A bicycle odometer (which laukhb0 4)vh v4d,l3c measures distance traveled) is attached near the wheel hub and is designed for 2k,bc 0)dll4v4vh hu3a7-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant a..)hgf r 1 bekudr/0zfngular velocity. Does a point on the rim have 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 chan1ghd0.k z/.e r)bfrf uge?

Could a nonrigid body be described by a single value of the angular velocityu1oflneu 7r38 $\omega$ Explain.

Can a small force ever exert a greater torque than bpr2sz9 xk5,va larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head thaxkh o(z nhs2nox5h49 ;n when your arms arooxh2s(nzx ;4h5 knh 9e 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 (ey:e+ h o4ylg w:hbnqn*2d g2at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Whyybgh w::d2leqne g on*24 +(yh? 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 legs with fleshcezpkw*rby00i .+ef : and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynz+fe b0*k 0:cp.ywr eiamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, ni,-r*l usr,iw 8rtge tp50u;narrow beam?

If the net force on ,xz m/(o1n m,5d b;or dvubh 50t,emupa system is zero, is the net torque also zero? If the net torque on a system is zero, is the vz5 p;heomo,,bdxt ,r 5(/0m u bu1mdnnet force zero?

Two inclines have the same height but make different a*e9 wom,w1s4x) y6 nmbvin+yf ngles with the horizontal. The same steel b*oe ,ym+ iwn6 v4nfm)swb91xy all 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 rollin plg shw44sjlj 0p2*l(g (from rest) down an incline. One sphere has twice the radius and tjlsw( 4s2*l0pp 4hjg lwice 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 thewhk+:l s vfh e)(e+qk( same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which ((ef: khl+s)qekvw +h 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 momentumz2.,m-ogepvdqi;j .t and angular momentum are conserved. Yet most moving or rotating objects eventuallyte,-omp ijgdv 2 ;z.q. slow down and stop. Explain.

If there were a great migration of people toward the Ear/a; ph/rx sf5zth’s equator, how would this affect the length of fx/ sp/zar; h5the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotl7q5hr 9+ i0ji tttw)bation when she leavej+5h)0iwt b7r tliqt 9s the board?

The moment of inertia of a1fgq8u5 i+wd l rotating solid disk about an axis through its center of mqlgi wu 158+dfass 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 gd tr9,l4; bh fyq8zm-each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain;9tzhql-,rgy 8 4d bfm.

Two spheres look identical and have the same mass. b0qq/m* xd,)n:r) f5ouqxfjo However, one is hollow and the other is solid. Dqrq,0x/*)bjn 5du omqfx ):of escribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal ays8uqc 7. *c )/gtp0n,e:f itr1vbjqzv bv9. rxle 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 acceleratf90sr i1/gy pnb*.78uveqtr zc. j) ,tqvbv: cion 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 rotac z3h;.iau9c 9 vbfmd3ting turntable. What happen3. 3c99dubzhf cmi v;as if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw iwl1- vlz+u ed05ygg9it quickly. As he throws the ball, the upper part of his boedz 0il-51u gvl+w y9gdy 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 conservation of angular momentum, discuss why a heli1lw 2j er/lkz *2jro-icopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operail 1wolk/2z2rr*ej - jte to keep the helicopter stable.

  Express the following angles i pqx9xe3b;1yz5n 2op;z6a mkyn 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. Calculate, using thejmwsi- 8c( / x/;j7o1kigzhzo i 1h8x/kiz jio/z cjs-mgo;(w7 nformation inside 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 2 vkud / a-e:. meuvjfub(a)d,km from Earth. The beam diverges a2evde()k,v:-.md u ju/bauaf t an angle $\theta$ (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. When1qmd (s0i7 ynal-gtm3 the motor is turned off during operation, the blades slq m0itd7sa (g13n -lymow 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 flo 12oclakq rsqr2rz-1) or 3.5 m to another child. If the ball makes 15.0 revolution ls)1 rraz2qkq-21orcs, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8. otq3mah9xp* 20 km. How many revolutions do the wheels m2ot9qx m 3a*hpake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculteni ,xqa 8+47a*fxsdate its angular velocity 4dxq ixtnef8,+ a*7s ain $rad/s$ $\omega$ =    $rad/sec$
(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 (Fige7 jk:os( zks5,w3mca)wziq2. 8–38). (a) What is the linear speed jz) owca5em:(izs,kksw2q73 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 velocitktm vh9e) gj2yj 1g3i:y 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 speed of a pointtv vzfy;e gw6*)j- o7l:e (wtz
(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 rotaz kspf:z d+21ktwf:k7qjrzqc.x(;: v te if a particle 7.0 cm from the axis of rotatio:rx+kz::qjw.t ( c;fzskq1 zk7d 2p vfn is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its cente 1.i(y sku/uk8u6 rw/ndm, strr from 130 rpm to 280 rpm in 4.0 s. Determdtsuumykw6r iu8, (sn.1r //kine
(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 radiuyvifzn :tb 7d+.dzo.m ,cyq;b m9oy 80s $R_1$ 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 d+ su.y)vfq-o themselves into a slow rotation to distribute the Sun’s energy evenly. At the start q +- vsd.o)fuyof 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 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Thrxi 18sdst)nuu zgxm(:-fe1v/ ough how many revu:fe(/8 m xuv1)s-g nxds1iztolutions did it turn in this time?    $rev$

  An automobile engine slows*jzow)nt 7,g l ni86oc8q- hnpk9-lop down 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 s6e-q.du i53wdq w fj*ptresses of flying highspeed jets in a whirling “humw eiu5w. q6q-3fd*djpan centrifuge,” which takes 1.0 min 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 240 rpm toc.pu ; o72im 9z5f bqv0gbd0lpf3vor, 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in ob59z7pob2v 0filvcf ,gpr ;.m0udq3 this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turzgu/7fu4 xs7mq / ,vzrns 1500 revoluqfv7 r74,xzg/muu/sz tions 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 65 revolutions as the car reduces1v7l 5lev dv9u its speed uniformly from 95kmd levvl71u5 v9/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly uzg ;0wt72jb* b7aduh from 95km/h ;7z7d uu 0w*abtbjhg2to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbing a hpa3 x/qmkd )u7ill. The pedals rotate kuxq)d/am p37 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 en0va:hq: o ;iccd of a door 74 cm wide. What is the magnitude of th hoiqc0:avc:; e torque 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 thpm;ld 1ufa6,e0r t) k: pxxb2te axle of the wheel shown in Fig. 8–39. Assume that a fricti 0k1eptbp)l;6 u :,xdx2martfon 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 massless rod which pbd8ldug2g2bqy./qq2blmn 3nl3a 3/z ivots as shown in Fig. 8–40. Initially the rod is .l3zul/2n3ma2/gb d8qnb 3q g2 ldby qheld in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylindxkps e +1;yqk48dj 3xler head of an engine require tightening to a torque of 38 81 ;y+s34kpdjkxeqxl $m \cdot N$ 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.ll *unzn),wdr9db ( 5/s7kzeb8-kg sphere of radius 0.648 m when the axis of rotation is through its center. b /d 5zel*nr97udks,z ()bw nl   $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The r 7(spoyg8aizv4x.(h rim and tire have a combined mass of 1.25 kg. The mass of the hu7oag (y 8.hi4r x(vszpb can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a quej-3aljyevvab o6 -m;c-8 )horizontal circle of radius 1aqe m;3a6) -- bley vujvoj-c8.2 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 w7n y,5t1p(b;sp, ub (dtxv uiuheel rotating at constant angular speed (Fig. 8–42). The friction force between her hanup ,v;ipd7xs(tb 5,bt1uuyn ( ds 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 objecz 8n65rl 2qetrts shown in Fig. 8–436n5r l eqr82zt about
(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 conm,39*sly vkt;y1ox zwsists of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at cu i6f,)-n 6mhdsr9lpaf7v5 xp 1f5fzthe correct rate, engineers fire four tangential rockets as shown in Fi s6fz dp 95f6fmi7v arh5px,cn)1uf-lg. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylind cd yt-m)sj mw);5w7 i(aq(janer with a radius of 8.50 cm and a mass of 0.580 kg. m)7wsc j-ma nj 5ya (w;dt)iq(Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a,s yh-fc) m5ws 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-driven merry-go-round anda 4kcbmdg6 i6k55 lme+ is able to accelerate it from rest to a frequency of 1dcg4 +66ke m 5al5ikmb5 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm ius+ xf)j+. *ptbrk,d:8k d zleil 1g,qs shut off and is eventually brought uniformly to rest by a frictional f p+bkk,dd qjgr1l+i x8*z,l)ute:s. 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 acce)6qfhgs j312 q2+da5 m ghcgx 3ivpuf3lerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, wh*u dhzlm6s(.( zq).jjprqq :nich rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly fromqn(): p(jdqr .6*mzs.qz jhul 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 logxer2jzw *a) l53xf91 xghjsyy/l8) p ng thin rod, as shown in Fig. 8–46*2j3xwyapg xl)1 x) rs z/ehgf8l 95yj.
(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 :6pwv duaeg-9t-i u6j 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 h/9x;t,hdq u m4rarf2 within four full turns (revolutions) and rerd th, fhu 2amq;4r9/xleases 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 i d) tf/d b3rt94*i2xtboazzn8nertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 2icuo9*x z zi/9l owx-(80 $m \cdot N$ 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 kh1ixa 7db4 o0slipping down a lane at 3. dxk7o1i 40bah3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Ezs+ xn /hxr3:ue-2tm pj29pxrarth with respect to the Sun as the sum of two hr r2:ep+9xmp2n3jst xzxu-/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 andv;cb/xoi,7 e4 syh4 qay8gc+k a radius of 7.50 m. How much net work is required to acceleraeb coh ;/xa+cyqk yv874s4i g,te 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 and mass 1.80 kg 1).5k 8fufnejit0o6 *lnx qktstarts from rest and rolls without slipping dk0 xt fj1*.8) nkqeli5f6outnown 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 fa(qgwp y -+ oyn ms9ol.c)ti4)wll and its lower end does not slip. What will be the speed of the upper end of wylt.mi (- ))copog+y s9qwn4 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 of a thin su)m+utw qisc;q7 (zcvj+ jenr(92k* string in a circle of radius 1.10 m at an angular speed of 10.4 2q9qr(z)w et kc+j 7nj*uc; (+smvisu$rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentzsw:3r 6a cln8um of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500azsc l:83n6rw 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 iso8 ip+k0kpjq 3 rotating at a rate of 1.3rev/s If he rqk0pi o8jp+ 3kaises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of ineri)j 7vys nuw0 8hsnel)85gvfoe:l:-wtia by a factor of about 3.5 when changing from the straight position to the tuck position. If8fun7n hjylolv wgvees8 s::i) w05)- 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 from an ir ove;*jt:y-e gv*i *fnitial rate of 1.0 rev every 2.0 s *g ;*otveji-y r:*evfto 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 vertical axis through its center at a freq;e.knw : ,b,i:mvsy5akhvcv .uency 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 ofhy:icas.,w;v, .kv n5ebvk m: 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 s1+,skdj1)um b uukb,ak,i 0re kater 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 angula(9c ba n )ng6r3c yfj80;eixsir 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 is dropped onto an iden.mx4qbn/dzqlpz1 9yy yf *1.ctical disk rotating at angulan1 f1qm .y* /zqx9bzcyd ylp4.r speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at lm-bfnvf u*n13zx l(gzs 65m/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 kgm w0+qtb cq7n5 stands at the center of a rotating merry-go-round platform of radius 3.0 m and 7+ qtqbw05 cmnmoment 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-round is rotating freely wn85 el jprhvx//16-q3y cxp xwith an angular velocity of 0p5 x xrqvw/ /cxyh83j-1pnl6e.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 evenf0gs+sbloj x pkp/ won9:0f64 kkw+g;tually collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest inte lw6ko f gsjpgfp/+wn;00k9b :so k4+xger)$\approx$    $rad/s$ (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 windsq hxzr1tv0* n3 in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass it:u63hm9wzhn iigt *09(b-v40leet n ksi q+$ 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 p;qr(udftxxf 0kk6ity(-s u,*f0 x*z3taua i7latform, initially at rest, that can rotate freely without friction. The moment of ixykxu3(u ia -fsr*z 0(;u6t7 xdt,iffkq*0tanertia 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 diam fcd *-37uib 8ilrick8eter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia dccib*-fli 7r8 uki83of 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 n-mn01)bg4op(vs fmx 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 slib-pn 4nosf(g x m0m1v)pping. 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 s9ckywxf 2,q f)02ztry) j;oq wame 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 as2oq ,zy fcyj );)rqwxwf9k02t a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m/ vqe-puxn-zkh e,+o.6 $s^2$ 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 r3 g(xl9pu0 +pwpkabp4 adius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the to9g(pbapw + u4l3 xppk0rque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of twoh l )xb/f7 irt8bh;9xl solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concehrx /bil)tx7; lf8h b9ntric) 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 its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear whkb-qciqnmt op8*j:x y94,pf0 eel ($\omega_R$) 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 great, were ror;o ,orlu4;+ykcdn g2:e pzek jzp442tating 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 io, lzz; jno4yk: 4p rk4regd2+p2cu;e s 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 ene()sxk lykw3q9rgy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 140 k x9lsw3k)y(q0 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 w1 k)lo *t pp w bsb3:/aa:7whofgr.z(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 g,22+q6cgsty h9lsa+o v e1rerolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., pwh1ig7 dj4d 5 )bv6,h,ymd,hw jh/q owe ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the momjw whpdqdh5m,j oi, 7 dbh1,/4v 6ygh)ent of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standhj8 iytpiv90m q1py-+ing 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). jmipi1v+ qp9-ht08 yyThe step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is maj:z )i k9m (6xnnc rr:r b7chh1mox-5yking a turn with a radius The forces acting on the cyc rm7 r :y 6(hn xmbco9r-n)hizx:1ckj5list 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 rovaz2h;+* 2ahml j:wsock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal c hwovaha+lz2 *2 m;s:jircle 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?    $m \cdot N$

  Model a figure skater’s body as a solid 1/u 0qg ec1/wq3q dw2ptx3qt ucylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, an13wgq/q13/u xqq dwtute2 0 pcd with arms held tightly against her body.   

  You are designing a clutch assembly which coniz2d (,vr;owsu)n pj 6sists of two cylindrical plates, of ma,npdivr j;u2)6zs w( oss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 al *f6mp7v iiejsh8m- 0qong the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume8 p hqi vems-mfji706* $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not 8g(ht/obc k, jassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revo6/swsn)(li3s yyo5.bw vnw)i lutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0w)lsb) 3 si/wv.5iws( 6yn oyn.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s