuss why a helicopter must have more thaojrbmu 6 )r*2jw , yp7d5j1gqq;nrr3kn one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radirje)oox)53no4i 90j r p.ywim f2.s kzans: (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 amazing coincidence. Calculate, using thei45 kah+3vgm 0(jaqzv44ye q nnox22i information inside the Front Cover, the ang mv4jg inah4i(e532va+4yz ok20nxqq ular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam d1xu-8 xqtbycy6 vn:9t iverges at an atxut8 n 61q:9yybxv- cngle $\theta$ (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.v(96fl g*sxfs When the motor is turned offx9sf*gs6v l (f during operation, the blades 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 to another child. jk ha4re7 5afnw(+yj6If the ball makes 15.0 revolutions, what is it rnwj(fe 7kya5h46ja+ s diameter?    m

  A bicycle with tires 68 cm in diameter travels 8 w4hk7771/vn ahpxr tad5gb( w.0 km. How many revolutions do the wheels make(t 4 7nbdwrwa a p77x5h/1hvkg?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate itsmjcrpz x cfg-7-8),li6 vxz*u angular velocityv *jf, xcr7xz-cg -8m 6zu)ilp 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 revolution in 4.70cmx6 zvx cbleu86j.. dm:vd0 s (Fig. 8–38). (a) What is the.j. zmlm v7vx60deb 6c:8cdxu linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its m2kt pmt)3;vxorbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a prx*vd+ w 2ngwx k xd 0- y6c,-0sgiv,chko+)fqoint
(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 centr 2rwe 2h e-ehv xop.t9.0qrh)uifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an ace9 2h-eve.p2r h)ruxq.tw 0o hceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniforda.quw ftm-(7 mly about its center from 130 rpm to 280 rpm (w.q7fatd-mu 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 radiu + ulhp d+*.- o0aowaa.alzqf0s $R_1$ 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, astronauts abt4s0v0 ww qw3w j8ay ;kxsxw:.oard 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 spacecraft can be thought of as a cylixyt;jwkwsw a q4 :ww 0vx80.s3nder 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 accelerates uniformly from rest to 15,000 rpm in 220 s. Through yev-i4go o+ *npzgk5xepykn ,v 46 (,khow many rev*v5vop4 ,+pkyng,ek(e -ko6inzy xg 4olutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rp ty-xdtt3oz:/m to 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 stresses of flying highspeed jets in 9lqkh.c: e, eda whirling “human centrifuge,” which takes 1.0 min to turn through 20 comqlc9ed e,h .:kplete revolutions before reaching its final speed.
(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 accelerati7 /u ipa:qr4he;q7xux ,jx;les uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on tu/7j hxpqalr;;:q4, i uxe ix7he edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev+g- sbj/dn9axrre+: k2.m hp e/min It turns 1500 revolutions before it comes to aba+m:je .- 9gprdnr+ex2sh k/ 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 revolutions as thoa4h4y( mot :k-7g krhe car reduces its speed uniformly fr-k(akg :t7h o 4ormyh4om 95km/h to 45km/h The tires have 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 rdt9;;a2d m dreq-t-ow evolutions as the car reduces its speed uniformly from 95km/h to 45km/h ;o-te; dmtaw d-qd92rThe tires have 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

  A 55-kg person riding a bike puts all hdl:a o/hiv/ x8er weight on each pedal when climbing a hill. The pedals rotate in a cirhd8x:i a//v olcle 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 *rnr1kibp:yqjn 1mr;/ l13hs of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the f n1r/mly1b3j prqih1k;:sr n*orce 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 about the axle of the wheel shownzxbyz5 :2 lp/u493xdo u/hgqq1 bj1iu in Fig. 8–39. Assume that a friction torquebg9q5hjy:/ xixquz dz12o ub/1u3p 4l of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m.bv b7a4tj2 z8msayzus 2+n*x, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod iss+ 4zsju vbm.ab2x 7y* nt2za8 held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder hed6cv: ivqtgwh t1kv318m (zm)ad of an engine require tightening to a torque of 38qhmcg6t (v) kmdv t1:3vzi8w1 $m \cdot N$ 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-kg sph0: ruxet 6,ppbere of radius 0.648 m when the axis of rotation is through x p0tbur:,e p6its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle *0-/vnopa 4ms7ykdtnod/ wt5wheel 66.7 cm in diameter. The rim and tire have no-5//47vwt* odasn t kp0yd ma combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotate1cac27a qv 5s3dmy3b3, rajz kd in a horizontal circlsy1aab z ac35,dmq7 2jc3r v3ke 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 bowl on a potter’s wheel rotating at constanttl,m -1sb ,9c 5e,s9qofpum ci jw.;er angular speed (Fig. 8–42). The fric;i9-.t9fp bles rc, mwm u5q,csoej,1tion force between her hands 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 point objectwph4+v g wy/z)s shown in Fig. 8–43 aboutvg+4/hyzwp )w
(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 oq5f4gt 1kq((2c u-ed9t xbcd /hb; rxuf two oxygen atoms whose total 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 s-becgeyn 2)v 9l)w5 ; t-yh8i4;jnd5uehjdd aatellite spinning at the correct rate, engineers fire four tangential rockets as showa n5ij 4yy edh5b- ;l)28c9- vndtdwg; j)euhen 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? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and ( yn;sn/s)l: dzn;ovk al98nx a mass of 0.580 kg:ao8zs(;sx kn /v9yd)nl;nnl. 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, acceleratikkdo544z,bivjkb :v .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 tangenr y ,l3f12yhp3l x;ulua,3pmrtially on a small hand-driven merry-go-round and is able to accelerate it frma32 lxuhl1 pfr,3p y; 3r,ulyom 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 (each 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 at 10,300 rpm is shut offkk ph:;-iuash ynml2: 2 k:b9z and is eventually brought uniformly to rest by a frictional torkm :lk ;2b zk9u2:-hahy:nispque 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 accelerates a 3.6-kg ball at 7,cuh rn (x w*:yks:/ec $m/s^2$ 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 5d l8p yjxi)p ;:3lqt:dkprg+ is thrown solely by the action of the forearm, which rotates about the elbow joint u);ktj d+g358d :l yqpprlip:xnder 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 rodd w1j0bsn i7mo4wh7ru*3t ;cn, as shown in Fig. 8–46.budj *7n1;whn0wtmi 3 7s o4cr
(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 consists of two v8 .oyu/edj0b 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 the hammer from rest within four f5dn: -sb3 -a 8onrksb jxsnt17ull turns (revolutions) and releases it at a srj bnx o8s n7bna3:s-sd k15t-peed 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 inertimvz 0:x1mhn s-zm d7:r+ na8nbhy6tv+ a 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 eiop 70; p a7xqog6+uxa torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slippinpfa.rp:n+t (hz;: kf og down a lane a;.f:ok+ t: arpznfhp( t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect tpuon4 wj/ fcf;u)bojwx iwn 67,w -a++h(mg3po the Sun as the sum of two hwi u)jp7 o(+j,xagfnuwwo6-+3c/4b fn; wmpterms,
(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 of 7.50 m. How x*f uz,v4qd pec0uunz4m4 5: kmuch net work is required to accelerate it from rest to a rotation rate of 1.00 revolutioz4ue,dq 4 zmucpn5kf*4v 0:uxn per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm + xu adjo1/zgartj,cy6.1dx- 4d) fe(j kya b/and mass 1.80 kg starts from rest and rolls without slipping down a,j 64aa -xzy/cddo+ (bgjd 1y/k 1ate.x jufr) 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 tip. It starts to fall anda5(vm djm e7r)f 23tew its lower end does not slip. What will be the speed of the upper end of t arj2 ted3)em(wm5f v7he pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg bau6rzwr 44 jcl8ll rotating on the end of a thin string in a circle of radiusc ruw6 l4j84rz 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 *kwn 6 c:*umk3w :4dims a)pm:qzqf.k uniform cylindrical grinding wheel of radius 18 cm when rotati:n 4kiqkzm:6:cmpsf*qwa.m )k3ud*wng 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 his2 ucf8fnatd3)s2jx+h;q(e a v side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, theajh2fuq2a+) xt;8fev cnd3s( 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 sxwjc-6, 4 ytkwqys7x vc8/av+hown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 a8 s+4 /xcx tkvyc6yvw,q 7jw-rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate fbbbrh s; v,kct)0nk/(dhk 62prom an initial rate of 1.0 rev every 2.0 s bb k,d2hc0)6kv(/; bhrnptsk to a final 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 tsc+ ylrb s-/ 6z7n,dlml.s)caround a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws 7tcl+ b ,/mssrl-)c . lzsn6yda 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 a figure skater spinning at;;0cc,kfwl a c86 qhx 1egu-rq 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 Ea6vq)5x8yj)ou4uc f ne6 3mkperth
(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 vo8od,ko - g,yinertia I is dropped onto an identical disk rotating at angulado-yvko,og8 , r speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsx vcx5iaf 6-8z at 2.4 $rev/s$ 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 023(tes t(jlyj9 k wxpa rotating merry-go-round platform of rat ( pe0s(t lkx9jjy23wdius 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-ro8m4exk9 +x iuo tye.j92c5 mpiund is rotating freely with an angular velocity of 0 ic.mt4xyjpku iem 9o829+5 ex.8 $rad/s$ 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 eventually collapses into a white dwarfoep//1rh c hec3 d)ua 3e)iku;, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Ao3c )au) dkr;/uh1eep/3i ehc ssuming the lost 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 winds in excess o h .kaup zjar21dgh;-;f 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 h nt;+da+spv8 cl9m w2ys;mu($ 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 plaq0eh:;d y1y9r3yg1wh) oz1 bh (rikftv4- kri tform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform-kh yf 9 yghbd(qok:30ri t;1i1rhye z )wr1v4 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 diamet9eo+u +l1eeo ler merry-go-round turntable that is mo1o l9++euoleeunted on frictionless 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 rollj,a+t9+/ j;cthbg e*j azmxx)s on the ground with the end of the rope lying on the top edge of the spool. 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 spooge x a hzx,;j9tt+ cjm)j/+*abl? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same sid0mz .mt63jd 5jzww-uge always faces the Earth. Determine the ratio of the Moon’s spin angular moment -.3wjmum0 dgz56zwjtum (about its 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 f3e 6seyav99( a9op8yghxpk2from rest 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 j ix3qsps-y: +of a uniform cylinder of radius 0.20 m acquires a rot-iypsq xjs: +3ational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, eachyui3grkq8 z55 /nzhs33soku( of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kz(/ s 3i3s5o5qu3k 8unykzgh rg 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 angular speed of the rear q(ge li1 q/jv.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 Sun, but with mass 8.0 timer ft.51ujqd6w s as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitati t.6 q1jfdruw5onal collapse to a neutron star of radius 11 km, losing three-quarters of its mass in 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 st0 ayn /ci . o;35v5cc7 */uwwnxhgdregored in a heavy rotating flywheel. 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 fly3v*cgywxieh5w./7 d/a0c go5 cnnu ;rwheel “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 illustrates an f6r 0zt-p) rtivi o+:fyocr:,$H_2O$ 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)-dq)sv cg+b.5( cdfj e is rolling on a horizontal 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 lm.v33b1nutyu5 q0fc e ength L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then.3105 by3envqmu t fuc 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 standing vertically on thwoj 2ex ( +d3rr5xu pzj2,ux*ke floor, and we want to exert a horizontal force F atu23(j2w r,*xud+z5rej xk xop its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling witsy0xv jz7. ;u.ph-eb fh speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on tx e.yzsf0 .pj;7bvuh -he cyclist and cycle are 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 i8s(; ;tc5idsw zjrzghm,z f ;0nto a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelsrz8sz 5( m;jg hf;d wi0;,tczerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, yattexda+0,4r;ag cm * zx6 uj* 3b ,y-tgo2lamaking reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her b* jg*,ytz34 - 6x2 tma rbaa cye;x+d0l,tuagoody.   

  You are designing a clutch assembly whd xhc-x jl6lf7t 5ee /i57ug2uich consists of two cylindrical plates, of - 6 ujdlexi 55xtl77fgh /u2cemass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radixwv4g4r/ n/ rumw 3-qgus r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marbl/wgxr ug4-3 qrvn/wm4e must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assuc j+2h, ;w eqkrl0lbo9*;vvtmn*tv* ome $r\ll R$ h =    (R-r)

  The tires of a car make 85 revojljabrtf qh(6wk t)9-p/xr . +lutions as the car reduces its speed uniformly from 90km/h to 60km/h .+tawh)qkfr -b( tj l/6rxp9jThe tires have a diameter of 0.90 m. (a) What was the angular acceleration 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