A bicycle odometer (which measures distance traveled) is attao1xcciu2p v; ;ched near the wheel hub and is designed for 27 oxp2 v1;ic;cu-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular vo(tu c 8u *4d)vbs1pf (o.fvicelocity. Does a point on the rim have radial and/or tangential acceleratiovico * )fov.cdp(t8f4u b1(sun? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by agf r 7 *y/1f4rq r)c-cjg.bdrs single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forc4py f-i:8ooey e? 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 sitvl:aut: 3ka19hr5 nia-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may he k31:5triu9halavna:lp you to answer this.

A 21-speed bicycle has seven sprot7q*0b.fgl ;2/f 7*bsmhdd2zf pd bleckets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a largeq*lhmg*f;s2bpt 7db2 f70de/fbld z. 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 r7mjb acgn/t)51 *v frfast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamicc 5m)rf 7 *jg/atbnvr1s, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) v1g*udx.e;w 2 b9w*sorvyz-nv9eth .carry a long, narrow beam?

If the net force on a system is zero, is the net torq5q46cashlerh /j mp),ue also zero? If the net torque on a system is zero,5hha 46erq)jls,/cm p is the net force zero?

Two inclines have the same height but make difo4j(op t bm2u:xir +j0ferent angles with the horizontal. The same steel ball is rolled down eajoi+ (t:ub4jo 02rmx pch incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rollhekq4dt6c0) n ing (from rest) down an incline. One sphere has twice the r keh)0qntd46c adius and twice the mass 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 radius and the samkz 1p wk5tl6w8e mass. They start from rest at the top of an in8wl65p 1tkz wkcline. Which reaches the bottom first? 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 angular momentum are conserved. Yet mosh w1 oqr4joa4,t moving or rotating objects eventual1wjora oh4,q4ly slow down and stop. Explain.

If there were a great migration of people toward the Earth’spa zii38fz* .d equator, how would this affect the length of the*d.zif3z 8pi a day?

Can the diver of Fig. 8–29 do a somersault without9jx3)o te 8j a58dawti having any initial rotation when shet) id85 ox jajawet389 leaves the board?

The moment of inertia of a rotating solid disk about an axis through i2jqbfn*nb j 37ts center of mas3q nb2jjbf7*ns 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 ao h7)4;xfack5kahk + q rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity ink7 5a c)h+hkk4 o;faxqcrease, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow and th ej*l7zy* 0yhhe other is solid. Describe an experim*e hlyz 7yh*j0ent to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle pointwxc5-h5 bva3w s west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, desc-b awwv5h53cxribe 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 large frei,krk, a bcdna 0i -s*ix8(jt2ely rotating turntable. What happens if yoc(jadk-,ntka0 ,i rx8bii2 *su walk toward the center?

A shortstop may leap into the air to catch)nbtl* g(h( i6vsam d- a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36)b-md) *inhltvg6(as( . Explain.

On the basis of the law of conservation of angular momentum, discuss why a he ejq0h *d7sug.licopter must have more than one rotor (or propeller). Discuss one or more ways the second dusqej*.gh 0 7propeller can operate to keep the helicopter stable.

  Express the following an.rj ; )yk)o)umiexl,fgles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidenc b*bek5hlz ge1*4th p-e. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Su45 elbb-hh e*g* pktz1n and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges/5 h be4ubbz iz2cwf,8 at an a,wb b4fe5uzb/h ci28zngle $\theta$ (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.v du , /afezq xx+xo3581ozv5g When the motor is turned off during operation, the blades slow to rest in 3.0 s.zzgq1 oxdax5oe xuv/+8fv35, What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. )kfigfc0k ,g)u4 ux 0gIf the ball makes 15.0 revolutions, what isf)gu,0cfig x4k)0kg u its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolunvs80 kp 5sbi +kk6mo) irf mr+r6ig;0tions do the i00 iofpisrg6knkbr8 mvs6+rkm +) ;5 wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter ro1p4 d ls- o-f ocfrj6yx-9dp;j6 qfhq,tates at 2500 rpm. Calculate its angular velocity, x sdp-pjd qf forf-q c1lyh94j-6o6; 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-ho;zvj :w7m wpbkii2)6r b 1k+round makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the line;bih2vijw+kwrp )kz6m 7b : o1ar 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 r oir.)d/ /t rjp8+saoszt;q7Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point 96s0*qeiopf n
(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 rooo5ypl a /1:k*1,+b2okftcfpgtnt ono *)or - tate if a particle 7.0 cm from the axis of rotation is to1n otobp,gy- /+1 2r)potcoof*l:a tk fk*5on experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel a( t +y3t bh;kpio 2ldp)5yt)pmccelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determti )lytbhp2 )( ;35d+k yompptine
(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 /s,z j68 9k2 iylnaasx$R_1$ 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 Mo wcue8,+;h dm 8sy 3ezpt ) wtiv)d2.s,pxudj1on, astronauts 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 a cylinder with a diameter 3mz;y8du )ej, s .cp+1sw wiedvu,p2hx tdt)8of 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 lx5oflc);+emmf 6t f,to 15,000 rpm in 220 s. Through how many revolutions did it turn ifof mtlx6 m )5l;+e,cfn this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcu6hl6yv 19ls /gtukvy3late
(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 thn mc:oy 9qa16ke stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn througyq16mcok n:a9h 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to cmypi nqidg)dtiu5,mb3vn(1tk(3 6l/50ea m 360 rpm in 6.5 s. How far wil bind (3 5mtmaqti)1d k u6mcgvi53/0ye,lnp(l 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 850rev/min It turns 1500 revo trdc.rf8 sivv,9: :3kxn 6lwplutions before it comes to a f3kx,d: .n 8wvir:c9pr6tvs lstop.
(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 speed5hlk 5l mi n sypu495tz;m+e;p uniformly from 95km/h tn5tkmue;5p 4z si 95hylp;m+lo 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unihen1cvfr u5 6,formly from 95km/h to 45km/h The tires have a diameter of 0.80 h6cv1enru,5f 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 weight1rkf z/lf)k w)4 or*xd on each pedal when climbing a hill. The pedals rotate in a circle of radius /4ork1dfk* z)xr w fl)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 2 hraown+j*1mm2-bivho k+o + a door 74 cm wide. What is the magnitude of the torja ov21n +hrm*b-oko+h2 mw+ique if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Frf 8-yfsl.4 4w9shzufig. 8–39. Assume that ash f4l9s.y -8ffurz w4 friction 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 ends of a massless rod whichi3tju ,o)-yskzlva :0 pivots as o) tulkzvj y,:3si0a-shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder hea xti/w zk ab/x9kmz.,6d of an engine require tightening to a torque of 38ki x 6/9wzxm,tbza/.k $m \cdot N$ 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 spherom7gdi ifo y;qgv/j /o tq**k623vl r:e of radius 0.648 m when the axi oq3i/ fg2r;my7vog/*vito:dj q*6 k ls of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm ipipr+vdjm -:9; xte3 zn diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be igno jpt rzd3i;:m -xve+9pred (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, l(bpqarkm u(2 )ight rod is rotated in a horizontal circle of raqa(m2u b )r(kpdius 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 rotatimdge4( 9c18 tke*n0gg h tfd*dng at constant angular speed (Fig. 8–42). The friction force between her hands and the cghe8c4ftd9dge1*dm(0tg kn* lay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of4nrfo:qbi yb auvmw;m6)0c5 2 point objects shown in Fig. 8–43 abomomc:;0bv4) 6 ib n5yr uwaq2fut
(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 go0 i5j1aitpv0j ya; )uc2e yo;+)mxvof two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinn qbt*pd(zhq :4ing at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the rz 4 (:tbhdqqp*equired steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius ofeaoq*(: -txi i 8.50 cm and a mass of 0.580 iet xiq(-:*aokg. 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, accelerating it from restrq8zlgjm 3:). - 6qot4:atf queulj6m 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 g5 3d;gq6njrxi (5e)ot zgl +xon a small 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 ogi 5zox+;gdrq6)x(5 3t gnljef 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 rotating1pfvjwd c3fai apwiej*6 q82(n 3wy,5 at 10,300 rpm is shut off and is eventually brought unifowfp63*i(iq5p 3cnevyw aa1,8j wdf2jrmly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accela7v gut h:1rxvk; 9*nberates 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 soletinpv95xj/w ksf; 7 6lly by the action of the forearm, which rotates about the elbowijls9kf tpwv/5 7nx6; 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 can1s+knq(c,-8ir2 uk wq fta+ zm be considered a long thin rod, as shown in Fig. 8–46 +tu qc8wf1zk+m,(2kinra-qs.
(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 thveuii +./f6i 8h p0 bc.z8uykwo masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within fou; 1yx n p)zw2bw)tcu/b:fh-hc r full turns (revolutions)tb)w;cpz21n xh )wf:u b- h/cy and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia of q-vu-ilb+ /p k$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine c2rs+*e p;h rjdevelops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without sl*a0af o.u np-hipping down a lane at 30.f*pau hna- o.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic l1qnk c+qs (1ldvx,:k0hewnb3/f x3t yabf-6 energy of the Earth with respect to the Sun as the sum of two terl qxdb,n: f10+3skhqw( lfn3v-cb1ktax / 6 eyms,
(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 masrq/0r wk75b an:hs4gfs of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it frq0:/bha 74r swkg5fn rom 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 1xyeni71 q., auiyp (owv-.ad 5.80 kg starts from rest and rolls without slipping do.7onap5iue ( dxw ayyvi ,1.q-wn 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 vertic-doko/a mk-g ) pb6g/65oxvvqally on its tip. It starts to fall and its lower end do5dv-gmq/ 6o o)bk/aovpxk-g6es 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-mzcfrr3d*z3 uhmelh+6c1 ni0 c,;6(wle)b axkg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 10.x u ie6cbmrwn1m,)c6zc0a3r(z*e l;f+l hh3d4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grindingtwa)m cu1z f2o8nctthp.01 t: wheel of radius 18 cm when rotating at 1500z1owmt08 tap c)c1:2.hutt nf rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotatm6p+6 rwgrjk, ing at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rota6 rm,pgjr6+kwtion 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 Fy yl/d/ l1qiu vd1jpo iyo b66fau2+y:. yfk3;ig. 8–29) can reduce her moment of inertia by a facto+y;b: dpyu3 yi/1i 2fla1ul/d.fyjko6oy v q6r 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 tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase kxcm h0*ob26oaj2 h3d her spin rotation rate from an initial rate of 1.0 rev 6ocj oxkb3h*022hmdaevery 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 around a vertical axis through xt2(69 aw8:hmrv q2ezyji wx,w4g5c yor j.m1its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of massryxjq4wxw2w h: i jt8,(ov9 m652g m.rzayc1e 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 ska 2dq,bfhgmb2h *zg6a ,ter 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 of2xa9e/5d 0mri .rrvc s 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 cylindy (nzd0 pae/px5itg+ 3rical disk of moment of inertia I is dropped onto an identical disk rotating at angular ypdxnz+te0aig ( 5p 3/speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a-f,)in:5 jv knkdtsvk 4/ l0i g.9tdzmt 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 :k 5ne8w,jyw4i(h zwmstands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of4kw, ehizwyj:w8 5mn ( 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 zer/jl o-xb )+aanxi+pq1m(5 an angular velocity of 0io x/p ( anjq)l1+5r-xmzea+ b.8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about half it;.she eq- a(dfrw/tf*s mass in the process, and winding up wi f-aqdfsr/th *w(e;. eth a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 1y n2f 8qjxk)f 1*s)rdb5f s4my20 $km/h$ 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 z:x bg69qx0 zi$ 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 platfon8 jrv6-s8shb3 wddx; rm, initially at rest, that can rotate freely without friction. The moment of inertia of the person pl83 ns6 wrjb8 ;xdh-vdsus 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 standtyuddoke +-5.rn,rh9s at the edge of a 6.5-m diameter merry-go-round turntable that is mounte ,r.h5o ytrn9 e+ddu-kd on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying on eyjay cb6tq p-7l,x)-the top edge of the spool. A person grabs the end of the ropey,al7y 6 -bxcjq- pt)e 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 move?

  The Moon orbits the Earth such that the same side alwayse u,n9.v u1mhx faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbitinmhu nxuv 9.e1,g the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of:quir84g 07mukkl ej,s ark9) 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 cylic./,rwm9/ kl*qjq sxry :ki m4nder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor/:x,mrmk yr. 9wki c/q q4ls*j.    $m \cdot N$

  (a) A yo-yo is made of two sol0.l9e i3lj5 rf hpi/zmid 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 d lij/i0r5z .3hp9eflmiameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, ho u(ardkyt7kwa 5:z:, lw is the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0a/i/ha6t exh9 times as great, were rotating at a 96ehta xia// hspeed 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 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 storedu9h 1x8srx4yb 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 b1xx h8us4y r9mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustraox am-(a7dc5dr t4j :mtes 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 surface at speed v aq6 (dmit,tcwp9 s/ o,-3oigw=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore fricti5 2k4zqd ;g-setf qeg;on) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and the ekzqq2ft;;4- deg5sg n 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 on the floor0iazarhof1jc h:/h .l7(3m n;samn4 gg8 -ahz , and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fiago7mj1nh 8( nm.fi4z- 3h:ga/0h sraazc;lh g. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn wyum wa60 t2jl//we:vgith a radius The forcewmyl e jt/w6v0u/2g:a s 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 m and beifq alqzh5qw-: fdf,)6; 4bhdgins whirling the rock in a nearly horizontal circle above his head, accel6 hqfwqf bqidlh:- z45,f;ad)erating 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 50-zdvako(ezpyxk 6 - as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spin6 -x- y(zde5kokzv0p aning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly whiaa9gy 7di* ov.ch consists of two cylindrical plates, of m*iao97v dg.ya ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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. 8–58v iergvpr07 hj).hr th 6(8(ry ua,l;t. What is the minimum value of the vertical height 07r6)avuy hh r (ltghj p(rt;er8,iv .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 ascna3)ugo m 1t/5h-bsqsume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces )(j(u2vxl,t 8:ictodhzp;cp its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceler8jc c, h(lpov;):p itzu(t2xdation 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