A bicycle odometer (which measures distance traveled) is attached near the wheel 4 bezd z(bjjsod.*/ xxyb:.y/ hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-jb:*yz/dz ( bdyx/jo.xe4b.s inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on x a):22k 8xyl(zud ysw fc3sr5the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangenty)r zxwds 5(c k2l3xuyfs:2a8ial acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body b((8miw5ssz/q sb f-+k9cozgqe described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explaijwd:g3 *.y igan.

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 than w8h-,uknlax oq93 w a5when your arms are stretched out in front of you? A diagram may help you to answer t5uonx 3a-w ,h8qkl9a whis.

A 21-speed bicycle h-my2erd;1lc)io5u nk/u pfeq f3l )*aa3h 4o tas seven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a kh 5iuao3lt * q2amo c/de)n;4-l)fryu1f3p e large rear sprocket? Why? In which 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 legy opde9: 3eu 17le8gdss with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is ao 13e7pue:d9e 8ylgsddvantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow iya ss2;9fy 7obeam?

If the net force on a system i0mpj zahfgl83u) 2a*/n8rhk xs zero, is the net torque also zero? If the net torque on a syste nh3u)xz*a2m kr8p8 laf0jgh/m is zero, is the net force zero?

Two inclines have the same height but make diff 49y a-pegj 5k68dfbiq gt00nierent angles with the horizontal. Ttaf8dniyigq 5ep k 6 90g-0jb4he same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (f2tw0 0:t zqgi-+zqkj3idm q: trom rest) down an incline. One sphere hai2qgzwzd q t-: t:t0jqkm+3i0s twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and zlwjo;:9ip xxy m4t z.b(l qm*.es- +mthe same mass. They start from rest at the topiy .zw.slp:lm9b ;4 (+xqm *ze-ojmxt of an incline. Which 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 angular momentum are conserved. Ye p -et99azlnx,a)p(fkt most moving or rotating objects eventuallyzl(fk e,ptpa-x n9 )9a slow down and stop. Explain.

If there were a great migration of pkoab09 /gzdtc nx,(v-eople toward the Earth’s equator, how would this affect the length of the/0( cd- vzta,ngk9xbo day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotattgx 2kf p; trfg89o/+fqf +0st(4vthwion when s(sf+fog4ff2 /p t ;q+xkhttvtrg 980whe leaves the board?

The moment of inertia of a rotating solid disk about an r- ; ons ihnh.wj4k09saxis through its center of mass ih.; -w4sor nh 9i0snkjs $\frac{1}{2}WR^2$ (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 rotating stool holding a 2-kg mass in each outstra9dhdo6 . n6quetched hand. If nh d966 ouqa.dyou suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow and thcq lm)/iw cf-y* 6 -plhec9q,we other is solid. Describe an experiment to determ) h,- q-*cq 6i /mpcllfywewc9ine which is which.

The angular velocity of a wheeek8yc9,-t y ssl 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 a8cy9tyeks-s, cceleration points east, describe the tangential linear acceleration 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 turrmeq2+) /evszntable. What happens if qse)v/ 2+ezrmyou walk toward the center?

A shortstop may leap into the air to catch a bp0+ fpg- sqrfxesb)zt7 ,0r*p all and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will nor ,zs0*gb+sf)pf-xq 07 ppetrtice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservdnv/afd 2 9qd-ij.ha7 0opm p+ation 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 t o/vahdmi.+7j f2pa9d -nd0pq he helicopter stable.

  Express the following anglesy/6;z lb gumf1 in radians: (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 amr rltz5s pq;*;vdusm2 p06senpi)-j qdii;)/ azing coincidence. Calculate, using the information inside the Front Cover, the angu mip e;;d)t/)i60zsp; uv 5 rjiss*plqdrn-2qlar 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 km8u/ o(yh;70ecdxwmv ety s(r9 from Earth. The beam diverges at an a9(0x7hyce 8o mvtws/dr( yu; engle $\theta$ (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 the motor is taq.13 ndwxw dng2+ f-gurned off during operation, the blades slow to rest in 3.0xd21a.gd-fg w nq+3nw s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball o*ih2 ji;8s*prfuxc5+kq(f :zyy oo r8n a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diameter? 2 ;hf5scufiyzor+i**r:8op8(k xjy q   m

  A bicycle with tires 68 cm in diameter travexg7ow.g mz9o79d kk-m ls 8.0 km. How many revolutions do the wheewx.9og9mkd 7go7km- z ls make?    $rev$

  (a) A grinding wheel 0.35 m6-wd2,espdvl( iuhkt vpq g0y.+0p;l in diameter rotates at 2500 rpm. Calculate its angular velocippll6uw-y. 0 iedphvs k q;t 2+g0v,(dty 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 make8bo u37 m:8z6 inek/wynosol7s one complete revolution in 4.0 s (Fig. 8–38). (a) What s ko/b8o 3mz8oywn7nilu6: 7 eis the 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 velocityi hb0fzi3,ab+ of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spqct- 0u-e vkt 3d)qe vlh3:dy,eed 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 7d 8sooj4h p+5f*d hbdtvxl/1*m /4uao.0 cm from the axis of rotation is to experience an acceleratia*p 44to/fjvu 5+omd */s hlhdbd1ox8 on of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates unifor :wrvr50 /xf1-h ingdy/7peu umly about its center from 130 rpm to 280 rpm in 410dwgi hy ru/ef/px7n 5r:uv- .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 dexl1)uz0pg 9x:, , kkb/hl ump3drg ;$R_1$ 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 Moony 6k z*a.oxc :pvk7hq,, astronauts 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-m kcxazho qp 7*.6:,vkyin time interval. The spacecraft 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 accelerates uniformly from rest to 15,000 rpm in 2u+ d dyqpiwbg7spjig *;- gmi//*36 xh20 s. Through how many revolutions did it turn in this tim3-jydsm qbwdg /*ipuh /g;7*i xp6i+g e?    $rev$

  An automobile engine slows dow.x2wo 04v7y s tee+nfsqc/9w wn from 4500 rpm 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 flyingvj1kr(u*;lir1 x8nt c highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachxrlr *j1i(kn tc;u8 v1ing 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 accelera- se fizg/6qb(tes uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edgq ezg-bs6/f(i e of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running au.g1r :zfxf r-t 850rev/min It turns 1500 revolutions before itxf-g 1 rrzuf:. 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 revolutions as the car reduces itum g+0u7 ucy,.tg, ehas speed uniformly from 95km/h to 45km/h The tir0,umg tuug. 7cey,h+ aes 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 tu,fbrbcv:y+gqs2kv d; (;:k m he car reduces its speed uniformly from 95km/h to 45km/h The t (d+qk,cg;b:b:fvu v2;rym ksires 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 her weight on each qm ojq k3 ,0dvbbd1/1zpedal when climbing a hill. The pe jvo3q1b1qmk ,d/z0 dbdals 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 on53xwodga f- f+ the end of a door 74 cm wide. What is the magnitude of the torque i5 gaf f+3oxdw-f 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 tejo83qi q ;n8the wheel shown in Fig. 8–39. Assume that a friction torque ni8o ;qjtq3e8 of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are ay9yn1l ca-e,cbnyg:0d/ rq2jttached to the ends of a massless rod which pivots ase,qay0-1 c/y2nnc9brlgyd :j 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 system.

  The bolts on the cylinder heatci,ry5affzq dt;7hto ) a491d of an engine require tightening to a torque of 38 qdyic ,h7oaa 54t 9t;zrf1tf) $m \cdot N$ 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 inert*1ath2 ik 3jjbia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its centekih3 t2 ja1bj*r.    $kg \cdot m^2$

  Calculate the moment of inertia of a b gskaq6 2bvzb4ha/ du1xil3;( icycle 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 ignoredlibad(ag bvzqs4ku;/ 23h 61x (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end x),w:p/+ i d wp*8rpu chce/,kli akd0 vxh9q-of a thin, light rod is rotated in a horizontal circ w8p)w0+d*q hrl-ia/c pdxke/h vxp9i,,cu:kle 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 bowle;to3 7qt,mkq0mn kj5 on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her; k,omm5qejk3q nt7 t0 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 objects shown in Fo (*sn nd5iz)mig. 8–43 mi5no* ds)n(zabout
(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 mass is -pzf ,th;uv aoa-cn* o2p79zm$5.3 \times10^{ -26}$ 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 corr)itj)mr.da sj2 :rbls)h8 ph+ect 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 s.lm2idtb+ asrh8)hp ))j:r sjatellite 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 r(f 6o6zypqi 9z7k;onc2/vpx tadius of 8.50 cm and a mass of 0.580 kg. C(kt9;qznxo6ipf y7 c2/vop 6 zalculate
(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 bwjyfgpsn6-6 1at, 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-dricy cqjzuiu0/;ed) 1;9tmifi +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 dtz+ )i1fccime;/uq;i90 yu jm 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 off and is eventually brought7z*pf(dm +kjbu d;g+m uniformly to rest by a frictional torquj(mdb7 md+kzg+f* ;pue 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- kj7zr;c6be*ikg 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)x dcetl-8/rs0jn .l ao 71nzsm, which rotates about the elbow joint under the action of the trisn as8)cd jo0.n 1tr xll/ez7-ceps 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 cl:ls;yezr4 gcaq,atq4 1 a j*-onsidered a long thin rod, as shown in Fig. 8–4:l;1e l44ja- g , rqc*aqastyz6.
(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 *xxdza696 u/oe)u5 -+ie3v0xtpx m zxm a5vupof 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 accelod* b1aag4:aa erates the hammer from rest within four full turns (revolutiaa1ab :gdoa *4ons) and releases it at 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 s x) fuiawd8kx l xu2g(0be17,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 d,tx a .dhrmnm*zu 2)x.evelops 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 9.0 cm rolls without slipping down dfk igt7a+9;da lane at 3.3k; dg79i+d atf $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic zpeps g9l0u*6f3f9zxv-j7lyenergy of the Earth with respect to the Sun as the sum of t0zflfl yejv6gs*uppx9 z- 793 wo 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 1640 kg and a raqg z3k.t-k,xv dius of 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? Assume it is a solid cv .kxtz,q3g k-ylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls withoutyaot zm 18o y;)2smv,t slipping z mytsmv;o2a )8y1t,odown 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 tip. It starts to fall :f8aoewvw 8r8 x/t: qhand its lower end does not slip. What will be the speed of the upper en8/8r f: w wtqo:hxeav8d of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end o6ag*ihfdhfkf5 icpek;s; n 9y 0da2,)f a thin string in a circle of radius 1.10 m at an anguld k9f h 6)e0ada5 ;,pfhkfy2;n*gsi ciar speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angula-5g24kvg winu r momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 12 kwn54iu- vgg8 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 7)c7ntze2-+rxst i3it 8gz vp, 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, the speed of rotation decreases to 0.8pt)r zi7c3-e n2tsg7zi t+xv8 $rev/s$ (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 inertia 2+ ali. ;8ousu)murm yby a factor of about 3.5 when changing from the straight position to the tuck position. +;i ro.uma)yu2s8 mlu If she makes 2.0 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 f1bgj pvrp6/hd02fpf 8rom an initial rate of 1.0 rev /pf2rb f0d 1pj8vghp6 every 2.0 s 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 ar)(: m/cywwp qround 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, approximately shaped as a q rwymcw/: )p(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 fdw4la .4n-c a*uc i;oeigure 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 o 9eie9j8ni6*6os da psk3q5pr7zyk5 hu5pg 5nf 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 cylindrqqot5r pzwypo q: ps.bc6 .l+-/qr0l8ical disk of moment of inertia I is dropped onto an identical disk rotating ar+p 5po:scb rq-tzol8ql /.0qq6 py w.t angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 k6 ii*8*(nvb nw7 sum0ke 96vcf3wvya$rev/s$ 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 a)ueo7,;y agpbt the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertiaay)oe,g7 upb; 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 rotating freely with anoeck+przb+/ l 4v i/1n angular velocity of 0.8o+v r1ekp cz+b/n4l/i $rad/s$ 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, l r:+6j4ac/ zflnc- r m9exisa(osing about half its mass in the process, and winding up with a radius 1.0% of its existing radi xfa6 nc rs+-i :jc/(e9lzmr4aus. Assuming 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 of,2sgy9ng 33 8l z f*v1yh/ootphcv9pb 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 mmr az8;54sp8hm e*am$ 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 withq.,81uv tfq j5hif ms:out friction. The moment of inertia of the1vsjq8.qim t 5f,hu :f person plus the platform 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 pers,dps2 8,;n qzid bm io40k)mku;uu( lkon stands at the edge of a 6.5-m diameter merry-go-round turntable that ismnqu; likz )ukidk4s(p,m ,;u db0o82 mounted 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 rolls on the ground with the nz+pi5/dej pel(0 pr 8end 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 spool? How far does the spoor dep0ln(p8 j +ziep5/l’s center of mass move?

  The Moon orbits the Earth such that theqr;x:+.9ix6 itj8t/s dw i qre same side always 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, treat the Moon as a particle orbiting the Earth.)d9i:q si6.r ew+ rtq8j;xit x/    $\times10^{ -6}$

  A cyclist accelerates from rest at dd ldz8 5t6 6vjo.3thfa 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:ju )m+/*fz-n ctghxi acquires a rotational rate of from rest- tchzm +uj)xg/fin :* 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, each of mass 0.050 kg and4/dr*u 4-b d3,zciz9f iwo gkz diameter 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 tu /z k3c id9dorfzb*wi-g4,4zhe 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, howdz0 ,0mrjkb, o is the angular 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 Sun, but with madz/o*uy-a4 wp sb;1:ojj5q znss 8.0 times as great, were rotating at a speed of 1.0 revo5s4qjna; pzbo/1uo d:-jwy*zlution 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 no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution autom( 4zdm6hg5fat;(d apjobile is for it to use energy stored 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 wip5 d 6atha(;fd(gm4zjthout 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 illustrates anpouz6d7f*b a /m;qwd* $H_2O$ 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 vag j1fb.ny en0 :8 y,6gxzo)kk=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 caff)e 6bh 86c0o aei1teinh/ p,n 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 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 ropiin6 ec oa/e)fbf1 6t0h8h ,ed, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is sv6r3i j vi6j2x yqze4+tanding 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 step has height i63qrzi6jyx4ej2 +v v h, where h

  A bicyclist traveling with speed k jdnf67ro a4v- j;g: 7mjw(hpv=4.2m/s on a flat road is making a turn with a radiuspj-v76;r: knghjf7(oam 4wjd The 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 and begins whirldv/bte(km 07bip -vbyto ) 1q)ing the rock in a nearly horizontal circle above his head, accelerating it fr1/t vbyi-bk) b (d7t0eq)vopmom 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 dauegn. )yv4 3thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched ard ag)ey4.vn 3ums, and with arms held tightly against her body.   

  You are designing a clutf+ql, jbcs 4r4ch assembly which consists of two cylindrical plates, of mass4qjl,+4rcf s b $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 a s1qn ky(hl) ,qg7afdu6w/*i radius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marblgyq/swu,q)*ad k a1f6l ih(n7e 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 no9-0de(p /qbsa;qc2q ami- oou t assume $r\ll R$ h =    (R-r)

  The tires of a car msw/ w2id6z5e y85huet ake 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 acceleration of each is2wwtz55y e8/ ude6htire? $\approx$    $rad/s^2$(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