A bicycle odometer (which measures distance traveled) is attached near theqf28(9m dgajz duvj9/ wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wh/f9dgdmzvj8a9 u j2q(eels?

Suppose a disk rotates a30alm 72e9cq oj: krm1bauip 4t constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, doe lqoap1 9amcmj 740:b3iuke r2s the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described b)rti 90 crd*8wyhso 3ry a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torq3s49zpizim ; y6ki6,im;wuki ue 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-up with your hands behind your h-whii 1ygxpip -5y5e,tr;i +head than when your arms are stretched out in front of you? i y-g +h1ii,r;e-pt hw yx55piA diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at ts8-u/k ii jhx0he rear wheel and three at the pedal cra8ih/ius x0kj -nks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to ruqpbp 61ht(/zl5wf nm9 n fast have slender lower legs with flesh and muscle concentrated high, clop6qm b( z9fn/t1plwh5se to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fnpd t/lyx6/4q ig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? )1gig4dm1wxb i,0xr bdj0 3ceIf the net torque on a system is zgg1)md4b 1,b00djxi xi r e3wcero, is the net force zero?

Two inclines have they(t-vkt b2mmb))-f) pz+sc.pt so/mr same height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed o fsmzm y)prs.pb)2vt kmtb-+)(t/c- of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. O/wk pv 6s 63r/ zuk6ww/*r/ynhz.q hbmne sphere has twice the radius and twice the rh6hw uwnp.6v3w kzy*qs zr//6/ /b mkmass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same r 1bk zc9j,r(uuj5x q*eadius and the same mass. They start from rest at the top of an incline. Which reaches the bottom fir,bq9xkcj5*uezj r(1u st? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and an7gbtcrm ;ze6db p39vj0p +0xagular momentum are conserved. Yet most moving or rotating objects event0e0a;pd zpm3v+c9x7g r6bbjtually slow down and stop. Explain.

If there were a great kb hk.s1fh/lp95 of(k migration of people toward the Earth’s equator, how would this affect the lenbsk/ .hf9okl(k 1f h5pgth of the day?

Can the diver of Fig. 8–29 do a somersa)gd)vyu , b9ppmlb;-vult without having any initial rotation when she leaves tv mpy) ,-bv b)9;pgudlhe board?

The moment of inertia of a rotating solid disk about an axis through iw .o:.hhh()z kmau w:oy m)5dzts center ). kohhw:zdhymouaw(:m . )5zof 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 c7n* ncw7s gtp9,vzl)or5; w:-memfr-kg mass in each outstretched hand. If you suddenly drop the t lm,9g vr r*c:)5 7pw;wo mznn7c-efsmasses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howeverfnch8 l9 dik6s 1z3;nk, one is hollow and the other is solid. Describckl3 zni6dn9h 1f 8;ske an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontaqmr0n :5:a4 zmhxg5xo6h/ha gl axle points west. In whathagq5zxx aog 6nr:m5 0:h4/mh 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 increasing or decreasing?

Suppose you are standing o-nqua k ee8oy8*o*;zpw ./ctmn the edge of a large freely rotating turntable. What happens if yop8o u.mw* oyezntqck -/e* 8a;u walk toward the center?

A shortstop may leap into the air to catch a ball and 0 wa(xet0i3aothrow it quickly. As he throws thet0 ow0(iaa3xe ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservationf wro,k dfo 9+valc;v.y (;k,w of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helir. +f;lkow;a, oykwcd v ,(f9vcopter stable.

  Express the following angles in radini a0hmzce,mhh a/ 2nw- ,e8v(si9/yuans: (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 amazink- ) 4ypkp/pdig coincidence. Calculate, using the information inside the Front Cover, thdp-i)4pkyk / pe angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Ea)ai fv*x ynr4cm.:p2cv.ofs kx2c +0a rth. The beam diverges at 4v xycn .ffm: 2+ os r*aap02xcikvc).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. When the motor is turne:2uexiolo;5+rl+ dvu gnm;3md off during operation, the blades slow to rest in 3.0 s. What is the angular v lliumnm 5++rx ;ood2g3u: ;eacceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on3 2unbljo5m ugfng 69tz7z ++v a level floor 3.5 m to another child. If the ball makes bf+2 ml t96z+73jvn5uun zg go15.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm * qa19lh0y;id:bpf4 gpz+dm zin diameter travels 8.0 km. How many revolutions do the wheels14lyf+zz;d m *pi09 hdqp abg: make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. C adp9d xcx54zauae 0iv2730f galculate its angular velo2za9ieg7a30u40 x a dxfv5dc pcity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Figotv 9b8 -5qhkbim4m0es-r2z.9i kweo . 8–38). (a) What is the linear speed of a child seated 1.2 m from the center? im5 rv b08so k-te9m z9k2-woi4qbh e.   $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Eak;l1t, y 4jrv jh/g,ctrgo *w30m/ adwrth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speloh) t5r ltvp3f 4h) *zapo09ped 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+kb(xy)b h(ddarcx +: y47oj e a centrifuge rotate if a particle 7.0 cm from the axis of rota+yxx kbeaj)c r(by:+d 7d(o4htion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center 5 6c6tlj8 dmot7dpqc.from 130 rpm to 286 d.75lt6 cpd tmqo8jc0 rpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius:2ifxm,snl ()2zey 0fb*gfga $R_1$ 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, astrona):zi2rtrp.oz j 3zb h4uts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as)zri2zrj4h3 opbzt.: 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 f9neu0ze kk co*h/tnl2k2, ,r220 s. Through how,fe2o2 kkr0l * ,hu9 nzc/netk many revolutions did it turn in this time?    $rev$

  An automobile engine slows dwrzu95n5n : s5xyen0x( ;*( zjtsceaqown 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 stresse van(dzim.8bq.6y apjng 0)3rs of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final sprvim3nnzy d8)0j a(q6g..b apeed.
(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 24ielt9ym*gr.8 wc 5ii-0 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have travele. eltw r8*gi-c 9iy5imd in this time?    m

  A cooling fan is turned off when it jlia2v6 .7yn, )neq ecis running at 850rev/min It turns 1500 revolutions befq2clvy enni)7,je.a 6ore 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 reduces its speed uni u5kwh 167fg2 zll6*1mdbxmg uformly from 95km/h to 45km/h The tires have ag lk6 zuf1127*5bglm 6wmdxu h 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 c3c yl 5tin iivf70a /((ranjl7ar reduces its speed uniformly from 95km/h to 45km/ (5c t n7 iayr(l0f7il/vja3nih 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 oeq-8wcv efid teg/b 2xl2 3t6+n each pedal when climbing a hill. The pedals rotate in a circle of radius 17 ctexqdcig/bf26t e32- +8v elwm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 555u *l tvzwir8 pjt7u,, N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exu v p*w,i7u8z5,rtt ljerted
(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 a e-)0 wfpdy-,jmq0ci ad9tm+of the wheel shown in Fig. 8–39. Assume thd0p+ t-maa0 -,wdmi cefq )j9yat a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, apd(d 2e7fw wp9re attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and(d2 w97fppwed then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylindersg 2l vw8 tjule/t39*p o7zg(oet;5og head of an engine require tightening to a torque of 38/*z o3p tw 9gols7v5l uo2g jgte8;(et $m \cdot N$ 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 of0r(17:dz ytufax ndm 6 inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its ca(n0 6fyrd u:d1tx7z menter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wrsib1upd;v-m s6.r 8 theel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The m8 6r u;mb-s1pi.dvtsr ass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, lw/ )lg o1+nvlyight rod is rotated in a horizontal circle of radius 1.2g/ l1wn+lv)o y 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 ontt7x ./ecz95utv p5r:v -zjse a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between herz.zv55js tr : 7vucpe/tetx9- hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment ofw27u;:gnrh8-qx* lm snuiv + q inertia of the array of point objects shown in Fig. 8–43 ns27 w:uq+vgli - x 8hnr*muq;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 mv h+qa(a,pir z0v*sgca. 0;gwhose 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 cylindrich0 /,0gy n+iz26fk,komy jfsdal satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the sai +/,yk2 jndykgso ff6 ,00hmztellite 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 i7w djt;(xxu1 with a radius of 8.50 cm and a mass of 0.580 kg. Calciu1 xtx7w( ;djulate
(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 batt-j-qf/f i -zg, 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 merrcpc8sj40 .jy yko77m sy-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 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 thk ojjm y4 sc7cpsy78.0e acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually p02j(l5 * elir(zy:dv1c bft mbrought uniformly to rest by a f0*5jbf2evty r(ld c ip( mzl1:rictional 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 3.6xq z,2d+hl f-t-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 s9;bfa3;kt l hlolely by the action of the forearm, which rotates about the elbow joint under the action of9kl;tb a3f;l h 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 olgv v)a zar8u1m5e )0in Fig. 8–46)v80gl)u z1a oev a5rm.
(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 of two masses, jh28 walltj206v3uga $m_1$ 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 br3;:ow2l-d rcnu gj q*++ akefull turns (revolutions) and releases it at a bl +2au ern+q: ko*-d;3 jgwcrspeed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia of3tys/k x;rf -v $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torqkwlu 01u;w( bh:10aep1ywkp y ue of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass a 1 t b9asmt4smbh43 9*unlqz77.3 kg and radius 9.0 cm rolls without slipping down a lane at 3.bm*qst9 h9m s zb3luna4417ta3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth:2zk-qiogu6*rwpgl0 xh ;w8l - oln* d with respect to the Sun as the sum of two t :*wul6 ;*8o wxpklgn-0ldhrogzqi2- erms,
(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 mal f:)somxa8. fss of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotaxol).m8f s :fation 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 starts fromnggc49 wl(r( e rest and rolls without slipping down eg(w rlg4n(9ca 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 w*l: *d2c m;jss lzau4tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.] lma*jl w:zss*2 ;ucd4   $m/s$

  What is the angular momenzlhkx)(rnstrp25.z ):pdx6 dt s o v)5tum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10l5vdtd()6.p oz)p2 )zrsn xtxr:kh5s m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grind)z*6b z*jgewp dys2lff6 r2a(ing wheel of radius 18 cm when rotating at 1500 rpmw(azfbd*z s2 ejl)* r2fyp6g6 ?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his s8;r acp95ur ) aiww)zjide, on a platform that is rotating at a rate of 1.3rev/s If; wcj)rr 8ui) a9w5pza 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 reduce herx,+ yzjni0mv ; moment of inertia by a factor of about 3.5 when changing from the straight position to x0jz i;,y+vmn the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rathb+ejc4c4m1cycx t 6q0 ynu2 3e of 1.0 rev every 2.0 s to +cn2m1bc xjc64qytc3 4u hey0a 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 alxpy*ybtz s b2/-ep-5 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 potte x2l /zbty*pp-5ys-ebr 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 angular momentum of a figure skat eqxy: s0irf25vuf);- 7x mfou6 cmif3er 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 wi38 q m1kr: *bamcn;oof 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 i ;ddchi+uss03nertia I is dropped onto an identical d;0dss uc3di+h isk 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 2izu1ozdgqp u sqx- b-l+e. (6;.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-2e.3j:vle gqups( u+.5 u.cr jzr 7mi5n;g hgsgo-round platform of radius 3.0 m and moment o;5vzigumn3shjq 2 prl .sje egr. 7+uu :.5cg(f 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 with an angular velocity ofk8nh2v qo0 7ls-wkat2 0ashkvo2-k 2tq0n w8l7 .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 collapkn7)ob( tfi+sses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. ) b(is+ o7knftAssuming 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 involves1pp/)kl *rvw winds 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 uq86af9wl n6 m d,1*kizt hvd0$ 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 pa0 sd3oc 9ky-elatform, initially at rest, that can rotate freely without friction. The moment ofk90-3dcs e oya 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 q+9:49yo v pj kenulx/6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and hav +ly enq:/p4x9ou9 jks 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 rope8 pw(yc -*isgebea/ x6 rolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move6y ecb p-8e/ iws(xa*g?

  The Moon orbits the Earth such tqj b--t6o 5wjraczm1)v77 eu qhat the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to -rt) uj5cwj-z7 aqob7q 1e mv6its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1v5:a ct)-m lmo 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 cylindse9isrym,+r w (qvw., o40w(lfo gy(1*xvsa jer of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate f+s* rov( j(1. wo e0s,9asli ywm4ywgv,q (xrthe torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mbh tcvtcfb53ryafec p9(950 8ass 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, 98pbyhtva39t(c5fc0c 5befr 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 ;f a(7lqrco 6tthe 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 timesl7wgc(kvnfr. f+u *.ksri )7s as 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 ofv+ irs7f sf).(.c7 *wgklnruk its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stored itskl (nxm x*-)n a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to*l(snmk) t x-x 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 illustrates0 ewml+hmzz+)9md9 f l 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 rollings5 l s3/+ooc .p4ytgna 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 lengthxp2-6(ylh zuwxj,m 6b L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as s,wjy6 hm 6(ub2plx-zx hown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is stan ommtrg9q.v0. ding vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, gmro.m .t9q 0vwhere h

  A bicyclist traveling with speed v=4.2m/s on a flat rdw6.ks l,94aiuz8s aroad is making a turn with a ra8s, s6ar4. awdiz 9kuldius The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.0 gdptgcvh (u-(d3f/d1 kny hz ,e+om.50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circlfgg dk1 /nzh+tpyd(0hd ov. u-cm 3(e,e 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 cylinder and her arms as thin rods51p0 g )9wwe hhbd+kglyt03ta, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with armsy5lt )hp9 ghke0btwa3gd10 +w held tightly against her body.   

  You are designing a clutatciytid ikk90hx ft775g2-v kal7:/ ch assembly which consists of two cylindrical plates, ofk 7f7gic 7dtiy- th52:aka9xk/i0ltv mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rad-dl19wbam qqos:i , f/ eibi.2dajp8 3:hwc 8xius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical heighti/ :a2s.wdmfdep 3i:88 h-cl1oqq 9awj,i bbx 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 do not assu0sm b6 b3q5aqxx8(alg me $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as th*c.,/ze.zhbna,yh qc e car reduces its speed uniformly from 90km/h to 60km/h The tires have a diamet, , /chhzcane.zy* q.ber 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