A bicycle odometer (which measures distance traveled) is attached n;d5tjx3:6plxbo+6cr b qn 8( nsz*nsjear the wheel hub and is designed for 27-inch wheels;dc5o qp j z6xx+3tslr*jb6n8nb (sn:. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular rj;rzu 6x nqn,6) mmt0velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular vel6t n,j0m6rn zu);rqxm ocity 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 des4eq7 9l;nz9s kc-qjvu0ww ab5cribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greatuo 5adf.1di l:er torque than a 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-6, 62et *d kll v3i;l1krh.lnwn:heajup with your hands behind your head than when your arms are stret d *:3wkan; lh l.1ee6tl2,hlr6ik nvjched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has sevem qx (a,a;:zjnp: yi3jn sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprj(q,najzi ;3 p:a:xmy ocket 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 to run fast have o2 mk+1 c4pibg y+e/jpqh/erbn* ( 7voslender 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 advantagj rp7*y+ib 2mo+p/k1 ngc4ebho v(eq/eous.

Why do tightrope walkers (Fig. 8–35) carry a lgy1o: sw0idbvst(t:* y3kb/e ong, narrow beam?

If the net force on a system is zero, is the ne* k)nzs k6y, :vk 3su.ahf(j2t(dskvit torque also zero? If the net torque on a system is zero, is the net force zerudvsas:(,tkkn*)(.2k sz kfih3jy v 6 o?

Two inclines have the same height but make different anglepd9j xyky/1c2j5a g9 ys with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed ofyjp2d 9/kc5a9 j yygx1 the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling gj a;cpc-8rov7 * wd3r(from rest) down an incline. One sphere has twice the radius and twice the mass of the or a* w3- dvr;8gcjo7cpther. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass47+x dtmuk6t rhly(04mr ro ,s. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? W(7 dx4 tr +yum0rks,ht6o 4lrmhich has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momxzicz9qn: / .+xr 2bnpentum are conserved. Yet most moving or rotating objects qzxri b p92nc/zx:. n+eventually slow down and stop. Explain.

If there were a great migration of people toward the Egu-iz7n(4j/. dnb wcn9x;cpt arth’s equator, how would this affect the length of the z94ngtx(;nn cdpb/ uic.7 wj- day?

Can the diver of Fig. 8–29 do a somersault without having any initialii4m*,:bu mu87 dtre ba 3ii9f rotation when she leaves tht83b*a7biud ,9m4 r mefii:i ue board?

The moment of inertia of ek e2 um+)cyi/a rotating solid disk about an axis through its center of e my/u)ie2+ckmass 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 sittkw8mai9odz df,06vs:jf0 ep 8ing on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increasez8wo s09af pde8, kv:dfm60ji, decrease, or stay the same? Explain.

Two spheres look identical and have the sameve -6ve qli5mpqf-2x. mass. However, one is hollow and the other is solid. Describe an experiment to determine whichv2fplq-vi -e xmq.e65 is which.

The angular velocity of a wheel rotating on a horizont5vtgs5fuu7x*yf j79f al axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east55syj *7xtffuf 79v ug, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of dh0vf0cmh/r4 2u u2ve a large freely rotating turntable. What happens if h cur/fh0ud ev4022mv you walk toward the center?

A shortstop may leap into the air to catch a ball anqc1zmnex7g+ us )jv dsa:;8j(:wdys3d throw it quickly. As he throws the ball, the upper part of his d 7m)1: gyuq ns+xjsa jd(sczewv;:83 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 conservation of angular momentum, discuss why a helvdzh );( gdnq1icopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable (vq;hg)nddz1 .

  Express the following jqd x 3rk;vwxvi1)1 rrqz/1 (e3q9qsbangles 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. Calculate, wnpk6uww;52 y using the information inside the Front Cover, the angular diameters (in pkun2;6 5wy wwradians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moo f w4ct n7xd0hrl*)j-jl0;zio05 yeozn, 380,000 km from Earth. The beam diverges aj40oi 5nh e0d0jofz7*rllyct; z -x)wt 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 blendeu tt .3 ad vwl.xdjwg(s15,i(xr rotate at 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 acceler(d3 vigx5.dljatx tu, 1s. ww(ation as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If tdjyfb ( lb v;(xt9i:6ghe ball makes 15.0 revolutions, what is its diameted ft jbb(l(x:vy;96gi r?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions do tad+n+zie ve :5swo(psz8x7z.nm .eq+hz7 +is a+x+wps .m. :q(eeo8zvn5denz e wheels make?    $rev$

  (a) A grinding wheel 0z8-u* r:lpb h *;xi7u ) aqb)lpeofp0s.35 m in diameter rotates at 2500 rpm. Calculate its angular vp ll ruq*za-*p bo)x7bphif0s ;)e: u8elocity 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-rounp+nxqm58v:6wdhh wd/ d makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is thedhx nq+/:v5wwmp8 hd6 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 owfu0gc1aruw( chb .s// h ,l+arbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spee ) *,f(udiwpysp,w-xst: bwv5d of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rot-+ hh,m i0f8 i qdo7sc2wzqt,sate if a particle 7.0 cm from the axis of rotation is to e c +q2ss,z m7-o8ii,d f0hqthwxperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformbj y bie:n.4r :xp.3unly about its center from 130 rpm to 280 rpm in 4.0 s. Det:xe .3bnn 4r.ibpj:uyermine
(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*ny)dnk,lw r0 $R_1$ 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 j0m (h( v+n vtrkty-e,1yf c2lApollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minut2lt 0m ((cv1 v-fy,tn+jerhkye 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 uniforml0eo :r9p at7imr 4wdl,y from rest to 15,000 rpm in 220 s. Through how many r4m0rerlo 7i a,wtd:9 pevolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1 nv9)0 luol+/men1 lmk200 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 highf-h7e ls am2mb ti1e+m*u8sp3 speed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through2epb fah+l s*3t 17es8mmu-mi 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 to 360 rpm in)k5tg12ern/oipp: v d 6.5 s. How far will a point on the edge of the wheel have traveled int pg 2erop1:5id) vk/n this time?    m

  A cooling fan is turned off when it is runng9m+2t2am oj 57imnk bcrw- t:ing at 850rev/min It turns 1500 revolutio- tmmj7mb i 9toangkcr+5w2 2:ns 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 revoozvkgu1vp h 2xryc2,r lek 4115y1sj( lutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diamete4oy 1(vsr jehgpvz2xlkk uc 121ry15,r 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 carl 87 v6qin71+qwaalc.cej-pr reduces its speed uniformly from 95km/h tnwqjq.rl 78+l c-a ic1 7p6vaeo 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 eacag; ba,m125 sevyydg;h pedal when climbing a hill. The pedals rotate in g;,1 5yebdg2smavya; a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of dmh*db bo;3i)mc4*l w a door 74 cm wide. What is the magnitude of the torq4hl db*;d3)ci*mo m wbue 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 s)cvffe *kh ,qmlz4 58about the axle of the wheel shown in Fig. 8–39. Assume that a friction torqlh5ez8)c *4v skqmf,fue of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are a/m *d- of-yx,u 9wh acy6nakcvhc(b59ttached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the hor9fbay h m cch*kow,x(6d9 5ua- cy/-nvizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder8gud a-s vv,78orkj2x head of an engine require tightening to a torque of 38 oavx sg78jd2kru, v-8 $m \cdot N$ 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 b+1ez+t bc526/tf wo fwnja 0ja 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its ctnt oej c5w+bf /+6zwjf 12a0benter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycl z+vx8zao) gi ;5fz(p2cfil y7e wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. Theyiafz)zc 87x f5(lv o2igpz; + mass of the hub 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 hor: gh i;.8myg)fdb*ruxizontal circle of radius 1.2 m. Calcul:udi fhb*yx. g;) mr8gate
(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 rotating at const 9)iwtu.etxb9 ez *n/kigqd8-ant angular speed (Fig. 8–42). The friction force between her hanigz )dxq eit9*/b8e-un w.kt 9ds 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 ofs.jk1irp-+3d dp h oj2 inertia of the array of point objects shown in Fig. 8–43 ab2jp 13d prsih.j-ok+dout
(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 bhs z7qbx54;p o6(6hr (hkvjr 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 satellit tsq)r,nxkm.z(o4pbq k +i/,ee spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If thxkks,/(ib, )pzntr qm4o .+ qee 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 cylinder with a radius of 8.50 cm and a m+*zppn.;gfc3im pl*w ik08z wass of 0.580 kg. Calcul*0m.l n8+p i3fkw;ci p wpgzz*ate
(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, acceler0ni +ay nou3(lating 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 is ab i9e eui19/g) d;bicoble 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 9e ci9u);e1obd/i gbiand 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 event;9 jvi0c:de6vw4 x 1kasvps2b ually brought uniformly to rest by a fricta:;b62xp k1 ijcvs4wv de0s9 vional 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. 8–45rfvpw;bt.b7 6 accelerates 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 aax:8wh 1edk1 e0gm1pis thrown solely by the action of the forearm, which rot1em:1 kga01hw8xa ep dates about the 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 thi 90m2.xaa m6jq)cumnon rod, as shown in Fig. 8–46. m2a9qujammnoxc0 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 pk z34o6ktyakasy,;1 consists 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 fouep;y1u g2hfvo .2s1spr full turns (revolutions) and releases it 2;op11y.pfeugv 2ssh 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 hprs ly cibf9f:.j- rt* dt60/aas a moment 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 develops a torq/ cl5o6cusv t)ue of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of maxwu51qlu:6e:71 2ahz a wubn iss 7.3 kg and radius 9.0 cm rolls without slipping down a lane at 3.3 q iw7xbueah21:zu51 a:u6nl w $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of tb( su my*yi2q)uoev1oq /*.udhe Earth with respect to the Sun as the sum of twid ( yus/e *omy) .uq1bu2oqv*o 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 andw0hik)72znh8fq+yvx190 zi,jv v q dm a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.f10hv9zd+km,ji8n vyz 7wvi)hqx q 2000 revolution 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/ i)ex3bj5;bugju eq tx/1h4. a) gpiz without slipping d)4xxq 1i.aj/tiu3e5; jg/)ugz e bbhpown 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 ;,2ioyrk3el 6-za7 gzoquw7sstarts to fall and its lower end does not slip. What will be the speed of the upper end of the 76w ;z-uaoky, srigl eqo27z3pole 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 t 8xdo7+(u fjbshin string in a circle of radius 1.10 m at an anb +fdjou7x(8 sgular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grindid:5gm3 a p)guz 2ta6dgtq7 lp55vi+ ttng wheel of radius 18 cm when r5tpg5a6 il: tqdapu 2mg tz5dv g+37)totating 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 platform that is rotating )opfph4ib t7 6+yuxa.at a rate of 1.3rev/s If h+ 6ou)pfy7.4xa pbhtie 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 reduce her mom* chxv4f 4jr/wl8zzyn)cp8z2 ent of inertia by a factor of about 3.xzlv2 4 h jy8cp84n *zf/wzrc)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 v08fsy,w. db68y7pl u dsvjuo7 ((yan rate from an initial rate of 1.0 rev every 2.0 s to a final u8yvbj7v 6sfw y d. syp,u 7a80onl((drate 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.en9rlrcv5v / z+f g:c around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center +z5 rcv:f gl9ne.c/ vrof 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 fbjgjgc: dl i0xq3v-:8igure 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 Eav) z6f,jbj9s fkg(*ks rth
(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 ide0 q lwxw /5v:x*g.wjqv6ta0 jyntical disk rotatingq5lvq/yjj* a6:w. 0tw0 xxwvg at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atkymau(m:r6) kd4 ddzdcd)- 1 h 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 afpjor/pe, 5;b+op /mb rotating merry-go-round platform of radius 3.0 m and moment of /eob;jo+5/ p,rp f mbpinertia 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 f x..e ,tty-tiyreely with an angular velocity of 0.tti-yy. e .x,t8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwn9b w 5bp8zt,wg:dac v8clz :2arf, losing about half its mass in the process, and winding up with a radius 1.0% dp,::zbz 5 98ww 2tvbcganlc8 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 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 excesmscw1c5)zro 7yf2 +lis 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 (b3 fjgksy s;de9d56 hhdh35y$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely withooazn:c((q61 zk qy:-dls7l w yut fria k61lqsn-z:c(yz(y:7dq lwo ction. 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-go-round tz q--/0tlpzh* d0r ohaurntable that is mount p l-hrdo-qza0thz 0*/ed on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the en6ou 42v9jma y.bsl 9q8*jufyqd of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What lej2j9 o4 bq.s*9yumqyul6a8fv ngth 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 faces the Ea+-rw gr(2ov5q2c y gonrth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In thg+2 q2 -5o rvg(nrycwoe latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates f:qi /iq1 eb8coa)rm1jrom 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 shoy25c ap v/ny8hi.6u heavlyn9 4et ;*ape of a uniform cylinder of radius 0.20 m acquires a h8c5ny 9p2./*e yvih4 yav ton6l;uaerotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solavqg+50 h4erf id cylindrical disks, 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 the end of its 1.0-m-long string, if it is released from rarq4g 50evh +fest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of cil:x;w fhem 6qmp 8+1the 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, bo+ 5*t mopcm+m -qq6 cec:akz6ut with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gra qqom*oe+ct+mzc6k5ca:6 m-pvitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollutionyy/p(e+ -p cleqh s7/m automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, a/yy(ec+/-hspml p7 eq nd 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 fhe)7w06d+tufh0 8/smse id xlt,kn+ 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 (hoop6*j m-o jk.+ cky4gnwc) is rolling 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.,e 6oj4 a/,wvkw 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 mav4e6a wk/wjo ,ss of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertica 2 kb)ef;lf -aox7hc;ii* xtn/lly on the floor, and we want to exert a horizonta2xbt;xk;-h/oe 7*a fn if )cill 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 h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn f -:lo*wlc +/zrl8zqp ifu/b5 with a radius The forces acting on the cyclist and cyclfz+ * if 5lql8-culw/po/zr:be are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a slinghnp+(+mbzc nwt+ w:11ndgge+ 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. Whad gpn:h+t+1mcbwn+ez w+gn( 1t is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skatern sy/)43wlo;nlaldc 1’s body as a solid cylinder 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, and with arms held tightly again ayd/w; sl1co3l4 )nlnst her body.   

  You are designing a clutch assembly which consists of twog +afefq33(m6twbtt2 5lh0gkg u9pg 6 cylindrical plates, of mas3a pbgtg wtl0(ht36596+ 2f kumfqeggs $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 o cx f wkcqxd:ea . kcflf7h:;z)1ll-,,f Fig. 8–58. What is the minimum;c,c:xx- ckl17)fweadlfh : , zf lqk. 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? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but doa / .*)nyaz2 iibi6vzn not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed u dobtcb79vf40 ewp9+4s k*gc0 ups7h o68 oelkniformly from 90km/hwv4ps cks0pt6d9e fkelo7*ch4gb 0+7 98boou to 60km/h The tires have a diameter of 0.90 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