A bicycle odometer (whl;m(.zsqr q gn9. 8*7ibysxq dich measures distance traveled) is attached near the wheel hub and is designed for 27-inb y.x qr8.n 9ld7(qzs;*smgiqch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at cons(l +;p p9qk/s,cbez qftant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angulz s,/feqlbp(pq 9+kc;ar 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 a single value of the muamz(ehx3 74angular velocity $\omega$ Explain.

Can a small force ever exerj f :wjp7z1p/9kymmi ,u dq4(gt a greater torque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficup l4(pkf -dk prgi9ko.9q20uaqq7 s/ult to do a sit-up with your hands behind your head than when ad427/gqlkiqupq pk -90ufkrp .9 s(oyour arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rearf .ci8 s40yyey wheel and three at the pedal cranks. In which gear is i4ycsy 8e.f iy0t 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? Why?

Mammals that depend on being able to run fast have slb-nv *wid)b/b ender lower legs with flesh anbv)d/n*i- bbw d muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, nai wlz pblc9*;:rrow beam?

If the net force on a system is zero, s3c ra;7x9gz ais the net torque also zero? If the net torque on a system is ze 3g79 cxar;aszro, is the net force zero?

Two inclines have the same heigh sv* ew)yj8d;ft but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline wisd)f; y 8*jwevll the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an im;uo q5 /4cj i4 une+5vtyhv4ancline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline fir/5ua5hvi4un4+4ty cvoq ;mj e st? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radiusyt+x0 p/ )uji(iax( xi:i;soj and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has t )a: i/i (jij+toxxx0ysip;u (he 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 aah5(, 8t y ( qrwwo0cgvp1x7yknd angular momentum are conserved. Yet most moving or rotating objects eventually slow down and (a,p 8gort7 vkwh cy(1q05ywxstop. Explain.

If there were a great migration of people toward the Earth’s ud4*q5n z mbe*equator, how would this affect the lengt nu*z5 m*bd4qeh of the day?

Can the diver of Fig. 8–29 do a some(6 idu; nwzp8wrsault without having any initial rotation when she lwniw;u z 8(pd6eaves the board?

The moment of inertia of a rotating solid disk about an axis through its cumwrp 5p44 ctf*w-zt11r /ivoavq )z, enter of mass fatw 4rpt5u -)pvqimr4zo,c1vz*w/1 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 rot-lwpr 18leu2t+g m9r d8czhp1ating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, durp9zdehclmtp1w828 + g1 l-recrease, or stay the same? Explain.

Two spheres look identical and ha ghxj:gm-r8 t/ve the same mass. However, one is hollow and the other is solid. Describe an experiment to j:mgth r- gx8/determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In e/:/ mpr0tv8.fjbc4ga.mdl d what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is thed:b td m mjv/e rl04.p.cag8/f angular speed increasing or decreasing?

Suppose you are standing on the edge of a large 5w( (7xhlbmx kr,7vnx freely rotating turntable. What happens if yob 5x,w(nx7mvk(r7xlhu walk toward the center?

A shortstop may leap into the air to catch a ball and throw it4 v1lfx3* 3kllq2a ;yks eeh8d quickly. As he throws the ball, the upper part of his body rotates. If you look quickyl f h4a3v;*1 x3kk82e dselqlly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law ofh;h,f.z b2 l/wqgevt 1 conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the sevw th, qlg1f/e2; bzh.cond propeller can operate to keep the helicopter stable.

  Express the following anglml vux3ozz8v n, 0 ktu-t80w6ves 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 coincidence. Calculate n5mvlc v-ap 95qyi79b, using the information ins7 mbqp5-vily99can5 vide 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, 380,000 km from Earth. The beam diverg,z; gcou:ljps 08 okcgy/em1, es al8/c eopoyg1gz0 k ;sc:,u, jmt 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 6500 rpm. When the motor ismwrm6vyego1 8 f)/xg, turned off duriny 8vmogw ),e x6r1mfg/g operation, the blades slow to rest in 3.0 s. 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 chilf 2b( y,uqvq3xzpq9ij21ua5xd. If the ball makes 15.0 revolutions, what is its diametx,3vxu91 uq5z iy2qjbaqf ( 2per?    m

  A bicycle with tires 68 c+(bny3: rz/quts rlzf/vox.3 (ty v8lm in diameter travels 8.0 km. How many revolutions do the wheels mak/q3.z+y/xt8 uvz: rlro(bytfl n3(sve?    $rev$

  (a) A grinding wheel 0.35 m in diagji8 9ujvhdy5x*q5o8ut 3da2meter rotates at 2500 rpm. Calculate its angularj2dx8u5q 53u g *ay9td jivh8o velocity 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 compl t)1jvec g90xiete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seatej1 v0ei)gx9 ctd 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit a pmmz,ox4/ zn7round the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear s3gj; zn387fgq)c xbx;)es fbspeed 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 ifs.u 8q5qc 7 5sp .4sbqckpu)xo a particle 7.0 cm from the axis of rotat5.q8ks.p so cqubp5cqx4 u7s)ion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its c-//6ql yf 1u,p ygpr mop(/auventer from 130 rpm to 280 rppl/,1v fu you(-gay r pq/m/6pm 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;tuoj95;m erf $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollolb kcnf/ o;o3qft; 3v0 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 tht;ql fbn k;/3o fv3oc0ought 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 tx so1xn(4gz.15,000 rpm in 220 s. Through how many revolutions did i.not1s(g xzx4t turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 23rajvl:c * k.l.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling srb wy ai95 js 49m:eq.f7u9 wen,v+wi“human centrifuge,” which takes 1.0 min to tur4m:9eysswrufwe.v9 a9i7, 5ni qj+b w n 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 diameter accelerates uniformlc18 q0s +feztcu22gu sy from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheze8210 +uqstu gcs 2cfel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1/ f5*eq,gx w 9jz5hads500 revolutions befog9s *w5 de/ axz5qfhj,re it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as thw01(vta5f2pc. f1hlfmn rijki40y d3e car reduces its speed uniformly from 95km/h to 45km/h The tires have a m0la1ihfrv0 (n y4jtf2f5.d 3pc1kiw 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 theds0ro8eal4pwswpn 6v:1 5o 9c car reduces its speed uniformly from 95km/h to 45km/h The tircsvr94a0 eop 85l nwws1:6 pdoes 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 pedo;ph vje7n 6-w38ggbkmx p(4tal when climbing a hill. The pedals rotate in a circle of radp;( h g37obxpw 4m6v-gkj 8etnius 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 h 8odpn;1 qwm3wide. What is the magnitude of theq; mphdon83w1 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. 8–39. Assumezrod3dah9 , e; y7mx ud0l8i0u that a friudz03h ,8x ;dmr 0a ylu7doi9ection torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attah5ceww h .,rl/f-a -fa c9an/sqccy15ched to the ends of a massless rod which pivots as shown in Fig.ccacl/r9ewcy a-f5.hs fh1a -/nwq5, 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head mss.f g2k2a 0oof an engine require tightening to a torque of 38 sa 2s0omk 2g.f$m \cdot N$ 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 inerti :hvt 28aub:ghz.avr 1a of a 10.8-kg sphere of radius 0.648 m when the axis of rotatiza t2rv:a1v:g8.hb u hon is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rim ; 6yw a y10gcuv.rc:nzl(9mqs a cuyvc96a wg l0y:zm1s( n.r;qnd tire 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 the endp0t-5 3 wprhd4ngzkut1g01asnnl6b. of a thin, light rod is rotated in a horizontal circle of radius 1.n-dt buptwg 6 r 0a.nkh0g153p41nlzs2 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 potteryy2z, +f iyb3.v6tj:civ4fz a’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N total2.aib 3iv6tyz: fj,yfzc+y4v.
(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 showk.bz*66 lxksrk6ww 9r n in Fig. 8–43 about.s r66krk b xlz6*wkw9
(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 oxygee6pqytk3xa-c9p6 4 wiy3)j eln 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 correct rat7b0 )/t dmrrnce, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius 7dtnrb)r c/0mof 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 radius of 8.50 cm and a mass ocdg3sl (b c 92)ro2k,tiydx-mf 0.580 kg. Calculatelrsg32 mt2x9 o)-ikb,dc cd(y
(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 l: cs+/ywk)*jfr8 icbmfd .g6bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small ha r3dkk( t 9xjhpp8ws15t* yk3xm1v6jhnd-driven merry-go-round and is able to accelerate it from rest to a freqvmk(3 phk6 r3k hsx*15tw jjx 8d9tp1yuency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventm*m 7v (+s7pxlgq7dhxually brought uniformly to rest by a fsx p(m7 d7mxh gv*lq7+rictional 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 ac1 fp/;mu7han0 zaie2s celerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the fuk.ib vl9o p kuv*q4 0r(/y(slorearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerateopvb9 vyqk0r /u((lk i4*.lusd uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig. 8–:a9l3 7 zc5l,n si3mn 2zzpghj49: lj ,zic h27z3as5zngnm3lp6.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masses hh :0 wo1j*ydyv8ey5z, $m_1$ 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 u j8 dd92a4mdphb fla/h,m cy-ks1.c- from rest within four full turns (revo-kd/29myfh , jmc1c.hbdlu apdsa48 - lutions) 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 momei82 e a-/6k n32 h,b0mzcmmqmlo enr3cnt 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 tomo*ze x ,ko+(prque 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 raf-gxh v*8 wtxlsga*h )x:26vatf3 jo8dius 9.0 cm rolls without slipping down a lane at 3.3 at-xotx8 h)lgg *s2 f83vj * xf:6vwha$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy ob)1ercfw s98mm,uj, mf the Earth with respect to the Sun as the sum of two ter1f8c 9w,bsuj e, m)mrmms,
(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 radiub2t(2;0iv nv6jf.5f 9q;wkelhygaq ns of 7.50 m. How much net work is r6;v(nlq9. ;f 25kehaq0ivf j nt2bgy wequired to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest a z (fwb a,); (,ihhkcovfv5 lybpha+8)nd rolls without slipping ha l b5,)+chb;pvyfzhva( wo8(, fki) 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 starts to fall ndlttc xb.pl3 8re(y(v.d 6l)nc w;.j fh3xu1and its lower end does not slip. What wr(dyw;vxlp(.hdl 3n3cbj1..nxtl eu) c8t6f ill be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the en fc dsv0bd1f7/8z3u -x(3ayyf .nfunpd of a thin string in a circle yfu1.( vz37pyax0cd-nd fs/nuf b8 3fof radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg unifo1di p; sm((b71kxbene rm cylindrical grinding wheel of radius 18 c ism(1b;bn17xdeek( p m 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 platform that is rotatinj -i1iww (p/ 1wjl7ulmg at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–41i-ujl1j/plm ww w 7i(8, 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 sh b7uew-/r: qkgown in Fig. 8–29) can reduce her moment of inertia by a fact gb:e-u rw7/qkor 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 her spin rotation rate b :7p-iscg*lqy -b-cbfrom an initial rate of 1.0 rev every 2.0 s to a final ra lbc:-b ci-* 7qy-bpgste 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 ath(h2 kvt-7)cj;qa mmxis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform di(qj ha) mhm2;ckt7vt-sk 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 momen*cdzept ; m4q(tum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular hp gv4b8f5- fzmomentum 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 momjg (iaph9,dyr; -4:w (z y,4lxnrm njbent of inertia I is dropped onto an identical disk rotating at a9dm- a4r z,ny,:l;( jynirw(hg p4bj xngular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a shh 8tad5slp/b qfh14r,jms ;u7f1i-t 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 wmbc,leq9ly :p *s+8 qstands at the center of a rotating merry-go-round platform of radius 3.0 m andyq8l, +wb cs epm:lq*9 moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity of tob+b+1x2zg8wsi: a 11r ck gy0w1sb ki1a+tyco rg1xb 2+8gz :.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 r9et586dkeh.b ad4q7k cdus5 into a white dwarf, losing about half its mass in the process, acbeuk arh9s85dd k7 d4e.5t6qnd 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 12j; ew2 yno9t43r p9y3en9o mve0 $km/h$ 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 ko g/c3 5b1wm -.szxtp$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely withou7u1;wlao fzq5u1 t;but friction. The moment of inertia of the peo5lauw1u17tz;; ub qfrson 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-mo7c jr ga:dl rwz(31k; diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1700 aok(j1:l7;rdz c wg3r $kg \cdot m^2$ 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 l ,o*scu nogqz1z u*ssez837(vying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding ontos**n (13u zz, cogeuqozvs7s 8 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 a3tbocog4 m5s.lways faces the Earth. Determine the ratio of the Moon’sbc4gm oto. 35s 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 of 1 a g jg;pox4,6t9,e a,xotrcrr)h.2mim/$s^2$ 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 cyl+ p3vp5s 1d55rh rhkivinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at cov+psd5k 5hrh1rp5iv3 nstant 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 mavr; *b x/h7 s5fksy,1qk1gov ass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.g svv 7*kbs5ho/x,kf;ar 1q1 y010 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 rr951fig8 ohndeo-7c;g1o ciiear 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 avexhgu* yf4+:p )4ufp s great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutp4:uyf eguh4px) vf*+ ron 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 usej : ;c-h2ujpoov ( k*m**vpswe 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 1.5 hu*vwcp ekj(-oo 2m*;*psj:v0 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 t(x85 pc5jeku,rp 1uk 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 horizon e. qz 4vefkqi 470,vm+jnhdn7tal 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 freely (i.e., we ignoarz7sk 7x 4g;are friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of;sa7 kza7 rgx4 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 / rnzt(5vjr -h bi2;whfloor, 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 ;2hw/vr5 trn-j biz(h step has height h, where h

  A bicyclist traveling with speed3bo -;iyq-dla )uou6b v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle arebd6ab3o lq-)-y ;uiou 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 a f35huev5 ex8u)t7t i7kaoo-lmjgm *f j7z70gnd begins whirling zj3x777a o5f5ggv07etmo)ef- u l*hkmuti8j 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 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 veu u:;9sx yt2as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the ane;s92yv tx: uugular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly w yzq:5 fa5s p6 b8qc 8+vjopx++tai*wyhich consists of two cylindrical plates, of y6ao8cqj++pvf 5t+yi*qas:w5p b x8z mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fig. sxl i ds4dc3w ,x,jgh0u0;-pb8–58. What is the minimum vghbl j s3x sd,;4wdp u-0i,0xcalue 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 $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do n+khz ivpu27,c ot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car rew o-qa(vn87vrmpvk3xx09 3 n sduces its speed uniformly frow3 vnxq0s9xpra3v -7mvo8 n k(m 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s