A bicycle odometer (which measures distance traveled) is attached near ty8 k3 bhhp,6kc2hsxh(h6 rc w:he wheel hub and is desi hrhckw:c2 hph3kxb6s(y , 68hgned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates ae ewc rlkjh1 9g/351yaxawf +)t constant angular velocity. Does a point on the rim have radial and/or tangential 9k/cf+lew3xrag 1j eh)5y1 awacceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of thenj yu,c*k--o s angular velocity $\omega$ Explain.

Can a small force ever exert a greater torwkz (3rns+5r3s;- uev :jltl bque 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 hawl;3:he t kv1mnds behind your head than when your arms are stretched out in front of you? A diagram may helel:w 1 vt3k;hmp you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and threewc,a0nd:dt7 a24 gpyljp ym81-/o ahx at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear spc yxn-tld/apjy4p2o7 am ad, 1g:0hw8 rocket? 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 w6o yi q,p09xji cojc(,5oy.dmamg .xtj070foith flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, exoa 60 oyoxtc7.m qc, 5jpy9 ij(. ,0fxgd0jimoplain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35)l8b c/gv2qlb* carry a long, narrow beam?

If the net force on a system is zero, is the net torque al8rmw8hb ylj:0so zero? If the net torq jbryw8l08 m:hue on a system is zero, is the net force zero?

Two inclines have the same height but make different angle-ojqfc63fa 3+awg 8gd:6 lxlus with the horizontal. The same steel ball is rolled down each incline. On whiqaf36u-wdj x8fcog:63 a lg+lch incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneousss5uss/i1,2 ct lod z9ly start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greau/ 9ds 5lsctis s,zo21ter total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start ffq9h g .f0/:m2 nkm5t0au0 ec5zdqbgdrom rest at the top of an incline. Which reaches the bottom first? Which has the greater sec9tqdd50z 0:n.f5m 0fb2ghamg uqk/ peed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most movingf8+8vex3 s3tiat0s*i5i zyp5ri i;b s or rotating objects eventually slow down and stop5t iivbsixz+*s3s5f 08a8e ;i p3r tiy. Explain.

If there were a great migration of people toward the Earth’s -qbjuj cu-ae+swn ,-xw+7-lzv6re a. equator, how would this affect the length of the -.6,uzu7 x-ae -njja+l+wb r swqvc -eday?

Can the diver of Fig. 8–29 do a somersaul ayuv ,:cnf7( vvo5y1xt without having any initial rotation when1o a,c75 xny vufvv:y( she leaves the board?

The moment of inertia of a rotating soly y8nt ig082fwid disk about an axis through its center off8wy2n 0 yitg8 mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating sto i;lcxp/*e ntjfg07b7ol holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular vb /lj7t ;g0*nifxp e7celocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the saa6r:a,c2 jxkqqrsc spd1w 11+me mass. However, one is hollow and the other is sol2crxp+jda1 kq6qw1s:a cr 1, sid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizokmrq;:p0q; ; 1ss-w pkb6hl dkntal axle points west. In what direction is the linear velocity of ;16:m-spps kw d kbq0r;klh; qa 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 the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating p,hkx uu r w. t5wenj3e5sb7g969ri* oturntable. What happens if you walk,e r5jrbhsnu9pe5 tg6kw3o7 x9.i*u w toward the center?

A shortstop may leap into the air to vwg* 23tgb9oy catch a ball and throw it quickly. As he throws the ball, g9tg wvy2 b3o*the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation o5uuz- )sn*jb0,aljy tu, ;jx of angular momentum, discuss why a helicopter must have more than one rotor (or propetj,;yjn*z5a)s l- ,0uxojuubller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles invuv9i,0xiyaye 4b/m8ohi . z6gid :3e 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 v 7umwzjw.4, q,zq tj+ohh59r amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (inv4uh.z, m5tw7w,johqr+9 qj z radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at (seh )j* e cts6g4d(dns d6;etthe Moon, 380,000 km from Earth. The beam diverges at*s s 4ece6edddh;(tnj6)ts (g 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 x548nyj x; b ,8jlistris turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down? ntis8r8xl jj5 ,x4; by    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anow ok6 dnjv9g5(ther child. If the ball makes 15.0 revolutjvgod k 9nw56(ions, what is its diameter?    m

  A bicycle with tires 68 cm in diame : 2+7burjof0u+oesj ster travels 8.0 km. How many revolutions do the wheels mak f7jjsuo 0++o2 bur:see?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 pe6n38/gd /3diyd agirpm. Calculate its angular n6/ip ga d3/y83iegddvelocity 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 masd0ju5 f o5dopjl+ec51h 5lx )kes one complete revolution in 4.0 s (Fig. 8–38). (a) W+d) 55fl5ljh o5s0jx dcoeu1phat is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around thcoeo anm)j2 1*g56b7f o w.sume Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of u6 d q1c n0)h;k1qzlpka 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 part4xmhug,,-0m)r bhb bwicle 7.0 cm from the axis of rotation is to experience an acceleratibh-x)g b4 muhmbr,w, 0on of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates unifor9q34 z es:hdp-b q uux0)8faoimly about its center from 130 rpm to 280 rpm i e3du0)9zq: pb-x fqshua84oin 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 radius2lx5,wkchfj ) )kbbpqa;l3t : $R_1$ 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 Apollo spacecraft put themsxhj/b439 gji kelves 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 tgkih j x9j4b3/ime 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 unifwz bqw,v8wy 5u.a 3 xeyz+g.rgh- ,3flormly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in 3a8v. w.qebrg- hywfz3z+ xl5 g,y w,uthis time?    $rev$

  An automobile engine slo uy*j zmyjfub. l0aq2w 90a,zsx) 44tbws down from 4500 rpm 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 mmh9qcx w4 k,c6)9:uwn zktv 5a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final c c9nm65w4:t xk)qwvzhu,9k m 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 diamppry2-cy5 2-dwyhapj k s()crc:; ni.eter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the eday-5 yrjsd (.;pcy n phkp2ci2c-w)r:ge of the wheel have traveled in this time?    m

  A cooling fan is turned off when ihe zx 9a.;6i:q - nk 16vtr.enpzlxytlh*:l+rt is running at 850rev/min It turns 1500 revolutions before it lnhy*kz.:qr9izn x a exlt6 l ;+.e1rp-:ht6vcomes 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 the car reduces its speed unild 3l6vwog77 kformly from 95km/h to 45km/h The tires have a diameter of 0.8kl7o7g d3l 6vw0 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 t- uy97hgi;k/f udgm8kon0x l/ yho18ohe car reduces its speed uniformly from 95km/hylh gxk0noi8k m7yo 1-/8h ;/ uudo9fg to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbing a ;a rac,w1fw0if)q lsnw (4:fahill. The pedals rotate in a circle of radius afscw;:)wwff0a al1n4,rqi ( 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 -/) zczhavs irnv79v2door 74 cm wide. What is the magnitude of the torque if thevzrcih) z72 -/a vvn9s 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 sh2ee,fo5nmzg+ u 7of 2nown in Fig. 8–39. Assume that a fric 7gnfue+, ofm2z25neo tion torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod which pi9-8ovfpye5n cvots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calcu9oy n5-vpcf e8late the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tigo0psz u z6mh83htening to a torque of 38 zso3z06uh m8p$m \cdot N$ 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 iner87bpa uut- +ma*r0gqr3 b+yvltia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its c 7+l -y0trpvba+qmuuagbr*83 enter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diot 8 1ho6t0msmameter. The rim and tire have a combined mass of o8o0m t6hstm11.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on ty43zpt01h g ru1iz 0y 9p;eeavhe end of a thin, light rod is rotated in a horizontal circle of radius 1.2yu pe4zv3yt 1prgz0 0eai;91h 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 rot v;i;id5 y vcbx4c3iy;ating at constant angular speed (Fig. 8–42). The friction force between y4v;byx; i3 ;i5cc ivdher 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 o;3/yr8j m9jbj(mzg r lf the array of point objects shown in Fig. 8–43 agybzm (rj8ml3 jr;/ 9jbout
(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 a2toa;h/go w xf 3of3l .ohp7),u. emqkf:;kmstoms 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 satells:bgx 9suj2/ sjifl*6 ite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 /uis: 2sl b6jgsf9j*x kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm a 6biky,f 1l4 h;yhjv76izv :sand a mass of 0.580 kg. Ca,a6 ks7 ;4hb:vy1yhvfjlz 6iilculate
(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, accelerating9eq t/ 0sl8ydq 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 hand-driven merry-go-round amx.qn40 0w;ia yvf ew8nd is able to accelerate it from rest to a frequency of 150 ;v084mnxf.wiwey a q 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 off8 7-/kuq2n1mh i9fbhq 2ilsqb and is eventually brought uniformly to req 1 l2i/m hq89b skq2fnbi7u-hst 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 acq y6-xdjqt,;acelerates 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 bal .c5q+e* tsoy0c)nuxzl is thrown solely by the action of the forearm, which r oq+0z)5sc.un t y*ecxotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade ckff8, :r h +/bvqbgh1u aumcov.*9zx *an be considered a long thin rod, as shown in Fig. 8–46bv9xfo c,r: *zau1vu qhb+m.gh*8/ k f.
(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 pt2s8hzm .z7 gof 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 wvy sip/3u 7j(vithin four full turns (revolutions) and releases it at a speed 7vu (vjys3p/iof 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 has2t5gz0( (xlex -ob rtz a moment 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 develo7ii8o .nrpo y)o bv(*fps 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 radr b3n*jf10pbd: fb3j rius 9.0 cm rolls without slipping down a lane at 3.f33jp 1nr bjdf0*b:br3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic 3 ay okg/ea9,ienergy of the Earth with respect to the Sun as the sum of two ti y/e3a9g,oak erms,
(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 m7tzr8j 57u t-kmtn br1ass 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 nz r7 j7b5k81tutr-mt1.00 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 and rolls wr s9urgv;mvq *jl2 ;t-pdv 7q(ithout slipping dowqvvlrr9*pst7 ;ju -d2m gqv( ;n 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. --a j egg-lfpj-3izjd5b mp4m4lx;z) 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 conservation of energy-jm-d -3ia g 45xmjlp;f4 b)j-zp egzl.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotati;l1dwjp 66 :rvg9 tbfqng on the end of a thin strl9fqdbw6pg; jrt1: v6 ing in a circle of 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 unifoyydri shi9) 7;rm cylindrical grinding wheel of9d;rih7s )yiy radius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that isbag3mhfd: g8uky*x x84t 32/b i q3sdu rotating at a rate of 1.3rev/s If he raises h sa2 g/ udx3ixq:4 33g8b8fytdbumk*h is arms to a horizontal 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 onedjf6pgzx xq;a9 7:z(z shown in Fig. 8–29) can reduce her moment of inertia by a fac6fqz9;pa7 jzd(: xgx ztor 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 from an ini z6nq am*siy9*tial rate of 1.0 rev every 2.0 s to a final rate of 3 iam *q6y*z n9s$rev/s$ 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 axiuo lu;nk*vq:r s9e 6)xyoeo+0s through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameolvus6x :u)y rnko9 ;*eeqo0+ter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.5q.uje wxn 9d9* $rev/s$ 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 tx9gp7 v:g l.w7 -bb2 l7tz xqvr(tgzc)md/oo 4he Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia ;u lyiv w ;n;d 5vc;5q-xdhm bx5oq7w8I is dropped onto an identical disk rotating at angular speedxo5 b;l dvm;u;qxi7v5h qwn8 dc;yw-5 $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at afl5 iu, y/xs*)-troy 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 stands at the cen+ tenz)kz:a d(k:ro m- b i-)jrc/y/doter of a rotating merry-go-round platform of radius 3.0 m ando- :jni (zrobtkac-md kr/)e+: d/z)y 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 rota 5huh7*gsey )wting freely with an angular velocity of 0u7hhse 5)gyw *.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 collapj)w1xz9 c0xnr ses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotati 9zcjx)xr 1n0won 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 k)gem*likz,f clb)+ ,.h.h hi winds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass snhi(m 3ne7 ps y)n)v:$ 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 plat9 c.yuiytqgftcw( 27-form, initially at rest, that can rotate freely without fricti7ttwu-2fq9c. yy(icg on. The moment of inertia of the person 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 the2l/p: wpq mkv- edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment 2/vpkmlq:p -wof 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 groune 7qbyd5n 7ny9)v l:end with the end of the rope lying on the top edge of the7n:lnqbey vd59)7n ye 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 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 Ea9 tmxdad;x0k (rth such that the same side always faces the Earth. Determine the ratio of th txxda0d(m k9;e 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 9 +yv,1cav+tqb vw**7cfy mjyrate 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 whtarq z7y7k(.7)(;tu rhiln in the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s intervalqa l(7 ktnz.hr(h )r7 u;7wtiy 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, ea6uqn0 ) ip:dr9ipnij )ch 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 cjn iinp9dqi) r0 p:u6)alculate 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 speedi4wo5 yp;olt8 of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were rottl,f,iugr x9/ating at a speed of 1.0 revolution ev/x,9f ,lriut gery 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stored iy .-qcg*1gb;*vf2 jpdgy5w3kun+ j xs n a heavy rotating flywheel. Suppose such a car has a total mass s wfy2d1 b-x;uggcjgyknj**3 p+.v 5qof 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(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 gtn80jozrwwdb5z3i dpn 3+4+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 horizont:3 fw8qgvz0sq al 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 an9 k/tu3 3ftk0)pboy eyruz. 2zd length L can pivot 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) yzk.0p ryb9f eut)t/o3k2u 3zthe angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and7cau(t 3 :fvds we want st(f37 :dvauc 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 h, where h

  A bicyclist traveling with speed v=4.2m/s on a fqo;ip rxnw *t1 jbh(e.vtc-;4lat road is making a turn with a radiupv te-;hnr*bq x io4.j;w(c1ts The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling civ* k n4s(e5b))lko6, cf b 9glgxk6cof 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 required to achieve this feat, and where does the torque come fro)ccg*ko bl v ck9 6k )g4sibx,fle56(nm?    $m \cdot N$

  Model a figure skater’s bod9 3jebek7j74cq :nas7duzf rt8f+gw 6y as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outst 6sze jauc7 gfke8qjf7b3n7:rw 9d+t4retched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, ofuam)j 6; -me:bj+wfyfjf -;au+f m:)ye bwjm6 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 radibiv -wd/ c- t8hn0+c:qm7rcfaus r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point -d7-afw i tbhmvc+:80qcc/nr of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not19eaf5ag5h r-x eh:l h assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces itbc:j0 s dgnd57d f)uc2s speed uniformly from 90km/70cbdj :dcfgun5d 2s)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