A bicycle odometer (which measures distance traqky4 u./ * kyw)ak3)ft3o ugsvveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens kw4ya*)3) tf q/ ks uv3.kyougif you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity.7ju )6ssgw jpz7l j*p5 Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniforlz s )s *7jp5wp7jgj6umly, 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 described by a single valuxb2/3i9oqyk4py7gvz e of the angular velocity $\omega$ Explain.

Can a small force eve h/nimge5zm1i4 d2)iirn08rl ma(w -v r exert a greater 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-up with your hands behind your head.io(wwh5r u,+7e 9h9 rtrlxem than when your arms are stretched outhw5remt o9r 79.uler hxi,(+ w in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at txnb7e avs0e kr 0l;r43he pedal cranks. In which gear is it harder to pedal, a small rear sproc7 3xev brke40r s0anl;ket 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 slender lower lyu x0w(um t5,*ca 7n3,ztwqfsegs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On th* s mzyx,7w(3 0t5ucfn,qw tuae basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narr0l4 4hneao qq-o)3tnqow beam?

If the net force on a systec96d8fcy83 hd: oi4qbzny a(um is zero, is the net torque also zero? If the net torque on a system is habdfnd9 3y : 8qzciou8(6yc4zero, is the net force zero?

Two inclines have the same height: k4 ,wxadrx)bvu76c c but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at thexav), ck47w:6drbxu c bottom be greater? Explain.

Two solid spheres simultaneously start rolling pl b cw.o-ct:+(from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the cl:-bow+.tp cincline 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 ai 873uxr 8sil kw2vydf2f /;a3j /oqn1z+ usvtnd the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the great8si; n+ oqd 3ixjvu2/3 t7vzskfu /f8w21ylarer 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 angulae)hn7rkw.eyj lj1/h.hg 6 6/s wfq,wa r momentum are conserved. Yet most moving or rotating objects evefe7a) / 1gww6jh e/lkh.,6njy. s wqhrntually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s uz 9gzlx4fox 2jb+q9o e9y*d) equator, how would this affect the length x odzbz fu 94qg)o+e*lj99xy2of the day?

Can the diver of Fig. 8–29 do a somersault without having any inz3 vm3,j:g(ljf-og l pitial rotation when she leaves the boap(m ljzgg3 o:f-l v3j,rd?

The moment of inertia of a rotati l65bveqhb- p-ng solid disk about an axis through its center of ma-evq6bp b- l5hss 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 o1y,;+44gg, oqur tzmb0 v ldjbn a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angulzr+;g u,bm yb14do qjl40 ,gtvar velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow an+ 9 vjuu;roi,md the other is solid. Describe an experiment to determv+rj,ui u 9om;ine which is which.

The angular velocity of a wheel rotating on a horizontal axle points cii rcuf.2 cmd*.ta4lie* l7je52tyw0iv/5l west. In what d 4.rc 5/e*ti.lyd i mfciue7v5 tl0c2 jil*2awirection 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 on the edge of a lard+ v,-,bvfem ige freely rotating turntable. What happens if you walk t+m vefi,db,v -oward the center?

A shortstop may leap into the air to catch a ball and throw i 1+5s:xhu5e aux)dndu or8,zjmb- 9x ft quickly. As he throws the ball, the upper part of his body rotates. If you look quickly y+5ja- u8mhx9) 5 xrxfsuzb:d1ne dou, ou 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,c y gl8.5.p7kk cyqxo8 discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can oc5 8y y.xplk7.8q ocgkperate to keep the helicopter stable.

  Express the following angles in raakz/;kh74yr4p zro ;k /y ejz.dians: (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 amazingl z-fhk5ql .i8 coincidence. Calculate, using the information inside the Front Cover,i.-fk8 hq5llz the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 3;;yqn 5*q pkgv,oyl olsu 9h.1iip8r* 80,000 km from Earth. The beam diverges at an anglpk. 1l5* syrq*gu;y vhn i9o8iqo,;p le $\theta$ (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 +f 4pksxhjq;zbv+,0 uad- ru:the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow 4vb pxuha+ j+0q;,zdu:sk-f r down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m qp-*5y r( odfoto another child. If the ball makes 15.0 revolutions, what p* -(od5yrq ofis its diameter?    m

  A bicycle with tires 7 pf (:ftwxvs nb5m0-m68 cm in diameter travels 8.0 km. How many revolutions do the n(fwbps7x0f vm m-5t:wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 250 sbo;xqk9so*q p-k)gl at1b:,kx9 kb 3se;ar7 0 rpm. Calculate its angular velk a-993r*goeq, )x:;qsb kpbo1s x7 kbst lk;aocity 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 (Fig. 8–38). (x13 w+hrn;rsv x k2:bra) What is the linear speed of a chilrrnx 2+1: rskv;3hxwbd 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 eg k9w5n.6. r9bo(qcya9ulnh orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of 9h;w5vjeic.mj;2q o79m 4nb8 jnevzh 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 rotate if a particle 7.0 cbzo3rs d,4*wu8qhpc kz;;v x:m from the axis of rotation is to experience an acceleratidpu*8qz v:os,k4rhcb 3z; ;wx on of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates unk 5g8 +l:m9kh g*fuuxm(8tjih iformly about its center from 130 rpm to 280 rpm in 4.0 s.t8m*jui 8 (5khkh:+m uflxg 9g 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 v 4f3wv g78z wcb4l0lj$R_1$ 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 M 30ch+bul;gp*gez wk ,oon, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly.wz g3 u;0c*lkb+h egp, 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 unif;gjw y 2 v hlx4+idkk6-e o0wkld.m07oormly from rest to 15,000 rpm in 220 s. Through how many revolutions djo v-d;7wloe g0 ydl+ w4m0.6x2kkhikid it turn in this time?    $rev$

  An automobile engine slows down from 4jeks *6j8u.ip500 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 stresses of flying highspeed jets in a whitiy95xl+c .p arling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachin.lyt95a+ xpi cg 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 24jzjp u64g:us,0 rpm to 360 rpm in 6.5 s. How far wz,su ugj4:6 jpill a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rj/fau .ytmwl( m2b*. rev/min It turns 1500 revolutions before. fm 2tu.(ymw*ajblr / 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 reduceb ) 3urpg-go2) zr:ntss its speed uniformly from 95km/h to 45k u-tzpg2r 3no:rbs)g)m/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions aljw7*lc b .5 b1utmg*:estkc: s the car reduces its speed uniformly from 95km/h to 45kb:5lb*cwu*j et:cmtgk s.l7 1m/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 pu7uqj7i k dru yixj :mv(n 0(.9:9xdcdmts all her weight on each pedal when climbing a hill. The pedals rotate in7 ud u m9 :d:qjd7ci((n. rjiyxv09kmx 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 mngi7n8 ih2kb+2x)eddoor 74 cm wide. What is the magnitude of the torque imndig+2 n )iebhk782 xf the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle k,ye z*;yh ov1of the wheel shown in Fig. 8–39. Assume that a frickzv*yo1eyh; , tion torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attau )dedy)2u,96yuq iem j,lx yd s1w(x9ched to the ends of a massless rod which pivots as shown in Fig. lmy9s dqe2xe1i6udyd( x,u9,)yujw) 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head vh4eqe15 k yn;i:bs 4bjg b 23gl;2rofof an engine require tightening to a torque of 38 g n;yh2 b34; svkfg 42:bjo5rb1elqie$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg spheo8c1/zyky a b-re of radius 0.648 m when the axis of rotation is throu /y bo-k18acyzgh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in dd41t f g4a9yeziameter. The rim and tire have a combined mass of 1e41yzt9df4g a .25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the mgfbk14x 4sz)fc)q 6pdzkt5bs b n99 ,end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calczc5g fn 6q4zs bpd)f4 bkt99m),b1kxs ulate
(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 constant angular speerlbyo3 n)tr ( 0r6me9od (Fig. 8–42). The friction force between her hands and the clay is 1 6lro 9r0ybe)nr omt(3.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point- ;clc; olqlg cs1 7(:j1s5korx1hmzz objects shown in Fig. 8–43s 1ghs;c(j;5 lz:kxclm7oo1rl- cq1z 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 atuicv:+6k(c gsh +(t kroms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at 41dczip76 * *(/0ov y,ha2mvaww c fdygro+cm the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite imo0/ a wyi+w(61o4y rpc* dh7v2 cadc*,mgfvzs 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 mxr0wri) , agu3ass of 0. i)ar,30rx gwu580 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, ax/ 4k6uk fy.dduuty.*ccelerating 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;sc2gd:xag/ gp+cg5u 93x:cww 9in ot hand-driven merry-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 the acceleration, neglecting frictional torque.pgwucg5g9xicx: nac9w go; +/s2td: 3 $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,x8+mx9 hkzo9n300 rpm is shut off and is eventually brought uniformly to rest by a frictional tnoh9+xmx 8z9korque 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*,5nqqk cfvh ,.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 theivl,wz1u*p jo 5,s. ne forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is auv ow5isz,, l 1*pne.jccelerated 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 cu(gzn57 ocn1m vfsc1/onsidered a long thin rod, as shown in Fig. 8–46.nvg5mc sco/n( u 7f1z1
(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 ofv ,iv k:/d2b9jj8s ccg 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 n aci.8c6:txmhammer from rest within four full turns (revolutions) and releases it at a speed of 28 inx :tac6 m8.c$m/s$ 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 hasc 1 tzhuz3iqv)6if9s. 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 torque of - oyhsn q j4x0d2dz/1dbd-hc:sa;bp.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 y0.7odqvjf-0fur/9gsnh7 g i kg and radius 9.0 cm rolls without slipping down a lane at 3.3u on00sy. di v7gg9fhrq/7 jf- $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum o ylf5gyr+c4 q3qhlt p-/1q/5 t5tsbku jjv-4kf tbqvlf/4+q kpc -g5l3 5jrh-kyyt1tj 5q/4ustwo 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 and a radius of 7.50 m. How v0 zi k/pzzb84:ivai4r7n9u l much net work is required to accelerate izvkzz a8ui4r:p9i lb7 v/0 n4it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1x aa2x-/prebi:n+ k1r ;z ip3e.80 kg starts from rest and rolls without slippingza rp; 2xeb+3pnr e-ix /k:a1i down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vert3bh5apbg5pxcj2 . y:c ically on its tip. It starts to fall and its low 53agb. j:pxcp2h y5bcer 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.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating 4*p w lgt4r(/k cku9z4i sqc:oon the end of a thin string in a circle of radius 1.10 mqg/4i:c 4*ksk rp9ucw( 4zotl at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg x;xv7iq 0 ba +1bu9qkruniform cylindrical grinding wheel of radius 18 cm when rotating ai;vk+0ux7b bx9qra1q t 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, handfi1eh +kp8l,ss 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, Fig. 8–48, the speed of rotation decreih p s,k1l8+feases 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 redk rcw4y2.n;am uce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuckc r.k;nwm24 ya position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase hfg 3et po))d r8cgy;9ser spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a finag d8f)39yo tsrgp ;)cel 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 aroundf:9(zir / q-akpwt qb v3w z;bfdf+)x7 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 mi+(9/xbw f7 zfr kvwqf)zatqd-pb3 :;. 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 momen/fls:i/ nxgesgf -c7: tum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angularl mkpf7c50 db6 momentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of iner4 .whq6hb6e6g(p cu iqtia I is dropped onto an identical disk rotatin 6u(cq6h . q46gwihbpeg at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atl1 tip5z)9sg 2zkthp vw esu 2yn,l6(yly4r(7 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 centegn(msuy10 sx:r of a rotating merry-go-round platform of radius xy g(:n1sus0m 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an anguli,j4f*fyf :onlm f71xh23rh 4p p jkh4ar velocity of 0.8 4 plmk44,r3*jfxoh2n fh j:h7p 1ffiy $rad/s$ 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 iq akw3)yh5ksu,pqsq4(4h3bbw m q.0snto a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assumingyk 4w.q3 wq4(buap3m) s0s5,q sqhbk h 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*ik3(xjkch4e4(tla86 wwi m r 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 +/ 659b;fl fzqg/smhtj3ivlu $ 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 frm;w 3sr:jv23 a x3iqxfeely without friction. The moment of inertia of the perqfjm3:rxxv i2 3 3sw;ason 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 6.5njd)acz /p o vv;8b;(v-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of ivca n)zo (vvb/ 8j;pd;nertia 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 bo0a5ejdc3wgu p80+e 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 re 0wo ud+5c0ajgpe83 bolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that u((jgn ys33h kthe same side always faces the Earth. Determine the ratio of the Moon’s spin angular 3ys j(k(nu 3hgmomentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

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

  A 1.4-kg grindstone in the shape of a uniform cylinder of ra27.c/d x2;vh/h n2rqdnd ke mgpos5h:q *l0 hidius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval a2/; dsex.0n2kqg nhh25 vq7hordi*mcl h:/dpt constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks w;boule. u(8u, 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 ol(uueu ;wob8.f energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angularyp*fd 1oi+8 rq speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times l;xvt4 vnimou5w9zy71p 0gx4f0 nkh* hl2km/ 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, lo4w70fylzm;t /x 0kkui v4pho1nvgn 5l29 m*hxsing 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-pollution automobile is for it to use energy stored inb-e;fcqx j58q 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 travel 350 km without needing a flywheel “scq8j-feq5b; x pinup.”
(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 illustrate686ui5fn c gazs 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 on a horizontal sur) qtt(3.uzmim/wg , cxface 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 l r-:zicg+ ,ck k(f5opgength 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 gr:g c+(fk5gor pz,cki-avity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. Itfrkb 4wl)j*)gb+ z,no is standing vertically on the floor, and we want to exert a horizontal f b f)j4groz kw)l,b+n*orce 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 onac9r(-rrcv * /ijvl +s -xgbnn;d:;lr a flat road is making a turn with a radius The forces acting on the cyclist rdv-sjbla rc-(;x9 ing r/c + :*rln;vand 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 o9 s+up)vrjcu0f length 1.5 m and begins whirling the rock in a nearly 0) jcuu s+9vprhorizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arm-oo(rh3,uiy)7mn0opqsz* m59o eus r s as thin rods, making reasonable estimates for the dimensions. Then calculatezsmo3uquim9(sr5rn, h7-oyoe0 o )*p the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consipshst+u)vzo t*, mh2jby /onrzr 2..7sts of two cylindrical plates, ofojr /7ro+mp.2zh*hv)snu .bz s2t, t y 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 rd5ss ipe)6n) radius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of thpr65 d)sin)se e loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but k (c01 h h2uz1.7dfklu,zpnhedo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as t0jt2d3 qa,2kg*bmko the car reduces its speed uniformly from 90km/h to 60km/h Th0j b*mag23oq2tkt ,dk e 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