A bicycle odometer (which meas )6 r emt8-1quwtj6qqbures 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-inctw6qm)e8t q6 rjb1uq-h wheels?

Suppose a disk rotates at consta5t c9n+9.p*a qd/vilkkj-djq nt angular velocity. Does a point on the rim have k/ ncq- qji59dvpk9*t +ajld.radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of thx /te pv1amo1b+yo,0ye angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a largerx-v. )uyyene , force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your h sv8pl;z;a o dhnsb;8i6,z,(g2 rb gzcead than when your arms arizn ds 2,ab;z p;g, h;b8s(z 8rglvc6oe stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at thzia , 45fy6qxoe pedal cranks. In which gear is it harder to pe,iqfa4 oz 5x6ydal, 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? Why?

Mammals that depend on being able tph0xn5;u( oyyo run fast have slender lower legs 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 advantageous(y;ph5on uxy0 .

Why do tightrope walkers (Fig. 8–35) carry a long, nar/)d7 2vzxxxiiem wbwp 99w.;orow beam?

If the net force on a system is zero, is the net torqr4mob (-tj )py+z8h7v 9c6-ni q duz. zybn7nlue also zero? If the net torque on a sysbz - .nm+i coy vznd9q877juyr)hpn6 z-l t4b(tem is zero, is the net force zero?

Two inclines have the ss 9:mf83wg9mg47 zy d*lz 2r motibdd5ame height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the f7 * 9bd 8ig:y5msro2tmd3m9ldwg zz4ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incl8 f1,ubqj xzl5k8x b*aine. One sphere has twice the radius and twice the mass of the other. Which reaches * bkl 8jzx85qu,xf1 abthe 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 the same mass. They start3z0.zlt h -zrd:.lla/;natmi from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at tan mll-30;itdh.r:z / .tzlzahe bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentoy wpvq,my;0) um are conserved. Yet most moving or rotating objects eventually sy),0omp yw;vqlow down and stop. Explain.

If there were a great migration of people toward the Earth’s equuwso8dvc1 xd9/y:g s)mt;;nf ator, how would thi g cd;x vdtuyf:w)1o9n/m8s s;s affect the length of the day?

Can the diver of Fig. 8–29 do a somersault wig -lri-i gq0-cthout having any initial rotation whe i0il-r-cgq-g n she leaves the board?

The moment of inertia of a rotating solid disk a9i st3d .ru 87fz 4d-karwm*jsbout an axis through its center of mass ida7jztrw8sku4rf9 .d *-3 sm 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 rotating stool holding a 2-kg mass in each outstr zo.tn0j1k vu+ uaqbxm; 36ori k9p9t7etika;z+pu0 t73j6 vutxno9q9k mr.1o bched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look ideb) :vq.y;wfhi ntical and have the same mass. However, one is hollow and the other is solid. Describe hybq .wif:v);an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points westtx2z f pt(;h8v. 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(zp vh;tfx 8t2 the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotzw/nyp9 jvm+* ating turntable. What happens if you walk toward the centev9+myj*wz/p nr?

A shortstop may leap into the air to catch a n3cm4hafh2 loyu/;+l ball and throw it quickly. As he thrc m2l4oy/h3l;f hun+a ows the ball, the upper 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 conservatibdov, ;o2osg :on of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the :ob;gso2vd, osecond propeller can operate to keep the helicopter stable.

  Express the following sk 1pyha)./ rqangles 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 amazing coincidence. C1ncwa-c+htro0,ev7 d/ 4gs eualculate, using the information inoec csur,0vda1g- +4 nht 7/weside the Front Cover, the angular 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 d-l; jmldk/6vj2 xbw+diverges at an l6md+2jl;v /bxj-w dkangle $\theta$ (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 rad3/,:4m1gzbndzf)qtx m7x u t te of 6500 rpm. When the motor is turned o xzzqt:bdmf/ t3d gu71n m),x4ff 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 boj v:40fia31* pctk lrf 4r+i3.5 m to another child. If the ball makes 15.0 revoluti 4j1k pa0 3t+:* bcrvili4ffroons, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 knp qs3*jtg3 mpk17o1 hm. How many revolutions do the wheels make?p 1k37os3n*g p1th mqj    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate itzn;j;y ,bo1ma (rf+ pys angulapa; ;ozbjfnry ,ym1(+ r velocity 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 onem,e1ckz,lxral g a 86; complete revolution in 4.0 s (Fig. 8–38). (a) What is the linearaa,mgkl r z16x, ;le8c 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 orbitt m kr+4kd09jq around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a po jac6fk8 v5p2 *2dnat,acys 1aint
(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 r6onaou m*,gl5lc9 n) particle 7.0 cm from the axis of rotation is to ex m5rocno*aln l9u,g)6perience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformsawh*b+:h yr;ly about its center from 130 rpm to 280 h h:bsaw*+r ;yrpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius 4w xyt usl i*0:0a+vbm$R_1$ 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 themhis18uv:q 89hrfjl hb5*uv 5cselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their tri 9hvuv*j8 u185b l5i frshqh:cp, 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 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 zl( mcwst16el /+:vtyq ut2 0krest to 15,000 rpm in 220 s. Through how many revolutions did ity6 :ztm1l02+lv e /c(qtkstwu turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm t4qp1 ur pwwf,47f6 ayzo 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 j38q w lq,ecf(xets in a whirling “human centrifuge,” which takes 1.0 mf3x(q lqcw8e ,in to turn 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 24(mc,ek7c;enky3 ak f ;u+x- ld0 rpm to 360 rpm in 6.5 s. How far will a point on the edge +n;kkyfa3lkme(ux-e 7,c d;c of the wheel have traveled in this time?    m

  A cooling fan is turned off when it i8 -70e,yzekc luu e( kl/rnoej i2/9lss running at 850rev/min It turns 1500 revolutions before it comes to a stop. ,/krele72cuny e los z l8e-(u/ik9j0
(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 makek(m3wev0q 1 wz 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 w3 wqvm 1(ezk0m.
(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 i x0p /crz.xas w,3az8sts speed uniformly from 95km/h to 45km/h The tires have a diametexczs 3.aw,p/0xazrs8r 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 pedal when climbing a hbweqe.5kdq ;( g;i,e gill. The pedals rotate in a;,gge i5beqeq.wk; d( 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 hrw7f mv5u( 0jthe magnitude of the tov ( mju70f5rhwrque 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 Fig. uk+*p+s obr /bs3,w8mv2vv / gmed+dshyr;:k 8–39. Assume that a frictvk8w y s ;h*/ue+p, 2k/v+ 3gmbmdvdr+ sro:sbion 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 a masslp s2ui yi-8h1ress rod which pivots as shown in Fig. 8–40. Initially the ro s1r8yih2piu-d 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 head oij0-n0xmvm gy59h3c t f an engine require tightening to a torque of 38- i9cj0yn 3hg5mv0t xm $m \cdot N$ 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 sphere of radius 0.648 m when thhvd1yqij q;ffri5gqx .vao jj131-)2e axis oqqjigrj1 -2.f ;i51hjxv vfd 3a 1qo)yf rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicyclz (t 0uo,)ysaje wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub so(ut,z0y) ja can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, luu(3 2v1 mxxqkight rod is rotated in a horizontal circle of rakvu 12qxm(x3udius 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 rotatingczc )ghj(*+q e at constant angular speed (Fig. 8–42). The friction force between her hand)h* gzce+ cj(qs 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 objectsih:bb2 avlzr: 5c(/g s shown in Fig. 8–43 abcb: :hvl( a g5zir/2sbout
(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 whxs1- kgoi+) rhose 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 satellite spinning at the co gp/ ;2xwy 9yef4v2/v ew/9 mi1xqansurrect 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 s iyena2e1qv2yupxxv 9/;/m9 wg 4wf/if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is aya 9b. nl- x 9+ipndftz-beh3/5vhv 5k uniform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calcuhd+ af3n5e9t. b9vxh5zky-b l-/pvni late
(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, accepa8st ppx *b2)obs. u.lerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and 2moak0de+f nmgn2/l- 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 opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictnl2mok-n+/ma 02d e fgional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotat4/ hd;.c k8bjo x9iduxing at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torox /jd8kb;ci4dx9h u .que 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-kgx 8 pf-mh2-0xpd/n zh7lhnxj* + gyfe+ 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 actw+ex 8,gxkyq(*7-7shb slxj tk)jrd- ion of the forearm, which rotates about the elbow joint under thgdh(j-x*ry, wtl 8-)bk7xqses 7x+jk e 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 rodb20-kvyv*)cdqs s9 iv, as shown in Fig. 8–46.9d0vb2k i sc)vy q-*vs
(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 consistg00b *t7 h*-cgzfejyl( .t*; fvx9j ho9iwn hss of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (eo ( at;dq;1tjrevolutions) and releases it at a ;qdjo;a te1 (tspeed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia of ih,6jq c26 kifvll/ 3p;2ttjp$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 956nuc;rm8p;rmqso a 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 a la8ojx82klfn )pnv o7)g ne at og 2x n8vj8 fo)lpk)n73.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with rer(qfr0 ut1oy7 spect to the Sun as the sum of tw(rftuq0 r17y oo 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 ofd) + wq wcnxi+0.q mo1i;ihqx. 1640 kg and a radius of 7.50 m. How much net work is required to ac i.1+iwo xd +xqiq)mn.0; hcwqcelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm anfchibu djh0wr/)e3 3 2d mass 1.80 kg starts from rest and rolls without slipping down a i0rh3f hjd/wu2)3bce30.0 $^{\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 start28c xghmc j77 x-)jaubs to fall and its lowe gxx)b772huma cj-j8cr end does not slip. What will be the speed of the upper end 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 :,n yzop(3orbrotating on the end of a thin string i3y: znb( ,ooprn a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular moment7 i1b9q2p5l gjx3x gkr56uws bum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500g9srbx 712lxu 35igq6kb5jpw 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 0c)ek rrys+-v rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation de)s+ e-yrcvr k0creases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one 1dq7k9 imcb*)iou2oj-; (kacqwp fv)shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3)cu9*c7oj)1 pvqow;mi (akbk2-dqif.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate frn4(uw9w 6iq(kv j- c zm;rf:pfom an initial rate of 1.0 rev everzr-vnffj : mc(4iqu6wk( wp;9y 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 around a vertios8x3 yc5de8z o;d4b4v d dq9ncal 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 flat disk of radius 8.0 cm, onto the center of the rotating wheesdd qov9; b4yenzc8x48d3o5 dl. 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 n64ql kjh+ cs e w2sd6y *h(4nn/ltk1rspinning 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 momentu4 q*bbxq0 9migkv dqlcf-47;sm 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 is dropped ontnj gc*jiifl4(acyi cg +/8c(1o an identical disk rotating at angular speed/(c n(icg1 4jc*fj+gl8a ic iy $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns dirx7st.(ht +e2ke ;3tr b jv(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 a rotating merxoik2t y1ep(20oo ,m rry-go-round platforme2y,op12 roikx0to (m of radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-rou 6qczrd+kbrg n(, hn)87q.eaend is rotating freely with an angular velocity of 0.,rhb +gc zedqn) a6n.(r7k8eq 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 collapsrakc5jlf)f 2hu 7m+1kes into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Aa f kj5 uk2lcf+)mhr17ssuming 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 12nfrl x el0jej (5*/8pkrn/z fd(-q f9c0 $km/h$ 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 cff+rj5a c*8 j$ 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 canq9r)6 f i/1v y cyl5edy7,jplx rotate freely without frict6lyjeryi7 )xv19 ,pyc/ 5fldqion. The moment of inertia of the 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 person stands at the edge of a 6.5-m diameter merry-gogh0qn4 bqvojy99 n++ p-round turntable that is mounted on frictionless bearings +ph9 nq o4 vqngj90yb+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 rollso fj7r lhxnvmwv edk737 .9tc-7rs8:l 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 wal r3hjnsv e8wtfxv.77:7 ld7-o9lcrmk ks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faceanm( 3fgl k,0zs the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to k3 zg(fla m0n,its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m/m5e c7zk fc,.t$s^2$ 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 radkj0v7b. 4 bw oa)x8agtdw0j(wius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the tovxjgkb)08 (w40bj 7 aaww dt.orque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindricch / )max7vqq;al disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of massv7 /cxm)h a;qq 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed :xdl bsd * g4/y7ugf)a4, xxavof 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 mass 8.0 times as grenf 2vz:mt.9 ltkkp5: uat, 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 uktnpkm .:lt9 :zf5v2is 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 e i1bzv5; u:dedh8 okby98 -kyanergy stored in a heavy rotating flywheel. Suppose sak 5uk1db9vyd;8-y be8zhi :o uch a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates bss9m o6k3 n)vvzd3 i)wj4s,ean $H_2O$ 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 surfac hfsm bnhc92 1qv33bl*e 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 8)3hi05v fggdelljg 5d psh7(sx 2eyxk5p,-lM and length 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 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 masdpjh0lyhslg5e2(8g)d p v 3s-f xxek5i5,g7ls of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius y8 fs1ok 1rwgo;3sfj-5k8 do e5b2lt pR. It is 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 (Fio8;5- btokssj3efp 2 r5d1oly1k8wgfg. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat )qdikg :ynl ;2 yj.kqgk37iw1road is making a turn with a radius The forces acting on the cyclist and cycle are the normal 2d3yjl; 7k w)q nq gi:ikyk.1gforce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 bek 54y /ze9uspcgins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from? 4kpczu9ye s/ 5   $m \cdot N$

  Model a figure skater’s body as a solid cylinder an1b.xltm /53 odwtta4nd her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a w3/b.mo t1lt4n x5 dtaspinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical platesq,jm*hegzo1 y ,-v3f s, of mavhf gz*,qs,y-o3e1 m jss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rough track ofiy9,bjvyrn ,( Fig. 8–58. What is the minimum value of the vertical height h tha(nry,b,jv9y it the marble 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 assuml zbx q6gp04)k fi )0uaxgzt7 c2w99ace $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniform+*,7iksi q(dmyop7a o-o b,9aon dl)jly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of eanijm (k,7a9s+poo7 o *qldib d),y a-och 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