A bicycle odometer (which measures distance traveled) ,3r ;69yxm a9*hkgnd ylorw6ris attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels; rywkyx*r9a3d n9lg6rmo6 h, ?

Suppose a disk rotattsp)zgu 6nc895 sm1d ves 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 acceleration? For which cases would the magni8vz51mngduc t s6ps )9tude of either component of linear acceleration change?

Could a nonrigid body be described by a single vwcww/*j lw 5xtc1: (bcs,hu2talue of the angular velocity $\omega$ Explain.

Can a small force ever 7t6oz+x1axhuw)y 6naexert a greater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up wikx ffs m6ey uuz+u:;5,th your hands behind your head than when your arms are stretched out in front of you? A diagram mame u+f,s5;zxf6uky:u y help you to answer this.

A 21-speed bicycle has seven s3w2tuifcb2 q;q qr r ned(4q8efgj8.4prockets at the rear wheel and three at the pedal cranks. I3 cqiq; n2u(88f4wrfeb4 qt egqjd2r .n 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? Why?

Mammals that depend on being able to run fast have slender lower legs w3cl+zm+, an1t qkqry:ith 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 advantageou3ykrq amnzc ++l,1: tqs.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beam?/1gc/krv. rro/p(t yg

If the net force on a system is zero, is the net torque also zero? If*l* lfv77 p3.mga jiqx the net torque on a system is zero, ismg*x7 f l*vial3pqj.7 the net force zero?

Two inclines have the same height but make cj.; u karl-uda* b6e0different angles with the horizontal. The same steel ball is rolled down each incline. Onr kulb*; a.e6ja ud-0c which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. Onef2n:6 ksu*ko/j4inzn kf /8 zg sphere has twice the radius and twice the mass of the other. Which kfoigk/:kn/ z *nf286s4zjnureaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They sta2cfg p gic60qzj4 7jh9c7kc 5mrt from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater tot05g76qc j j pic7m2gccf4khz9 al kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum arl :g7 o-pgiwi5j,el *g cs 0znunj:3,re conserved. Yet most moving or rotating objects eventually slow down and stop. Exp g*epjlljz:5, u n-0in:irg, gwcos73 lain.

If there were a great migration of people toward the Earth’s equator, how would b*-4mzhab4jb this affect*4bbmjz 4ha -b the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotation dqsy1j6 aw1.k when she leaves kd wjq6. 1sya1the board?

The moment of inertia of a rotating solid disk about an axis through its center m0rh * h/md,0dg:vsmv/dgk1 uof mass is gh10r, umhmv*/vsk0:dd dm/g $\frac{1}{2}WR^2$ (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 mass in evnly)ha 5rx/*q s6/gnam 3:po,kdv8mach outstretched hand. If you suddenly drop the masses, will your / :no3vkgd )nlv,6a qym58h a/*mxrspangular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one89 y zet,kn6a ly, phmawo791s is hollow and the oy9y pmt7h6n az8l o s,e1kwa,9ther is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle pointsed8w4; :z4sid 8f mcdh 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 point at the to e4s:8df c;w4zd8dmihp of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the xb3:o+ppeiwub6 f9) vedge of a large freely rotating turntable. What happens if you walk toward the6b i39vpp+f:u )oe wbx center?

A shortstop may leap into the air to catch a ball and throw it quickly. As bwtimvm7 e)dt 33b; 7nhe throws the ball, the uppm3d7ttb7wm i ) ;ebv3ner part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discusss,ri:phvi ai3 *ca ;hris0/, v 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 stables ishi i;3v ,c p:/airav*0r,h.

  Express the following angl skl88gsgr *,gf jx0, 2pu.o*j u1hnbyes 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, using the0wc yixwla1b-g 1;qy 2 information inside the Front Cover, the angular diameters (in radians) of tby11alg-xcq;w02wiy he Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the h81r bvsyg5d;Moon, 380,000 km from Earth. The beam diverges at an angvhb 5sy; 8gdr1le $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotatzolge(/ y+t)/ i xfkkn*1 u6mke at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as t/lfkkg/eon+6x mky 1i tz(u*)he blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m fn7mfvpi1/x 0s4t ;i7hi0y hkto another child. If the ball makes 15.0 revolutions, what is its diamete4;7ih n mt 0pfv/17siix0fyhkr?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutionsrt4yhty:i t t3lg:(ue 8*8o cl do the wheels m3(y *ctt::ygh 84t t oulire8lake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 250sgi4i3( l6eom0 rpm. Calculate its angul( img4si6loe3ar 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 makes5 idb52wxxeb6 one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from twx xb i2556bdehe center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocc -7ms;msxqm fxm,d /i8iu9gkk8+zy , ity 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 speed ov4zy snks7 -b / 6ub/tocxym49f 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 centrifugs)e30t3 tmya .(kpqmh*al li :t4pbi)e rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration 4 y):thqbpk *t303m( )ias il.lmeatp of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel a8z)uckwk. /o 2taz xdy45u*fxccelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determinoku*dz5.yc8t x az2k4/wxuf) e
(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 s5vstg 5t-zu6lpblhn:, 1 y8w$R_1$ 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 Apg*5uawvd ;x4yp * 0unlollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated fg 0;dwpau*xun* 54lvy rom 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 )-w)safe b5 )xs)yxveto 15,000 rpm in 220 s. Through how many revolue5x)ss y-) abwx))efvtions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 b w gq29)dbh2fhptm63rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling “hujbiqy(7:5)p l e qg4oaiwsq1 i.6jxm 4man centrifuge,” which takes 1.0 min to turn through 20 complete revolution(jabi:4iyl56. jiqqs174 q wgxeom)p s before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to n6sebqwsa5,8 360 rpm in 6.5 s. How far will a point on the edge of the whebe saw58,q 6nsel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850mx gf5l.r9hj6o9 uhn 6rev/min It turns 1500 revolutions before it comes to a stoph n.glomu6 9x695rfjh.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces i4:w*ibb bwfl; 4lsjtt2 b6s 9q;u-e hsts speed uniformly from 95km/h to 45km/h The tires have a diameter bibh4-6w sl wj:es*9 ;slttf4bq2bu;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 au1d ean1ym(ff9ie5uhn/ue e oh ;27)r s the car reduces its speed uniformly from 95km/h to 45km/h 2e d1yue er /in h7ma;hf ue19(uf)o5nThe 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 6,bpofvh.nb1.tp z - lputs all her weight on each pedal when climbing a hill. The pedals rotate in a circ,.pbzlbopf tn1. h-v6le 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 do/:ay, hv/lob,. vbu e-y8kzhjor 74 cm wide. What is the magnitude-/uo bv zkbjh/yahv,:.8eyl, of 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. 8–3w m:d f6ub6fg:ixje199. Assume that a g6ebfju1i9 xw6d :m:ffriction 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 epi9lf i2tidya v:*10y, cb ei*nds of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then relfi0t*9*:b i e2di,v p1y yicaleased. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engiirnbuq a4c(38ne require tightening to a torque of 38 3(uqira b c8n4$m \cdot N$ 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 oyi.ma rt ,qcb)gb) b7pd*z/p.f inertia of a 10.8-kg sphere of radius 0.648 m when the ax r*p)da., ).cmgtpzbbq b/7yiis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertif7dep86b c2 oka of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass7pb8k2e o6cdf of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, lighhm0m3;a kj9r+h k )qqkt rod is rotated in a horizontal circle of radius 1.2h kq qa+khkm; r)j0m39 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 con:+hza hgeju+2stant angular speed (Fig. 8–42). The friction f2gahze j:++hu orce between 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 in5yb,f(5yq moofo-q 1o Fig. 8–43 abou -bfyomq, 5( o1yqo5oft
(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 )o y 70vvimjm)ojn i7c5q/g5awhose 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 sostyd*r0y *o1atellite spinning at the correct rate, engineers fire four tange0d*1 os* rtyoyntial 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;w m b2j yx7fr-yru/ cz7tt8-w with a radius of 8.50 cm and a mass of 0.580 kg. mbf87y7 r-t-cwz ty ru/2xj;wCalculate
(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 s3)b0ca dskq( a bat, 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 handfo(g6pmpue:njqe-8 0b w;yl: -driven merry-go-round and is able to accelerate it from rest to qn0 -(::yfe68mp plo;jubwge a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off b3 d31ssroj5g and is eventually brought un oj313srg bd5siformly 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. 7erd-2*dwn)k u. eqol0+ pyx z8–45 accelerates 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 ;oivj g5p+.q lthe forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly fromvqij gpo+5.l; 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 cotj ou;ee6tftzb.ms; k + r+h).6wzf3vnsidered a long thin rod, as shown in Fig. 8–4eeutwm)+z.o fjfr+6 zv 3bt6; t;shk.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 co4a rg 5o./dla5sa/eqynsists 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 the hammer from rest within8/4p;waz nxal four full turns (revolutiona8lz pnx4;wa/s) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia of ht- yrt0ajl bdxsa q h58a:,bb;q3z27$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine dos b+5vwytroemdn6* 8);mzbp 4p+c3 p evelops 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 w t6x mv9 8p(oxnwsj30radius 9.0 cm rolls without slipping down a lane at 3.x0v6xm8o 9t3 pwn( swj3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy )i, ,vye)8n(a it3,fyzgogv rof the Earth with respect to the Sun as the sum of t)) gyne( 3f,i ir8,gvoytz,vawo terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.:(yp /p n.*thz dode8f50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? pz y(hd*.petdf :/8no Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and masy mj(ivdu*q n b/*e6z/yk3m*fs 1.80 kg starts from rest and rolls without se/**yn3ki6dm jy b/qm*v u(zflipping 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 vertica,i1g xi5w+hdmh89 t (l m9hqtmlly on its tip. It starts 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 ground? [Hint: Use cohw,98t(xhil h9m5d 1t gqmi+mnservation of energy.]    $m/s$

  What is the angular momamasx:j 4)p: aentum of a 0.210-kg ball rotating on the end of a thin string in a circle ofxja):4 : saapm 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 uniform cyljppz070 ih 6avnsf:3yjnus/0 2rxkg)indrical grinding wheel of radius 18 cm when rotating at 150rgpnj:y n s03)/u akipvhfx2006z 7sj0 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 rotating at a rate 6m1bwr o 1 20qq1eufr*ohx2pvof 1.3rev/s If he raises his arms to a horuqeo2rw1r1 2 m o0*bhf1 xp6vqizontal position, 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 showsdl(vs 7/iooj ( f; dorkiz(t31/l-b yn in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what 1 d7lt((vdirsjf/bi k;z /y-sol(3oois her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rj9e.v sgs,9vwp k(kf -ate from an initial rate of 1.0 rev every 2.0 s to a final ra,kg9fp(.v sjvwsek 9- te of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at a frk-/x8e g lnhom7+ 18j idannd,equency of 1.5rev/s The wheel can be considered 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 ge h7d-8dl jkn,aoi /+8 nnxm1the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figuryz0exsa6q46)hai(q7ch esa/ y (tb . be 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 momentum of the Ea 4,lq4.amoyc erth
(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 off*vnbj gy*e+0t(m qj4 ;o ,tur inertia I is dropped onto an identical disk rotating at angular spee4**bft t ng,qy ;vrujmjo(e0+ d $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at a,s9q hc hr4a62.4 $rev/s$ 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 merry-go-roxpvf6 5zv(1o ound platform of radius 3.0 m and moment of inertiv poozv5f61 x(a 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 m3 +s1g0l2m4mmjz xodvelocity of 0.8mlgm4 j1xmd 3o s2m+0z $rad/s$ 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 collaps/yiq0z 5g - jzalb998bqp6i5ohzu+ ai es into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of 9j6/z-l 50 ibiqa8pgo zz 9q5ubiy+haits 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 120) n4rq cl;fq5c $km/h$ 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 v*l2.mqiqj,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 platfo)e 4v2ez7psmd- smnbf dk7)f8 rm, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform md d7s)7ff ev2bk nms4ez)-8pis $I_P$ 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 db)zd(7+7qpj9cm;5mq ujc qk qiameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertiab)7+j; qmqj kz5qc(dcp7u mq9 of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying ond60gj b/* uftn 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 behind the persuft* j0gd n6b/on 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 p:ej5qts, j,ffaces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a partijp,,f5 ejtqs: cle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m/9kq 4,u h q8fjtwxu5i3sjf +4l$s^2$ 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 )axhx./q 2rdh*dusn ( a uniform cylinder of radius 0.20 m acquires a rotational rate o sndu/r)2.dxax* (hq hf 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 0 y54 wv0i18ftrhqsdo2g (mkx6.050 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 ei k fw61xoh84syd5vgrm02 (tqnergy 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 thx+m 24mn*amqi)z,gj yoqjh 3 )e 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 o-b/sr zt( qrjh6bfe02wz 2-:f owq7v uur Sun, but with 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 th22rrqjw t(zb6u:0 who-fe-zq s f/ v7bat the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use en9hao4 7+rb+f h( z +s ke;-gmqsp+olenergy 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 neergb 4eap- zs+h7ksn;o +o9+ +lhqf(emding 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 illustrates2 sq-/fnvvinbw 7ky8: an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at subof+6g *pgz5 peed 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 ignore fnas.atnwn6b/w50sd fg9l . w, riction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod.t6.gsdn/nwa9bl a wn,5sw f0. 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 f,n(q;*.f,nq 3 iqxarvp d) bzfloor, 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 height ipzf 3q)qf,(nnd.*,q;rvx a b h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road iq;et su;rz9hk;1 io8ls making a turn with a radius The forces acting on the cyclist and cycle ar;z; 9hk es; 8irolut1qe 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 1sk umn/-n(t,c .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 requi n ,n(c-t/ksmured 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 mcu*. wax 1r-uarms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spi.u w-cmuxa1*r nning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assevrc666x y l7i4n zzc. to, +hzupv7lo9mbly which consists of two cylindrical plates, of 6no x .uzpcv7, 66z+vhrlcz7o ylt9i4mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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. 4om6f0wz 9so3v pdz) uaa ,r:i8–58. What is the min4fad :mpwsza uri3oo9zv 6),0imum 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 $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do no72fhsqy - c i1gul1:tot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car redu8chm+y7mlb s9q,ykq5a 8jui -jf5p 2lces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration ofh5 y,bil2u qla8 spk5m9qf+jymc7 j-8 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