A bicycle odometer (which measurer h 1)5xu+aziesbq+*as distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use iuh)a+ rz 1*+5 ixasbqet on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Dj(0o/, l*)yccfq4,8ti5t zyirk o ylroes a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocittlkj,4)z 0(,oyliry 5 y8rcq ocf*/ity 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 a single value of the angular veloxr2crsw/:6wqlw7ry 1 city $\omega$ Explain.

Can a small force ever exert a greater torque than a largerkjhovq8jhq/18/wz4w zk m*9i 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 s8ug. d3lip9vdo a sit-up with your hands behind your head than when your arms are stretched out in front of you? A du 3vg 8.pi9ldsiagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three c kiw*k 262ew:o bry5jat the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a w6 b:2eyo2 5r*cikw kjsmall front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run w-0ds3n) khurvn)p h4 fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageoku)30 n w)hhv rs-4pndus.

Why do tightrope wal7j-2u:tpwf( l7 xvh-632 ickue kmg fr( py.oukers (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque alsspn q3rvllu3x /61+u.cas x 7do zero? If the net to3 su .6urdcqa3/1x7ln xlsvp+ rque on a system is zero, is the net force zero?

Two inclines have the same height but make dcibswpa.*f 6q0d9scv (z+gdn( f w/z(ifferent angles with the horizontal. The same steel ball is rolled down each incline. On which i(w0 p(*dz6(fsgcz+ ad./wsq nfc ib9v ncline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. One o(0u z2vh--ebz exe2csphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greaterc0 b2u(ve -z-ehoxze2 speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder ha pv,,rpuusq( 3ve 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 spev,(pusp,u3r q ed 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.fj c 1gpkxo*ul+yfo t*;pr 5; are conserved. Yet most moving or rotating objects eventually slow d+g xf1of c.l 5;uo*pk*;tpyjrown and stop. Explain.

If there were a great migration of people toward the Earth’s equa6ni 5(c0eg7c ;c 4yfvng0valztor, how would this v lvgfc57ciney;6 0g(n0cza4 affect the length of the day?

Can the diver of Fig. mz mzil;;f l/38–29 do a somersault without having any initial rotation when she le m3;/zfll mzi;aves the board?

The moment of inertia of a rotating solid 3br j0flf0urg t;o;2pdisk about an axis through its center of mass; 0ubf rp23to fljr;0g 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 mbm9ud6 ni,hflg -3awh - w/c/unav9 ew+9)afyass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increasnevaw +l,w69 u) chdw-9ybfi /g- fnh/3aamu9e, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow ane+3cudtl9 w)a aj; of.d the other is solid. Describe an experiment to determin+olcdj 9wu )fa; et.3ae which is which.

The angular velocity of a wheel ro;d(ra a6e *uyxtating 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 u6 ;e yr(ax*dapoints 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 largek po*bl43. bib) sc1ij freely rotating turntable. What happens if you walk p o3.bbb jc*4 lsk)ii1toward the center?

A shortstop may leap into the air to catcvh(5dbpw ,9rs h 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 diredb, v(9hs w5prction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum,f4t yrdqr *ygj9w;g*g6vn(l9ng aw,2:0 cppi discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter 0 g9,**;t g6nap4 qnpdy9y jw(ggifwrlv cr2: stable.

  Express the following angles in radianh /irmfq n.p71s: (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 Ear 8yvhoy,nbcv4 ma+6c 1th because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diamete,vy hb+cm8 4 6oanyv1crs (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moolimiz9 vd70o s-n u0+bn, 380,000 km from Earth. The beam diverges at o zls-v +d7m 0i9nb0uian angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate s.8q ksru-eyvw3 i3g-of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s3-v8- wrgsueyiqk .3s. 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. Iyju+ ip* w7ix.u -m9spf the ball makes 15.0 revolutions, what is its diameterwu*s i p+xyjp- .7i9mu?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutionbw,v0 b6)v flj,xfnk 0s do the wheels makvf0,bx wlf)bn60, vkje?    $rev$

  (a) A grinding wheel 0.35 m in ygou5u i ajsvz 9pm++19litgvae420.diameter rotates at 2500 rpm. Calculate its angular velo v j laui9m 5vp 2t+og4+9iesaygz.u10city 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).o+uc rv 8v oyxw zz3x( y(3:iirg;1(sf (a) What is the linear speed xzy( szc3vifry (r8;u govo(iw3:+1x 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 veloc;(rv8c t gzn6lpq-g w4ity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spe2lnn56l9bs s med of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0nndzyzg t 12*)fs*g/)nr swn. cm from the axis of rotation is to experience an acceleration of 100,000g*nzs)y/f2)1n. * ng nts wrzd $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 2vtbqvx0g( g:)k g.i )ft g13qg80 rpm in 4.0 s. Dete)gtq(b)vg:q t . igxvg3fg01krmine
(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 c vr1(:t10uerw( klwu, .oziz $R_1$ 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 thpz4x jgdv-oz xu(*i:b7v+ yi)e 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)ob+-:*ui pj4vxvzx i (gz 7dy.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 accelerat;v, z5-f jbt5sgxy5zs hz5.g fes uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in thsx zv gz.-5, stzjy;555fhg bfis time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 8p7 b6e3gf 7,e plb**jz axas3,yrucu .(wjma2.5 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 f* dle9i1 +vzcm y7do*yor the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1yv* yle7*izcd+1 9mod.0 min to turn through 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 diametervoon8)w.h6,m+ghe;:fy3hgy r /fqaj accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge g6+8wg; :vqyynhae)r fh3o.jh/f, omof the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runn6fu3b e bmc-k ,c2vwh:ing at 850rev/min It turns 1500 revolutions before it cov,:6 2cfmhb-u3bke cwmes 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 revolutioc.z2tcqos )sb jj0 n-fu)q,l /ns as the car reduces its speed uniformly fromso2)q0 jfbu n)lqz /c- j.cst, 95km/h to 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 rev r/x6cn)lael)+l w,wcv flx;*olutions as the car reduces its speed uniformly from 9 n /xlx;alc)fl) *vce6,l w+wr5km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbing np.a.0za /ur3s c l/d,k f *t)be+qpuqa hill. The pedals rotate in a circle of radi+ busza 3 0qpdl nt/frq.), a.ek/*cpuus 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 no4r r;b;bzh/door 74 cm wide. What is the magnitude ofb4z;;bh /or nr 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 the axle of the wheel shown in Fig. 8–338iwc*uadtg2 2c qota*-oyf /9. Assume that f/g*8tw3ou ca aqito2-d cy2*a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the endbci5 6 kqw.;ats of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position;w.a t6iqk cb5 and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torqu a (+rzb;1tcph9rhd *ae of 38ah rh*9p+tad ; z(cbr1 $m \cdot N$ 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 i v4nhv9ect; /cnertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its center. ch /4vctv9n;e    $kg \cdot m^2$

  Calculate the moment 6: .pzg)uqf,78jhzwnlsdf +n of inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of nw, )d:h z8ls 7nz+jpqgf.6uf1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end oe+vp1:gwsv x 6(g-l myf a thin, light rod is rotated in a horizontal circle of radius 1.2 m. g+ g(mw1vp-v 6x yl:esCalculate
(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 sp5lwt bgk+2sdn5*xab. hj(z7heed (Fig. 8–42). The friction force betweba2 t b5k sxg*hd.7 +5ljwn(hzen 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 array of point objects shown igak1;q:t lpj fj1) t7in Fig. 8–43 ag)tj 1q 1ja;l:t7ikpf bout
(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 l;cjh5:svu d 3whose 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 the correct rate, engzkl4qy(k yy v.p/) 1qtineers fire /4.)kq1qz kpy ytv (ylfour 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 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 radius5jc4:s tqeg,-e ove(u of 8.50 cm and a mass of 0. sq :vg-eoe,4 tejcu(5580 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, accelerating it uv9fogn2;h,0 cvt 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 taz0x9apmi4.2 y 4ba lp( p6opiengentially on 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 of radius 2.5 m and has a mass of 760 kg, and two chili9paa ip4y m0 4(6xbp.ol2epzdren (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 and46vse,jo zx+er6i3c u is eventually brought uniferzvejs6 x,i3o4 6 +cuormly 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 accelerates a 3.6-kgcd b b+.)1s-y6qq-qt oofrh+v 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 ,4k4vixe) hj-ty c5myby the action of the forearm, which rotates about the elbow joint under th5 ,mhxyvytc4 e-k4)ije 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 (-ix i .gc)dkabe considered a long thin rod, as shown in Fig. 8–4a(.i)gd-icxk 6.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine ;m2gw fx2euuy*. ayt5 consists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates.sjhth5nrk; + the hammer from rest within four full turns (revolutions) a5 thsh;rkjn +.nd 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 ofgqk0lu7h )i)oh;k6 ld zer9m 2 $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine y 7i g0(+a ;te1gtuxbidevelops 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 slipping dow*nb0 ze;jct *fn a lac jzf* ;en*0tbne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with bt jr.fs0l5 gnn33yx2 respect to the Sun as the sum of two termf sr 0ltxny.jb2ng3 53s,
(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 edb 1ednx+1 zb.pu-3jmtv:i/i +rx z)much net work is required to accelerate it from rest to a rotation ratd bzejb:dxi1teim-+rpzv1/u3) n.+ x e of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm anszn,z 20ofya3c 8 cz(zd mass 1.80 kg starts from rest and rolls without slipping8c3o0c,2 zaz( syz zfn 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 vertically on its tip. It start8ptqclz),2 p ms to fall and its lower end does not slip. What will be the speed of the upper end of the pole p),l2zm 8qc ptjust before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the ennky,1x8o.*tiiw 3:pfvbixan (:x 1u zd of a thin string in a circle of radius 1.10 m at an angulann.ypwa :k utix8zibxf3:v ,(1x1 io*r speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinb vujd z,8kphvf r(7yc-s;44d ding wheel of radiu( 8yb4-cuh;sd kz 7,vvrf4p jds 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platm5c* u8 wgz*jtform 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 rotatio*uwt g5z mcj8*n 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 moment of inertia bzwprm k4 cn/k///oex: 3/ snuoy 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 tuck position, whazk c / 3os nukenowr//x4:mp//t is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial 38i 2yce/fpqr rate of 1.0 rev every f8c 3iye2qr /p2.0 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 rotatingbc/1fjblgl.qz +*gv 9 around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be consijb l1g9/g *clqzf.+b vdered 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 o)1fu)2 ai nj0 v,wmfvskater 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 momr)5 h3wmlxzf zs f 6)6gc+gpc1entum 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 inerti /w.fhn:us8yi 8gv j;la I is dropped onto an identical disk rotating at angular speedj i/ny :;gsvuhf w8l8. $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns sj o7+lm8jx:eqf c0q( at 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 standszrtf 2xg 2 l/*af;7uv.uh,sy x at the center of a rotating merry-go-round platform of radius 3.0 m and moment of iner.ltf yufvu x7z,rx / 2g*has;2tia 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 wk 0oqv/9 (q am0 mnkrh::-5lbwl/oxcjith an angular velocity of 0.8 borxcm-o5h:am0 09 /n/ lq(vkj:l kqw$rad/s$ 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 collapywos)c d d463pses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would)d34odscy w6 p 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:pj (7piny f-e winds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass 5q 7o +t:b2liib +parh$ 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 platv9./rup l8r uda0jb8q form, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platfp80qa. r /bl rjv98uduorm 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 meyxe(y dp*0f xqx*h ur*.m gs*+rry-go-round turntable* hp*g (eysu +xf 0q*x.r*xmdy that is mounted 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 pb z4y+xj f)i6 ut4u8pground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls bexz6 i )tbyuu4pj p4f+8hind 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 Ea 2*oyph/ g:iibrth such that the same side always faces the Earth. Determine the ratio oy*:p goi i/2bhf 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 orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from 7kjm.9zrzks5 rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cxo8j-lh-s wcy zh.a.: ylinder of radius 0.20 m acquires a rota.oh -y.hja lw-cs8:z xtional 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 solid cylindrical disks, each of mass 0nm1tcqh 8 j;)b.050 kg and diameter 0.075 m, joined by a (concentric) thin so1)c 8j;qbnhtm lid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the f 54re6ubio,l 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 as great 1jviz6ho 2s8q, 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 zqjh6vsi821oin 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 u)gosxxs(e, fjo gg 40li v5ep+t)b 2.ase 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 should be able to travel 350 km without needing a flywheel “spinup.gle + jgx ss(40)a5)p,bxitoegf.2vo”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an ppp.9wkc0g2cr3df n($H_2O$ 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 hori25dxewq g kmnhl:-j02 zontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot free*+r0 kwx*d mtds2 mlq2ly (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) thet* 2wxr d0m+*k2s dlmq 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 ra1r*suy*m kjdm9k1h kgosm3 nak i .-(;dius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has *m9ng-o id km*s13uh (m.r ;y1ksajkkheight h, where h

  A bicyclist traveling with speed ke+x :6q 1uhrfmgjpbe1b3 /1p v=4.2m/s on a flat road is making a turn with a r /r 3ppfxbmb1euq:k 16g hj1e+adius The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length :75qx+p3su) crw ilpm 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate r qpm3x 5cu+wi )l:p7sof 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as t*b ep:z m;c+tphin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular sp;ez:cpt+bm* peeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of tw9i9w q3 spo.igl7v h*co cylindrical plates, of masc*.v9piqoh9s g7 wil3s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 track4k *4g u7/lo+4ucsbth8ke)1cgdmzpl 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 the loop without leaving the track? Assume dpscm)l 478ucb*k4lk zh4g te+/g1ou$r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but v0ckhgiu/(9 sl0vhjrdm g+9 .do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the carn;ul u2wz+ 0if reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angulni+f uw;20zular 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