A bicycle odometer (which measures dist0ktds o/ynlj.z8 +nzh7 .lo/hance traveled) is attached near the wheel hub and is designed for 2 kh+nodol/ 8yz.0lz/j7sht. n 7-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the ridq.2ma u78f uam have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point q2f 7ad.umau8have 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 singlevq kh q+8cfm-5 value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explais4n5ku8 toh9/.ebyf oen. k3 cn.

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 ygri /em0t -bpcc l8jot;g53a 0our head than when your arms are stretched out in front of you? A diagram may help you to a i-aj3teg gcm;rlob 05 pc/t08nswer this.

A 21-speed bicycle has seven sprockets at the rear wheel and 7uux,*ngo rh- thbm87 three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder tot77u,h*bh8xnomu -rg pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have ejta.4 5 he8soslender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this dih ao.t84 ej5sestribution of mass is advantageous.

Why do tightrope walkers (F7i9 4tj (t /p n:uldelis0h)slig. 8–35) carry a long, narrow beam?

If the net force on a snij 81(y2mk5cqysx*5 q le v+bw;zvs+2lhdi (ystem is zero, is the net torque also zero? If the net torque on a systykj5(vlq xve81y n+*ci5 s+2; 2bqiwsd(hmz lem is zero, is the net force zero?

Two inclines have the same height but make different anglesaxy9(yf.qmerp/2 obv . fu r53 with the horizontal. The same steel ball is rolled down each incline. On which incline willvy(rup x.o3fqe/ a29myf5.b r the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultanewu36w/l1cmzt b os7 9aously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the /sl9bct ww3auz7o6 m1greater 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. Theog7rhf d*ckk e4,i/ 6dy start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinefh ,iko4ddkr/ge7*c6 tic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most f/.6u9x vh qa(w+hdr xmoving or rotating objects eventually slow down and +dw/ (fxhh9u.q axvr6stop. Explain.

If there were a great migration of people toward the Earth’s equxi4 oyuus vs+ka(5:z( ator, how would this affect the length of the dau5u x4yks ozi(a: v+(sy?

Can the diver of Fig. 8–29 do a somersault without fem6n8ts/p 7g8,ox i s. h.cmyhaving any initial rotation when she leaves f/x7t i eo6ng.s,ch8p mmsy.8 the board?

The moment of inertia of a rotating solid disk about an axis lnpx: /bkyr hkir8 q21(t3zzhs)9i,pthrough its center rlpsir:2 (ikpxhy t3zh q) ,bz9n/8 1kof mass 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 outstqdb:9 qp5 +a4crrd6deretched hanc+rq9q dp5e 4:a6dbrdd. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same masszi+y n7 b.bj *.l6ziax. However, one is hollow and the other is solid. Describe an experiment xjbl .+*yi.nzi7a6bz to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In8dz0ft zo*5yf what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed incryo8df5z0fz* t easing or decreasing?

Suppose you are stand)* nv1mfn8vy io+00 dopu x(xuh 55vxting on the edge of a large freely rotating turntable. What happens i0ouv50 m* x + tvu(fvin1np85xy)h dxof you walk toward the center?

A shortstop may leap into the air to catch a ball and th ;)tqd c.aexl5row it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotatec; ldetq). 5ax in the opposite direction (Fig. 8–36). Explain.

On the basis of the lt mla.l9xoc+v0yxrps1,b 1b (aw of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the seconds rt+lyav,x lx(m 11.c0o 9bbp propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a)gwko k1lk/ mt/*pxi.aq 3(co0 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, u4 kcf.z- xxdq,sing the information inside the Front Cover, the angular diameters (in radians) of .-z ,k4xcfxd qthe 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 diverges as6g)tkea ul,p*rp; ,t t an anapgu )el,k*t 6 p;,rstgle $\theta$ (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 atut rwbe8-8t y7 a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as t8 y7b8wet -ruthe blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If th j28r9aiz;oyk e ball makes 15.0rj2a z ;9ko8yi revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diamey)8p wnsoaalp79b*; n ter travels 8.0 km. How many revolutions do the wheesn7y9;op8) baw plan* ls make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 20.0ujjs pgh(.txn a*3okoiu- 500 rpm. Calculate its angular velocity o.noh t(ja-3u pj0ks*i.0ugx 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 ma*ecxt:*p;zn k3xzj 07 c )6iniw6 weeakes one complete revolution in 4.0 s (Fig. 8–38). (a) What is th)e*e766 w:e0in*jaik z3cc z;nxwtxpe linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit z*7n- dioru 1faround the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed wg::uwi w r) *nsd2h2b6jv9jjof 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 cen 1zk4 vnm64opsh 1mqvmm:7fg) trifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleratio6ph1m vv4o)qmkf n 1 gsm:4zm7n of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acc:i1n ga-ewf.gov8r3cs n2abc/- : bmyelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determine3.:2n-woeavri a y: sg n-cbb8mf /cg1
(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 radiu7sd* nw,g ka9rs $R_1$ 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 Apo: xi;5w xmt c/2.v3lcqypk.jfllo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the st kl:qcm5c;3 pvtf2yijx. /x .wart of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 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 frf6q8inr5pb25 r 9vn2l b1usua /h(ioeom rest to 15,000 rpm in 220 s. Through how many revolutions did i ui(nfqbb rl5 2 5avru2oehs16 i8n/9pt turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1p:. j u8 k/pc7e2ck 8agqoqtxn1 i/ox/200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whi min)06n rjlmz,g9 qg3rling “human centrifuge,” which takes 1.0 min to turn thrg3 mn)l mg0rj69,qinz ough 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 acceler.9 rnsbpn 9sv6b re;0)ayb//j xdx)gd ates uniformly from 240 rpm to 360 rpm in 6.5 s. How farejn)dvbn.dr/ b 6ag)bss; y x r9x90p/ will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turn)278ovmeji1.r fg3hqtp izz 5ed off when it is running at 850rev/min It turns 1500 revolutions before it comes to5 zi1eqh f) m2rtog.iz3 jp7v8 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 its speed uniformlyxnj :-9,loukj from 95km/h - :jj9xu nolk,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 s -5xhb vb+8bu mn67a,c 7gdxkxpeed uniformly from 95km/h to 45km/h The tires havecx m5+b , n-7kbaduh 76bxgxv8 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 climbinyw1uideg7b8m z;x2 3mg a hill. The peda1demy 278wxbmi3zug ;ls 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 55gpcdz4lmo +now5 :; *f N on the end of a door 74 cm wide. What is the magnitude of the tol*ogd +p :fcnw4m oz5;rque 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,pqovs u5fsa*ww:) p:skn ,9 vmk ;n:i shown in Fig. 8–39. Assume that a friction torque of 0.sk qw,:,o ki mwfa:ns:n u p*vp)s95;v4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, areru,-k/gjp9b 5zcjxiz+6(wx f attached to the ends of a massless rod which pivots as sx(fr5j/z-9z ibkc6 jp u,x+w ghown 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 head of an engine require tightening toh( u(ihviss *0rh0fi6 a torque of 38v hs s*ifhhiri0(u0(6 $m \cdot N$ 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 10.8ka7ib q335 lol0jia l0-kg sphere of radius 0.648 m when the axis of rotation is througa35li3k lo70j b0qial h its center.    $kg \cdot m^2$

  Calculate the moment of inertia of v+o)p0kvci6 p8o ,lt9c d;wuzk -3mjl a bicycle wheel 66.7 cm in diameter. The rim and tire have a combi 38d+ ,0c wkp)lt;omuljv- 9kv6cpzio ned mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram balj kl:dxxim i;al70in* k- ,0usl on the end of a thin, light rod is rotated in a horizontal:7il muldisx0k0a;x kn* j,-i circle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotati 0 to o;jwwm7/eea6rc*ng at constant angular speed (Fig. 8–42). The friction force between her hands and the ccewm/o6e ;a0r7 *jotwlay 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 sho8bwc . le2cxlld.bn:,wn in Fig. 8–43.n,wlced. :lc 8lx 2bb 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 consists of two oxygen atoms who nm:n4vvngo( +se 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 spinnixhc+ q9p+nveh)4pr .o ng at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 3pn +h +q.v4)hpx rce9o2 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unifo1; juvozas*d fm1k 4j*rm cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calculat dj s1oj u*z;41akmvf*e
(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, accelerating it from rest to 3r71/rjl)atxpo;t h55 ag 3so v $rev/s$ 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-gmh yaamrce6. (h/r7 /mh9ff4ko-round and is able to accelerate it from rest tory/hhc/4(m f r9akfh7 am6. me a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is evenkr8zs ul9ru16 tually brought uni1s 8r6zlku u9rformly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball uhs z/zp8l(wc vp535lat 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 solel+6axk,,x4tryme z) pzy by the action of the forearm, which rotates about tyxtz,)zep a+rx4m 6k,he elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in i1c0p .c l3pyzFig. 8–4c1y3zcp .i0lp 6.
(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 con q.w tlmuztv2 c33;j6ssists 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 turnsazmgg aalox2q 6 4. r*78p5ytv -lbl-q (revoluti7 llg-6b*q q 4-2mravtpy 5x8zaaglo.ons) 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 momenteg(xqpia gb29u 8(s c6 of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine dsos. u3 0vc 9gnz;zw3nevelops 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 slic)*h1um 73c1r yhc/sxx0fo3:p rxqz fpping down a la/hhrc0 xu fx1zqy)c3 3:1pfo*rxcms7ne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sunp0 ic( *4(dlbcn0 ezuo as the sum of two term bei *p0ocncdz0(4ul( s,
(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 o4 w,jemah+ 0bfr9lcd(w3z l; mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revoo3w0lfc9a e +h;r4mj w(d zbl,lution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls witchf)e+ 3y1sv6voax*xwghc; 0 hout sv 1w) 0o+g*c 3y;xahxv6ecshf lipping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall and it7 f3ho(1(hngpoc t: w/c2yr yots;bw0s lower end does not slip. What will be the speed of the upper end of the pole just before it hits0o c1c(2 p n/rthg wfo37:ys(hbwo;ty the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular mom(kf v37o+8t9 lveayl all; cn;zw-n;d i h4bk5entum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular spetah4zl9yfn wl;(a 8;lekl+d7- cvnov;5 3kbied of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinb.l9gogpk 9smki- hku) po9q3(.2 vjjding wheel of radipjkvj ilb 9mogg)9( 9sp3kuk2h..oq-us 18 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, on a plt6 l,vxcs .ox4atform that is rotating at a rate of 1.3rev xo,4x6v.stc l/s If he raises 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 (4p-;y.3xbe. l: i8x eo/s qnuwftzr xreduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the neb /xp:r.itewls.;uz4x y qf38-( oxtuck 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 initial ratetns .act2d -a3o: ic4l +jdih) of 1.0 rev every 2.0 s to a final rat 2c)jli dot+t:-iacsah.3 4dn e 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 ir4xd h 1tspk;b-bz2byr (m7(frequency of 1.5rev/s The wheel can be considered a uniform diib1zh 2r psmx4( r-(;d7btkbysk 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 wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angularh/zfdxis9)5bg lh9n a 3vl +2r momentum of a figure 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 of the Ear5wmcpm 7lq0 hz: 54pwrth
(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 idenxg4l;p.k + gvp8m i5 d-q*od(*sgir cctical diskd;xc ig(k +.5gv*do8p pqslcgr4i-*m rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at cxpf-gvee- jh )7sqyq, 76 7gh2.4 $rev/s$ 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 a 01-vuik.36aqe isbtrotating merry-go-round platform of radius 3.0 m and moment of inertia 92i.utq k0a 61i a3esvb-0 $kg \cdot m^2$ 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-gok5q cd apju:s+6r 43svxdfanco836i ;-round is rotating freely with an angular velocity of 0s qkv fn4d3 crx8+a6sp5o;a6dc:3uij .8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses intuteto+7mb (q )o 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 mo ettqu)b+7(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 wiwqd hk)8e udkgyy:hq 7o2g-(9 (efr.ands 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 qorry.a7b6)o i,cn,/4wd.xfy qf)ez $ 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 nz6 n )e iorbi.2n*9rerotate freely without friction. The moment of inertia of the person plus the platformn6 ore2 irei9*z.n bn) 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 dia3 g(+ 9lj rjfj.l ye3ewny+.abmeter merry-go-round turntable that is mounted on frictj+3(e3arb +ln fwj.lyj egy.9ionless 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 grsd-w j2w c-az9ound with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the personc2wj-a -9dz ws 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 1klj *: :i-i4siqdq)c0 0fd gebq;e4xg:pkl s side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (abouqs ilex*dfq:b4i k;qec) g-:p0 :0sk jdl g4i1t its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates f0uevv7cg g35n rom rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m p0 1uew, sexmwil)a8k- w.)jl8mvyf, acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.1llxp-,m) wkuee.f)iawwy m s08jv ,8    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical dx77 8fk om pxvsclbtm53z )99fisks, each of mass 0.050 kg and 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 tpkxc5mxf7sf 9 3 zvol98 7)btmhe 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 th3p n3qd*dn0k/pk sh6 ee 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 mass 8.0 times as wrkce*. gqi(gws(t( .great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its gswk(.wge ((cq i.t* rrotation 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-pollkwgf) xlg :8g)z mf+s .:.campution automobile is for it to use energy stored in a heavy rotating flyzsflg: )f:a.mc. 8gmpkgwx+) wheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a 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 r.b+6r9 anf buxaj: b)8bir8pan $H_2O$ 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 horizodd3/-t2-ru;( 5fhh hfyn-szmg yfx5 t ntal 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.k6ra9h i3kwm:zk4iq 9e., 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 3 wikk:z9imq9 krah46 of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on thfs9g9h m 36h:k p0pflie 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 h, where 3g s:fhi6ppk0l m9fh9h

  A bicyclist traveling with speed v=4.2m/s on a flat roa f+0zrxdpj+ xtx)imh. 2gr9f *d is making a turn with a radius The forces acting on the cyclist and cycle are the normal9m+ *gtf. rxij dxr 2+0hzxpf) 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 suy;l tdafh1z;e w7z/ 0/ (fdpmna27dd ling of length 1.5 m and begins 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 torq( f hey1/afp l/nz d72 z;duaw07mdt;due come from?    $m \cdot N$

  Model a figure skater’s body as afswqki*bmfa.3 yt :z9ur-4z( kkq.4 a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then4mra f 9-:b kkqw q.fyi3t*au(zs.k4 z calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two5.f*o vd5ja4 zigu+l6j rsg*h cylindrical plates, of masld .* ou6v4s5+ijf gjagr5* hzs $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ani 3rc7y 5lgq0 iros(r3uib57nya/ - iwd radius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marlqiri3gbuw0yi3i sa/7-cr 75ny ro( 5ble 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 odj2ev9r 2 s3xassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car redufd chk,a -( pr3i(/qsv2y ynt:ces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. c2t (na (3q:kpyh,sdy-f/ivr(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