A bicycle odometer (which measures distance traveled) is attached nea+30jkojkwt p5g8ij- *g-ifk zr the wheel hub and is designed for 27-inch wheels. What happens g-0 fpokw *-zk+jijt gik8j35 if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotatejzjay*4 yk8 2 b/vwh6r.0xygvs at constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acch k80a4 wxj 6vz/yyry.gb2v*jeleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid bod.miuz+6 ynaqlbc4-/ )y qriy -y be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater a fck s6ktg q)i,.ip1)osp*b6torque 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 9/gxsz4n 2-gshuwe8ythan when your arms are stretched out in front of you? A diagram may help you to answer thi xgy24eshs-gzu/8n 9ws.

A 21-speed bicycle has seven sprockets at the rearm2,x l)tqxph w v8xn:d951c e9zf8rqz wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? n9zhqw d5 f ,28lmx xvc:t)x89qe1 rzpWhy?

Mammals that depend on being able to run fast have slender lowez0*3g86nhqkx wla0vkiw,3 k :y t4m srr legs with flesh and muscle concentrated high, close to the body (Fig. 8–3t3k:0x4i*m 6n8zwy lwrva03sg,kk q h4). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) car c7euvup3ke e8u;x2pg+* /ch vry a long, narrow beam?

If the net force on a system is zero, is x /ez)r cp6d*)eg mvko/1sf mwri8+g1the net torque also zero? If the net torque on a system is zero, is tk+im8fr1*ep6er/z mswx)c/1 gdo g)vhe net force zero?

Two inclines have the same height but make diffkhip/o j* g,-oo b8gg/erent angles with the horizontal. The same steel ball is gj 8hoo/*o-pbi,gk /g rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling :+tt u( -98 fcbyddjqf(from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bftc9y- ddj+ qb:t( fu8ottom 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 same mass. Thtdzyhc i dmhs8 (bda4i,8d03* ey start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has t(da4d0t h 8dy sizdh 38ibc,*mhe greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most movin vjn9 h3h9 p k0v:e++epdvko3ug or rotating objects eventually slow down and stop. Explak0 eev339 pknhvv h++p9udo :jin.

If there were a great migration of people toward the ,w,v4cwu tdt5 Earth’s equator, how would vc,, d 54ttwuwthis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault wicb a w+ e6czi4t/uzso 00v+w k90l/ihpthout having any initial rotation when she leaves t0b+/s/iou+ht wca096kzzpw4 e vl i 0che board?

The moment of inertia of a rotating solid85lr5 kiofxae q lznvm 5:-1ti; n+r2s disk about an axis through its center of mqf xn ik;+2lz 51nlsm5t:r5i8ar- ov eass 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 ukv,/ (e. t8kicr0zj1 7slnkx rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increajcv0lk1 txunz.8/rk7 s (k,ei se, decrease, or stay the same? Explain.

Two spheres look identical 7o ;ebmgb* rrqxrv5u lx *9:2aand have the same mass. However, one is hollow and the otheralrb*e x b52q ;m:ro7xr*gu 9v is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotag -n;xjvx1 z1yting on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this- zn;11xgyxvj point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the ego59 s: pke; dewgrcy 0u8d5l-dge of a large freely rotating turntable. What happens if you walk toward;5u-sgoe:cw k0 5de lg89r pdy the center?

A shortstop may leap into the air to catch a ball and throw it quickm 5icw9j8p cpv2st:a1ly. As he throws the ball, the upper part pcm5s9c v8p2jwt1 ia:of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular;u r,3cylqxe16hcfe-;- gglj momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one -g c;ufh 6-1 y jxre;qg,c3lleor more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: krh-w.xapkz pxsh t)5va92-8( ,z law(a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate6: yamue3yn4hd t *+vc, using the informaty*n +atu h4m:vdecy63ion inside the Front Cover, 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, 380, 3i;ax6sa r bwuco43me; 69. l5bkwghu000 km from Earth. The beam diverges at6m e uu.x4bg;ah;5cr3aiolb 3s9k w6w an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 650* t+i d,/-bkw*yn ooyz0 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What isbn *kt od,/*iowzy+- y the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to aa r,c ,*)rj gnm:bp,vmnother child. If the ball makes 15.0 revolut:b,)rj,,cgrn*p ma m vions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revobvsdiq,3 e8p6,sdddt 1 g2 6solutions do the whes opbssq6 6 t1dd ,gd83v2i,deels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotate q mgvsfk +q*d1az9/w3s at 2500 rpm. Calculate its angular velocitya mvk*q1/9 +wzfgsd3q 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 t1: t15e6dbnnutil br)*nm3c complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 *1l1 tdub:b3erni 6t 5)tmcn nm 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 o4evxc9o53ik c f 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 spee 5t4kkbb7t)e oxsa,3 td 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 7.0 cm from th ma:uf 0jhfg3c2-qrh2 e axis of rotation is to experience an acceleration o0um -f rh3cg2h:2fqajf 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center epy9 eq7otu +jljsh;(wdo77m(l:+ue from 130 rpm to 280 rpmu9 eelsh+ j7e77md;wq+yutojlp o( :( in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius g4j*7l+8p )fm atq doy$R_1$ 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 a/w 1cc nsvrtm+;zhxn 39 7mk,tboard the Apollo spacecraft put themselves into a slow rotation to distribute c+r tt/n;xm3z n7h 9w,1vkmscthe Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm (7vpan qecjt,s ):, 5s+tpvzxin 220 s. Through how mazs+ v5t,cspxjqap(e vtn7), :ny revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rf4h,dugm l s2j1s e*r+pm 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 af9 k nnwk-3e k66pq(pk whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions beforek(6p-k3pwfkknen 9 q 6 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 uniformlyyr(olk6 hb)l+ from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the lr+)olkyb(h 6 wheel have traveled in this time?    m

  A cooling fan is turned off when it is runnin9ld8x.a bqzb w-ott+: g at 850rev/min It turns 1500 revolutions beflt:w +xt.-q9abzd ob8ore 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 a73/(uqvc-rwhy b btg9s the car reduces its speed uniformly from 95kcbb(vyh u79qgw - r/3tm/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 revolutions as the car reduces i)n)g ofil- px kti ek8s;+,bz)ts speed uniformly from 95km/h tos kb;nkzipgx i-l))o+e 8t,f) 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 hefb;zf15 ;n2qchctv -a9 u 8zzir weight on each pedal when climbing a hill. The pedals rotate inuc95zncqzz f8;b;fh1-av2it a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide.wojle2ivk5yi5( b36 f What is the magnitude of the torque if thel ii(3jyfke56o v52bw 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. 8–39. Assg60g5r ex(d2 tqmo.b1yij1rj ume that a friction torque oe1ji1 d5tx026 groq y rmg(j.bf 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attach)dcx,p 61c m0 xf6muared to the ends of a massless rod which pivots as shown in Fig. 8–40. Initialld60ccx xumr f,a61p)my 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 of an engine require tightening to a t* :ifq/ vz dbi3l-f-lyorque of 38zl - d:qiy-bl /*fiv3f $m \cdot N$ 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 momentbx5tw45bc; s9awvp5v of inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotati;vs 5p bac4t x55w9vbwon is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bic 8qjbinaobs;7ce5g ff06q y48ycle wheel 66.7 cm in diameter. The rim and tir5o qfb07jb8ns8 a gie4y6;cfq e have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on tkldb cmas( xjk;kua+ d;o-2;9he end of a thin, light rod is rotated in a horizontal circl;x9ds ck2+dua;-mk ;(ba jk loe of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at copd,;ip im6r 57ouv9ornstant angular speed (Fig. 8–42). The friction force between her hands and the6ri9up o7p, ro5v;d mi 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 arcfs7gc. h,ay 70m,epv 03q s08of woavray of point objects shown in Fig. 8–43 v , 8qf 0o 3fo0s g.,se7av0chpmy7cwaabout
(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 consistw(lv3b6 9 v (lasx5n+swy.u jfs of 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 spinning at the correvtk0v)p d4( wcnkgpb: ofr6: /ct rate, engineers fkb/wr k( v0p:npodgt4c6:f) v ire 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 is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder whx: ym17y(k 5 xrgmhktlk+8c5t5q 2fqith a radius of 8.50 cm and a mass of 0.580 kg. Calctmk:1r2t8yh5kmlyk 5 5(qqfg cx +7hx ulate
(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, acbx/la;iz+x ; 9mvbu,bumu1u:celerating 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 smaa).:7uc66uxlypm qwn ll 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. m6wlaupx ny6)uq :.7c Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually bbmz41re , ibzs9 apl+(rought uniformly to re1pb 4zz+(i 9 r,balemsst 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)ou3* uxlt 9j5k/ o2y k1sq1jljgy a/e 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 isfz c;5p xxfn7- thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from -5cx;xfn7 z pfrest 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 bladsk6;j9rt+ej z 9du(mtnw9qj 5e can be considered a long thin rod, as shown in Fig. 8–46.t6s59 j jm9wu d(k te9;qjrnz+
(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 twa n0k-/a:zfdwcxq(2 wo 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 accevdu v *e(;1fphlerates the hammer from rest within four full turns (revolutions) and releases it at a speed of 28 dv*;uf1hpe( v $m/s$ 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 momenthz z2fs+a,ow8 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 dbj6 ;jxkco+f+ un2c9de+a7k 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 x cy,r/4u;/hkrer 4xtcm rolls without slipping down a lane4hue4k r x ,/rcxryt;/ at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Ear*n)ftft6;s5 f8a icwa th with respect to the Sun as the sum of two termsftact 8w*f ;ia)snf6 5,
(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 mas,z2c pg0/yfxf4qz:c4eb7xi u s of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 2c7:04 zbc fzfp/g e4xq,yuxi s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and roa: 8omzho5xe* atrp61lls without slipping down zah: amep*xo5r6t o81a 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 s/ rpl.uf: c)mmtarts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the groumfu .mpl/cr :)nd? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum o2is y) 7rxezv(f a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 meys v7iz)2 x(r at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical g :wl d* 42opu4g6n wn(vtg6uqqm 5yrq:uxt/6crinding wheel of radius 18 cm when qw lrm uto4q2qgd y46*:pnw(:/6cgtvxu5nu6rotating 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, han,j/ ezszxm.kwqo3 l28ds at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal , ezsmk.l8o j3w/zxq2position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce z awr3zmcgsmgk-*a 4f/u: -c t1f + ek6,cgv+xher moment of inertia by a factor of about 3.5 when changing from the straight position/sgec*wa +cuxkv4-,1am - ft+zgm3fk:crg z6 to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rat3g lu i ;4 5h7rgtcbc70wugk9ge of 1.0 rev every 2.0 s to a final347ggckh;tw7ucuil g g0 b r95 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 verticalfg2dtp9rqi o gg 3u*(1 a2qv6q axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter 3g2r *gg9v2pqq1 ( udqfi aot6then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3. ;gaj ox+cjf505 $rev/s$ 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 69ba 0n(kf5ulpfb b ;uof 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 cylind7dms 8yqwq2w z;r8qo5fe:wolo (xo 5;rical disk of moment of inertia I is dropped onto an identical disk rotatin2x ;: ooqf8qr w;5zw wl q5y7(moesd8og at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.km .t/f3p(2,vrbps srw mbs5.l-2 v gfhh jd5:4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating me;sd*;o(l;zvk2ot8h k qpfba: rry-go-round platform of radiutb f;z;:8op;la (khq2 k*o vsds 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 kjyts ab)/8y, with an angular velocity of 0.8 8yb/ ,)jst yka$rad/s$ 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, lomg/t((b:b dv8 *j alqesing about half its mas8/q(jd tlm(: gvbe b*as 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 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 1zea l5ec t1n ma(,m 572fv9npx20 $km/h$ 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 ozf if*fs; iy 3w.,k.i$ 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, initiuf+, nw 7ijitlok0r2;ally at rest, that can rotate freely without friction. The moment of inertia of the persli k +0uro;nwfj7t2i,on plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-roudgfa5:ef qkhknv (4u4s2htn -a.y ve : zw/6,ind turntable that is mounted on frictionleyu .a4w-ik,(vaf/z: ensqd2v5 n6h:t k gf4h ess 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 withbp 4ba5i8 /t kcox/6fp the end of the rope lying on the top edge of the spool. A persox8b/p64p5 ac/t okbifn grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always xiay:y n1/8o 6vni/o bfaces the Earth. Determine the ratio of ti n x8voy/:1iy6oa/ nbhe 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 rest at a rate hlj.(sd 6 tep)lj1q(oq-wzf7 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 i+ xyc4b zo9eqyp8 f5w ae67b;dn the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. yayfdq4 o 56bbxze78p +;wec9 Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of-t6lc,)oiz-: w ec5yalt:stl two solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reachtz)6lsi,o ew:c --cl 5t:laytes 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 th0ski) m qtmhny p2(x:9e 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:60 d6tn bkv2na)cstc mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all time0ts v:at c)db26cnn k6s, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low21k8t46k8p y mzi0 h; xwhduyd-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniformhum8dyhi zkpxd802 6 w 4;ykt1 cylindrical flywheel of diameter 1.50 m and mass 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 illustrates a ,t -ayhxozv*hru2q1in/7em1 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 horizontal surface at speed v=3.kx4nmm1s-b 7 h3 $m/s$ 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 1eis 5(r zluzcaggmjy s1 08z(a:q8c: 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, a c5cg re:(jm 8sz:81za z(uilqs1agy0nd (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 p,p ;paw,l+iz7d 4ila R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle s7w il,4l;+,i zdpap apo that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road 2dgmqntclu,h )0jy/:;aq b: m is making a turn with a radius The forces acting on th;j )ldnq2hmbu /y,m0c :tq:a ge 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 slikq mpt9 yn-k):;e. z)l-vvpmhng of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque requir-t)n 9k-lz pykpm )hv eqv;m:.ed to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s bod0gpf p;zjatl71 ;oeo8y as a solid cylinder and her arms as thin rods, making reasonable estimatf017;lgo eoz;ppt a8jes for the dimensions. Then calculate 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 consists of two cm 5 eszjii1j:,ylindrical plates, of mass ,sm i5jj1 ei:z$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alonrlbq*;5-aa. q c k h*fuet+a6.lpxe9ag the looped rough track of Fig. 8–58. What is the minimum value of the verticae. *u+ebx.q;qarlhafapck 6l9 - 5 *tal height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assumeb .r--yca u4xf $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as thcjf(6 3s *jdd3akyqm (pj5q5ne car reduces its speed uniformly from 90km/h to 60km/h The tqy5nfjdjsd3kc* 36 jq5(p m(aires 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