A bicycle odometer (which measures distance traveled) tpw fd93jze ;g8a6vw4is attached near the wheel hub and is designed for 27-inch wheels. What happenjw94; 683gep dazv tfws if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Do45ne0i1f7np4 v q zl6:d6h9 j qw8*uyvuh jccves a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, doesc1y f9v5*junl zu6qph4vqjc d wh e046n8:7iv 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 cb5 ,/y uuijdyejs+0 5a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger9qqn53bpi- e zjy4i dh(xh.( g 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 diffic5 : kq23r wc tcrs*2vp(sa+l.oa)vmpyult to do a sit-up with your hands behind your head than when your arms are stretched out in f :lv)2 wa rqroc+p tyv*m5pc(. 2as3skront of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wh/ao:ut 6i 1zileel 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 front sprocket or a large front sprocket tio:i6az1ul /? Why?

Mammals that depend on being able to run fastwg m2-rs3i0(bu04oqw3xbs c ie r ;vo2 have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational d 4u (gxv20ioq20rsi-wbsbe mw3ro; c3ynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fign;diva0 3*t tu. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque bbo6,jx5 q zy /ycws7,also zero? If the net torque on a system is zero, is the net fo5 ,z,yy qob/6jcbsx 7wrce zero?

Two inclines have the same height but make difffc3,x5q 4nol/wf:g zs erent angles with the horizontal. The same steel ball is rolled down each incline. On which inc5q: lnc3g4o ,xs fw/fzline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an1rhqi62 1lsfvknh; tt9,l5q y 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 greatern5; 2q, 1ytqvs6rtlf l1h9kih speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same m.cc8tj bc*yh7 ass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater c*.78tyjc bhc total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved.+/dstuezh aw+ic0( s 58z4ri/qr-us(z; bfiq Yet most moving or rotating objects eventu uw-+s dq(usiiazt fz(zsbhqcri//5;4 8 0+ really slow down and stop. Explain.

If there were a great migration of people towar8 dl86n ts jol*10cvss*laes 0d the Earth’s equator, how would this a8l0v j ot0sslsl8s6 n d*1ce*affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without lft*oqs c3 drxi3,b w zlqqcx0.t39s yc.5i77having any initial rotation whbi97 qsocy d*.fr7lw q5tl c3zqx3 3.sx,ti0c en she leaves the board?

The moment of inertia of a rotating .- x6cp3rg:5rjsdm f osolid disk about an axis through its center of masj :.-6focdrps5 x m3grs 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 rotatingu4l imm9: wdu) stool holding a 2-kg mass in each outstretched hand. If mw :udiulm 9)4you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howqd m72b hc./ n(jh6h7fwrm. xcever, one is hollow and the other is solid. Descxhcm b/hncr76 wf qdj2m7(.h.ribe an experiment to determine which is which.

The angular velocity of a wheel rotating og 1u:n :tc:n.xzxp 6mp0;fiiln 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 accelerationf::x.np czl1m:i gun 6;ipt 0x of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. Whxe6eok yur0db,6 yo6 9at happens if you walk toward the center oy66 6b yod90u,xeker?

A shortstop may leap into the air to catch a ball and thr3swm y wj,*jd-do.(j uow it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly youo . 3*-u,wdyj (wjsdmj will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law,vfc;m-c4c ge of conservation 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 hef g4;vec-,ccmlicopter stable.

  Express the following angles in v*nz :g;)q/ft(if qt aradians: (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 beca r6qqqrsj.vxt 5;1)kl use of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (i6.q lsxq5 ;tqr1)krj vn 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 frp:sx; ldw1)() +anaelwz rn u8om Earth. The beam diverges at an angnel : w)s1(z8)lp ;adaw+xru nle $\theta$ (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. When thrrc*g/d0b /hc;w6 bgse motor is turned off during operationsb/ 6c* gwrhc/gdrb0; , 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 o)g*zz-mg.ec (a :u; 3c oyvmbyn a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is 3*v. y (a-ucz:z;omcm)gge byits diameter?    m

  A bicycle with tires 68; y25x ef;mes 9jpnj:dztn* 8d cm in diameter travels 8.0 km. How many revolutions do the wheels ma tj28 eps9dd;;m j*5f:ny xzenke?    $rev$

  (a) A grinding wheel 0.35 m in diac(ur)xlc8: 4xw3hwiz meter rotates at 2500 rpm. Calculate its angular 3wxwl 8)c4(:cirzuh xvelocity 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 4.0 s (Fig. 8t .,z/vkd6rje–38). (a) What is the linear speed of a child seated 1.2 m from the cenjvr/6 z,.dkte ter?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) inf-y,itn2 1b:uafz sb7f. v5dg its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear s(mxkk +5h p0oq/urqa3;6oupw7 x 2 uufpeed 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 i0 as *tca;wkpa *:wlk jnvwu8v-;b(a;f a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,000tcw vn; bp- av;kw;ks8* a( u*wa:a0jl $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center f7hd cyussgrn-xwq/ 1c:8o,3from 130 rpm to 280 rpm in 4.0 s,s 3 f-qury wo1d:s 8/nx7gcch. 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 s o.r+/asx-ad;i0s wde7tmevn ;z m-6 $R_1$ 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 aboard the Apollo spacecraft put thp9ya4c myn7 .temselves 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 cylinder with a diameter of 8.5 mcy7.mt9 an4p y. 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 22ex;mn8i cmh 440 s. Through how many revolutions di4xnieh4m ;c 8md it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm ioowsa)-gf 67a n 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 a whirling *x 9.g8ihcdz76uxqx i “human centrifuge,” which takes 1.0 min to turn ux6cii7xx*8 d.gqzh9 through 20 complete 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 accelerates uniformly from 240 rpmn3w7l 4cem ua6 to 360 rpm in 6.5 s. How far will a poin3w4u6ce7 lam nt on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned o vs065( k bc tk(pn8a)xh9zpjzff when it is running at 850rev/min It turns 1500 revoluti9btva8k)psxzc6( k j05( nzp hons before 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 6zgn6p-cm0elwx0cz z 1t 6z2s2 5 revolutions as the car reduces its speed uniformly from 95km/h to 45kmnzgcz60zsxtl1p c-0m ez6w2 2/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 revolutions as the car reduces its speeegohkf4qn. y .d3o9 5wd uniformly from 95km/h to 45km/h The tires have a diamet4od9w gne5h.f.kq 3o yer 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)i g-gps n*gh; bike puts all her weight on each pedal when climbing a hil *)p;- isghnggl. The pedals rotate in 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 wide. What is the maykuflo j34n ndce (+ b0im//y3kbj((wgnitude of the torqfiu j bmn(yb(4/jckk/dy0 3e3+o( lnwue if 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 about the axle of the wheel shown in Figl6 1zwqx kakuc*10(vu 5t- lyn. 8–39. Assume that a ftk0xkc-yu1 q6uz 1wllv (n*a5riction torque 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 axmxf)cl k y,d(okebu 5.v7(4j massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this so j x(7.yk(dml4x ,vuckb) f5eystem.

  The bolts on the cylinder head of an engine require tightening to a torque of +z o rog0d;p-t380tdo;p rog- +z $m \cdot N$ 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 inerxd /:*ueu 7. drduxot-tia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is th*ud trx- e7u.uxd /o:drough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in d(cdicr 8r- s8yf6;9jvr-udd p iameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ig-9sf(dp6iyud8r vj-;8c r drcnored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of 2ubbp id p)e1l/-j:9 /hlhpwma thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculadmj 9/ p )i:bhwp2plb-e/u hl1te
(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 poo(jdh9; bg,5 (jhwgplz,y u:,gjrj gr*zjz 9*tter’s wheel rotating at constant angular speed (jz zojpg,:j gh*j(g yw 9 *;jgulh, rr,5dz(9bFig. 8–42). The friction 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 gtfy b -+1jimol.m4a*of inertia of the array of point objects shown in Fig. 8–43 aboutio-ja1l*f +m.4 mgbyt
(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 total m f -)uo7.i v1w8qqsmjcass 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 satv.qxcqmdwa+g27 9s7yellite spinning at the correct rate, engineers 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 rpmvg 7dx79yqwaqm+ .sc2 in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius ofd57*hdtsmfv q+vrs-ef2un( / 1 dua 4t 8.50 cm and a mass of 0.580 kg. Calculmun u 4+(d-sdf*7dfvq t2 rv5a/1s hetate
(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 swink.- cown,3pt bjtv6q; 4ocx lqvp84h2 gs a bat, accelerating 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-dri2 sra:(u+vzlgznb 2(g ven merry-go-round and is able 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 (each with a mass of 25 kg) sit 2:r z+nz(agu lv( sbg2opposite 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 sg:w *zss5r db-h2ng /mhut off and is eventually brought unifor mzgs-d5:nw2*b /gsrhmly to rest by a 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 accelerates4ho9 n;mo.xr lfv -k-x 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 ban8 c)4bvd+2xc i 9fvpmll is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, dc ncbf9)mipvx824 + vFig. 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 bl1 7luybm 3l(a v1w)bblade can be considered a long thin rod, as shown in Fig. 8–46alb(lu3 bwbv)l1y m7 1.
(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 yb4.ehpr 8z be: v;ya: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 the hammer f e kvpwv3j q 4(n8lpy4yt0;c4 from rest within four full turns (revolutions) and releases it at 3v40( 8fvkpyel 4twcqnpj4 ;y 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 mom . c(t3hxrlgj48j *rasent of inertia 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 dt7 75dwyi kw gojac662evelops a 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 9.1mux 3atn*s aenqc;3 ew9 *w4m0 cm rolls without slipping down a lane amc*tw1mxwe e3ns*4a ;qa3nu 9t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum f*- ikj8z+ *uuno 5ymbof to8f*nz+j y* ui-k5 bmuwo terms,
(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 164mxjp- b0gy,+e5+fq kk f/ t-av0 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revag/x ybk0jkmp-tef+f,+ q -v5olution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls wyu qx ms1cd+9 v:l2t*dbulo 74.3oncmithout sl1d voxst*lu73dbonm9uc+2l . :qc m4y ipping 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 bafk* ,:pbmap:quu, c nnk7d9;qlanced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the groundkk*apqm:pd 9 u:bc, u f,7n;qn? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-k2 bpxyly h:73y*ud.6 b2iev4yz4 cjtn g ball rotating on the end of a thin string in a circle of radius 1.1042p lj6y:b4 yt2b yydxec.i7v z 3nhu* 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 cylindrical grinding whl9i,,7rifmwlhog 7 0 ueel of radius 18 cm when rotating aim 7u0,,rlg l7fi9owht 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 ry5nud 04qx5mtotating at a rate of 1.3rev/s If he raises his arms to a horizontal positiony nx mqu05t5d4, 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. zcz8fg/jk,( j xjnob: 0*up 0r8–29) 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 rotations in 1.5 s when in the tuck position, what isr(fz,pjbj nu0xcgkj* 8 z/o0: her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase 01qdhyle i:j2her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final r1jd2 y:0q heilate 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 rotatingt lqjd/3 fgd24.r:crn around 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 a 3.1-kg chunk of clay, approx d2.qgcr3jt:nf/ drl4 imately 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 3.5 7b)reu 0qdda *$rev/s$ 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 angulaqbomz:g6l., r+ cm7e-a ix)a hr momentum of the Earth
(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 i hf,/n h/k8ny 8wo(puks dropped onto an identical disk (hok /u y8n,nkfwhp/8rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atqqfj a-i:wy g,90k gu1 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 a rotating merry-gort*zd/ m,,y ed-round platform of radius 3.0 m and moment of inertiy m/r* de,d,zta 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-round is rotcxrrr4o 2t3r+ ating freely with an angular velocity of 0.trrc rx42r+o3 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 dwarf, losing aboutwc+sb1d 97uguwuh mz 4)v)xhk vq/vie3,(dg6 half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate bqz wvk 1u d,6g(9 w3ve d/ )u)vbuh7xms4cih+ge?(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 of 1bto,dpsfvu; 1 4 c43uu20 $km/h$ 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 ssus//+bq 6kg/b;rv( bro +rd$ 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 roi 9 vs (2nbr x+9fh*ep8ksl6po0 3yhcqtate freely without friction. The moment of inertia of the person plus the platform chp+h fi9q b80y 9s3vx*op n(k26selr 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-gvb 545g)o /2j givoom8h-x;czqwpsr) o-round turntable that is mounted on frictionless bearings and has a moment of inertia rg)bo q5vzi)-hogps 2o;4m5x8 jwvc/ 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 rolls on the ground with the end of the rope lyinf9ri1ncc/:pybn m8nakv , y03g 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 k/ my0,nbc8v pi ny9 fa3rn1c: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 the same side a 8hsg gt)px/;16 lhm7uywt3lyk8 egd 0lways faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treal6k ex;d wggyh)/801lpt83ums t gyh7t the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates f;dibpy:jlu.lxfez ;53 a.jr4yzt:9rw u 4s0o rom 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 of a uniform cylinder of radius 0.20 m acquir4fmt*0vyy y- fes a rotational rate of from rest o-*04yy tfmvf yver 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, each of mass 0.050 kg and i,ieaxg 7c86jdiameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of 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 itsajce 8i6x, 7ig 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 wh6tkwzp+f.te l8p2 n;peel ($\omega_R$) 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 timesj cl91q ndjf5 mi00n)nxu9db , 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 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 jdfiq9 m )9x nd5nnubl,010jc no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy 5mqr ce0o)3.zfu.hf4 roo t6fstored in a heavy rotating flywheel. Suppose such a car has .h ouorc.0te )5 qzf3r6ofm4fa 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 q /ue(:ao* fn)08gcbtaf khc/tes 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 horizontal surface at speed v1t;e3wl2ve /n ik+0ehky5 pne =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 pivot freely (i.e., we ignore ra r+p1n04h38qnr xgq7ygn 4bfriction) about a hinge attached to a wall, as in Fig. 8–54. The 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+n nnp3r0y81rxghqgar4 b74q. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It tu *qiy3y/k.h.- l hv;6uh oklis standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The yt vkk6ll -hho*;.uihy.q3/u step has height h, where h

  A bicyclist traveling wit ;or.kof3z )kijwivq* 2v,s-jp) u i4ah speed v=4.2m/s on a flat road is making a turn with a radius urp)* fs-2v; j3 4j )iwqkia ,.zookviThe forces acting on the 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 into a sling of length 1.5 m andci)ogzy s9s ::lipbg n,hv9 +2 begins whirling the rock in a nearly horizontal circle above his head, accelerating2l+bhsz):pg y9i g n,co :iv9s 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 ayx ck3 f5;yr*gs thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and 3 g5r;fcxyyk* with arms held tightly against her body.   

  You are designing a clutch assembly whiciml :,ov*5dw8hki n5mh consists of two cylindrical plates, of mass*n,o8k: dhml v5iw 5im $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radius r rolls along the looped ro /-m c-owkk7 bvmcxw,;pq c-ng:6e8chugh 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 highe/mxn-8k-b7cgc ecmv,-co 6 ;:hw qkwpst point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do nolqi2c e4yw: m(*;f 6v wp+vuxlt assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutionsh8sn t-xaggcx1s -26 dfcfq ;. as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. 1qa s;gxgcxd62hf-fst-8 .c n(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