A bicycle odometer (whichfq3p o jsl( xw-7(cup3bl*9)l t istl)ye(xt/ measures distance traveled) is attached near the wheel hub and is designed for 27-inch 3psjc 9t tblil((p)*7lxy u3s qftwx/)ol-e(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 ona :.f0arp qes3 the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or qfs.0: 3earp atangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by d*:,hd kov.nfa single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger for2hzs(3l*6 .mb0mr 9l b iestoece? 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 difficul.,is)a d *dk3 qu8lfdot to do a sit-up with your hands behind your head than when your arms are stretched out in front,8kilds 3au fdd. *qo) of you? A diagram may help you to answer this.

A 21-speed bicycle has seven spe q;;i6m av*hsrockets at the rear wheel and 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 gea;ise vqa*mh6;r is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fastr vr*id1zmc8z s(7 p u3hz,rt8-loy w, have slender lower legs with flesh and muscle comt( z dyw irzz*-1h3v,orr8l8 u,7cspncentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers 6wrh w )fkrb: pcx 9/34moep3lg (xtz1(Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net e vdtbi+h +3 1ag9p6. .lu-,n oxklpoitorque on a systpo h3 +,x.l+av6b .gdut9ii-ko ep1lnem is zero, is the net force zero?

Two inclines have the same height but make different angles wiy kt(fqxi sr8up/,p5 9th the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be gs q,u8f5( itppyrxk9/reater? Explain.

Two solid spheres simultaneously start rolling (from r yj4s0fqs7 r12e. r,gty aycv7est) down an incline. One sphere has twice the radius and twice the mass of the 0y 4 qve 271 arj7sgt.cy,srfyother. 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 cylin)mpi k )nwuc;+der have the same radius and the same mass. They 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 kinetic energy at the bottom? Which )k w m)upi;nc+has the greater rotational KE?

We claim that momentum and a,;j. 1-ojjlu hspju4i4 aa r8vngular momentum are conserved. Yet most moving or rotating objects eaap-uj,ojv8us.l ; 4j1h4ri jventually slow down and stop. Explain.

If there were a greath*ugjj/x ; dd0(.oxxb migration of people toward the Earth’s equator, how would this affect the length ofju*xjghxb/0od.x d (; the day?

Can the diver of Fig. 8–29 do aa8ep7eky (r*c somersault without having any initial rotation when she leaves tp7ek(cr y *ea8he board?

The moment of inertia of a rotating solid dia- mu7hyo d;mti*6 6vhm bg/d:sk about an axis through its center of mbtui6v-hd *m6d/ma;:o7mg yh ass 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 ib zqp/h(pf oswoc(94+ 2iscx+n each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? hw+ c4o9iz2oppf s +( sb(cx/qExplain.

Two spheres look identical and have the same mass. However, one iv)q3ubanh ikr, 5y4wk; (yc5fs hollow and the other iw5 a4y crinv,y5)kbq ;f3(kuh s solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotav3mnye :c.kiz j+44wmting on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or dec:mnwcm 4yzekj +3i4v. reasing?

Suppose you are standing on theab5 um3fqo+3 x edge of a large freely rotating turntable. What happens u5+mq f33xa obif you walk toward the center?

A shortstop may leap into the air to catch a ball ahadj -pud )j74lwi h7y -2mz.ct0ras+nd throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that .jr0t7jdpyc4 -m)auzalhsh iw 2-7+dhis hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, disnb)ozn3s7x gp w*q /)k4zo lbd(fpu54cuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to(z)of/b wg 7sn*xd3p) z54bpq nlou 4k keep the helicopter stable.

  Express the following angles in b) .ky;i qc+ iwo:p,jfradians: (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,kd.1*kba 8(j(mjw h wostw (6i using the information inside the Front Cover, thaj*s1whk o( (wtd8 b jk(6mi.we 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 ;)l;k:yvsv cbkm from Earth. The beam diverges at ;k:vvbsl; cy)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 atu3brj*4 hm 0i:)xfsyr.+ zv2jlw 3wzg 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 the.r0 4f bjjgy3z)xw+3i*svz:l2rw u hm blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the n1 xmfo*2v/id ball makes 15.0 revolutions, what is its diami1f /xo *2mvdneter?    m

  A bicycle with tires 68 cm6 :5vo khq(*cc0--frbuvr,j 8stbj zd in diameter travels 8.0 km. How many revolutions do th5v,dcsb8bk:q-zuo j jt*cr r0 f6 -(vhe wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at o ty .kp snod7):6g-vs2500 rpm. Calculate its angular velocit kyp:so )gs6dotv .n-7y 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 b++/4yzjfj1e ,8iyl h4mfmm m4.0 s (Fig. 8–38). (a) What is themf/ymfmmij1h4zl+,+ ey j8 b 4 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 around the Sunx r3f +/rd.qvr    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poi*,bqij5 vv3ohr::m- p i(xsrpj4 b0 t*n apbl5nt
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a part1mc++b pl)hu.h oyub7u c+2xvicle 7.0 cm from the axis of rotation is to experience l+mpbho7xv b.y2h+ +ucu uc)1 an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its centekxvy)4 ec d qfuj0d1)+3mo qpoa2v o5+r from 130 rpm to 280 rpm in 4.0 s. Detery3qa) d4co 2dmu+ kf q )5+vjxopve0o1mine
(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 ijteg)440(uybi iat .$R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo space ; 1o-p8 mmyxbr5mt4cicraft put themselves into a slow ro c- 58mm;p rim41yoxbttation 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 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 , vem5 znieglqn37j:)15,000 rpm in 220 s. Through how many revoluti5enm) l vij3g7ne, :qzons did it turn in this time?    $rev$

  An automobile engine slows down from 4500 f fdph+:-mg :grpm 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 e mfkq7m+1 d8 y9job9vthe stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions befo81 yk+dmm9e97 qobv jfre 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 x2vl yhz;q+d 0accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this 0l;x+ dzyvh2qtime?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 15k2 8+c6a qbx0bya3dw c00 revolutions befo bk3a8+ xc0wb yq6dac2re 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 make0x yj m30qwq:mmzdn6 * 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires0n:md60*xq3qmw j zym 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 revka8c:/f-vq8uv:e c c golutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diamet/cf egcau-8vc : k8v:qer 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 c1y-;+ inhio8jtt2 mwu. cqq4climbing a hill. The pedals rotqwqy+h;jtci-4 umnoc2t. i1 8 ate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is 3*m0n pdm :-o4mg7m0wbb0cz2mzutf xthe magnitude og2mw3c xm 0d 0z -07unbot*mz4:pbfm mf the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about ufxkr ,nx a jjzp)2w7o+ yyov504r i3+the axle of the wheel shown in Fig. 8–39. Assume that a frictionwxio + 5ayx3j2, y0jzvr ofp4k)7n+ru torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the enxd7h*w sx 7,rjds of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal positih,r 7dxsjx*7 won and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an enginew v+vbuo*gouo fvj-6bw(m-kn;v j ,b,6ah-s/ require tightening to a torque of 38 b*v/wv-w- kum-js+f vb6obo ja,,g(h;vonu6 $m \cdot N$ 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 ab.tb, h9 ifd5g 10.8-kg sphere of radius 0.648 m when the axis,i.5 tgbfhb9d of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of ipq op,ikkt s/t8/.mh-s f-ez9nertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a.spzip8h qmok t f9 te,s-k//- combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the ei0n ezr5a( hsf4p 0p5hnd of a thin, light rod is rotated in a horizontal circle5arhhnp4p s050z ( eif 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 rotating/du e3 ep0wwg( at constant angular speed (Fig. 8–42). The friction force between30 ewe/p(dwg u her 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 of inertia of the a4c3 -fge 4q cz sq3f3lpm5y6qhrray of point objects shown in Fig. 8–43 abefzpf6sgq 3h54ml -q3 43 yqccout
(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 whose total mafmj*q h-2 na5ass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the ce:q e-v0r zo) 8-. 70odylz6dy hfguccorrect 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 oy.e q-)l -ch8o00ezy7zcu6vd odrg f:f 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 cmd w)b6qqez,9bm suj 90 and a mass of 0.580 kg. Cal6szq,q0d9 b 9mwe)jb uculate
(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, acceleratinirjt-+70*syxt t2;b,-wuyz.gs8 cy( iif gz ug 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-rotpr2 4w ;mj :1kxb)z kz09hzwaund and is able to acceleratrx zt9km 0h)bjzz42;: pak1wwe it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting 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 broughtl5,4 rh0h ibk :,leon/v rz5yh unif /0io4,:hr b,5lzehlnh5vr kyormly 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– oqb1z u77/laih;sy nbemcg.n7/7 e-y45 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 is thrown solely by the action of the forearm, wf5ha8ff5 g zz. zkk9n/hich rotate kfn9 .fz/hk8zag5z5 fs 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 thin rod, as shown inioi( b4i55,3 idxjgjq tvd,j* Fig. 8–46.i iioj5 d *,vi3jd,b5tg4( xjq
(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 m +q -f,,l*yszeb/pwva1xl vmzyj avx;8yi;5* asses, $m_1$ 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 ) u dr)w(m,eutwithin four full turns (revolutions) and releases it at a speem,ut u)wder()d 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 ino 0lua2mseen s 8*z93uertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque -gqxt)v)kapeu:7f 8 g 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 slix nraoagl(2 (zck6s .-pping down a las(za2coxg r (-l.na6kne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum ofl q11b 5ugywo;,k6x9 rgvwzf9 two twub9f 5,9 kyvl qrgo1z;1x6gwerms,
(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 ohg,;3nph2 3l7mjj kxwt i073odm;ci2w bh c5z f 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 revolutihjlb5t;n32 , w7jwm3 32kiczhh 0;md 7pciox gon per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm rdi 03sc65wdj 0be13yijf)za and mass 1.80 kg starts from rest and rolls without slipping down a s ibe0yrf3 id0)3d cja65zw1j 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. I uo 6657ffpsex 0yj1ymt 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 j76ef1y5op0 su fy 6mxthe ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thin j3ypoa7nm9,k *rx: tzr g, uo1string in a circle of radius 1.10 m at an angular speed of 1z* p3o:xt19 ujka gnrm7o,yr,0.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical+53yq(z ay7b o0fifjwi/-n e h grinding wheel of radius 18 cm when rotating at 150+ a h /(5izjy-q7fybeofwn3 i00 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, handyexhv hr4l,8 s+d;f /fs at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fidl4e/, x hrhf ;vf+ys8g. 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 jkwgbv3j ::/ cmoment of inertia by a factor of acjjw/b:v :k 3gbout 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 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 t7ykx5x mm-27rfwkd/from an initial rate of 1.0 rev er-/xm27 kxkd ty7mf w5very 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating:oepnr; j -cgg c0rfk45e16qk around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be cong e:-pfkejc;k1rr0cong4 5q 6sidered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating 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 skater spinn88v8l7lx u,t8xt)kzhkc z w9 ring 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,iny 3c6l;yex 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 mog. edulone-o 7a8 b9z:ment of inertia I is dropped onto an identical disbo aoez:-nu 7e98l d.gk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns agjfuj(y6 oo5jci 42 ,22ntr hat 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotatingns- ncbx+ 9(gsxz(zr 1 merry-go-round platform of radius 3.0 m and mome-ngb+9nssx((1 c r zzxnt of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating fre 1 3ae gjv)hwgwq*x)u7ely with an angular velocity of 0)wq3uw)g vxhga 1j *e7.8 $rad/s$ 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 collap s )kut1fu-0zazs ndc89;v+ tpses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of09;zzutsp vckt)s 1n +dufa8- 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 windg0xat6 ft; xtul6p28; czh esq. oq*;:se )ueos 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 wvo 2n*i-+ vy.xtg pq)$ 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 freea ah*dhp:h19x tj:a / fe2n7zs,brln 7ly without friction. The moment of inert/n9h7 :rh,12d nbh:zlfa teaj7 x*spa ia 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-rou7 i7odvhu l((.ffw0yt nd turntable that is mounted on frictionless bearings and has a moment o7 l(ovt(f. 7w0ydiu hff 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 end of the rope lying on cz6e,nlxoyh k8-39yivh 8js; 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 z8ex;6hcoksylhy8i - j,nv 93without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. De:tw-vv5pb f- tcdvm))termine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter w))-t5vf-dm p:vt cvb case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates fo3lf;mg:x0sw3w ksb3 1 :jw ucp1 sp7nrom 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 ib vf -pl.t p-9ov)i-ssn the shape of a uniform cylinder of radius 0.20 m acquires a rotfp9b--lv .sp)-v t sioational 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 shmnod;qf g5+s v*g3 c0olid 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 itov0 chd3s +* m;gq5fgns 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 th3f,c9e mmzra(fu/l 45 p6qjxmh5xk5je 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 . vmv. old*h+k1nfgv8/lbbv 0mass 8.0 times 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 of its mass in the process, what would its rotation speed be? Assume that the star is a unvfh1g*vl kvo.v0dnbm b./ +8l iform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobilek,7w9ug usp, f 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, and kf,u 7pswug9,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 illustrate h7:*k0n ;xr ssksvfu4s 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 rolling ra4ttjhwa 58 vd649 nqon 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 p(j7i 2kql5g 9 r3 vct79o0zpyoeolu 3rivot freely (i.e., we ignore friction) a ej7pr0z2 (3v ry 9tlc ooolqi93gk57ubout 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 shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically oi(hu*.eqohiqj.cy ) gp7 k(c +n the floor, and we want to exer)y g+.kopich ( j (e7*qiqc.uht 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 h

  A bicyclist traveling with speed v=4.2m/s on a flat( zng wd2w;gj4p3 0vql road is making a turn with a radius The forces qn d3v 2jwl0;pz4ggw (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 0.50-kg rock into a sling of length 1.5 xt8 l m0 tncd4v./sv85cm 5hmem and begins whirling the rock in a nearly horizontal circle above his head, accelerat xhnm.04t8dcmt 5vscl mve85 /ing 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 cylindb (fmo: c dbr*.1af:gier and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular sp1 db(a.: ocbf:fmgi r*eeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindri3ys fb3**pjgv b6t ch ez131ppcal plates, of mass3p*gvtbh p3 jysz6 1eb1c*fp3 $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 of Fig. 8–.jvv86k0vnnn 58. What is the minimum value of th .vnj n8nkv06ve 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 do not assulz e2:n.jhon7 me $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolu(* zh2n f ;mkew2uvg;*wc, l5dods(tbtions as the car reduces its speed uniformly from 90km/h to 60km/h The tires hcfvt,gn5omb(*2 s;u hd; d(*w zelkw2ave 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