A bicycle odometer (which measures distance traveled) is attached near the wheee:of,c( hv*q hdhc4l /l hub and is des hc/h eq4o fdcv:l(,*higned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim havud(+ o n3fdjsr6:l 8 )vpn.umke radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point havk+8 n36u:nd )ps(rdj.ml ufove radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular veliudia / fkft6,.cgz6798 q4dyv3vs (znp6mp aocity $\omega$ Explain.

Can a small force ever exert a greater torque tha2:gl ydg:/uss7q*e)x/vcn sl6 h no(on 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 49gr3qj7 jhgp with your hands behind your head than when your arms4hrp39 qgjj7g are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at tz/32 q, coak u;e/xjs7pd hr2fhe pedal cranks. In which gear is it harder to pedal, a small reac; 2 pqdjao ,k//u2xerfhz3s7 r 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 hr ij (/v7s2hv)gjw s60akgt6m ave slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dyjgt sjw67) /vvs06agh 2rikm( namics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35+a;t r(fre+ebu8 v0wgt5ym7y) carry a long, narrow beam?

If the net force on a syste xbch1z)e422nu ,(xk gbge8pt m is zero, is the net torque also zero? If the net tou2h gc b(en)xz1, t2b ge8kx4prque on a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizonevlf2;v6.:wzdk1zx f qi1u7ital. The same steel ball is rodi fixl 1 v 2qzv1ez7uwkf:;6.lled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) do(pw w6j1j,zho z ea87xwn an incline. One sphere has twice the radius and twice the mass of the other. Wawzzhpj86eo,( 7w1 jx hich reaches 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 cylind0gxn .a/p.f tf ny.(ejer have the same radius and the same mass. They start from rest at the top of an incline. Wfp.g(te fan .0xn /jy.hich reaches the bottom first? Which has the 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 and a4 s4:a-oo0f0j;glxrf3 t 21tbx bihz dngular momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Expl0oa3o2r; f-xx:bfidb1tg t0lz sj44hain.

If there were a great migration of people towarj*bqv:-bkm*begn;5q7:c4ha * f glj bd the Earth’s equator, how would this affect the length of the dayv jb4 mq5ge:7-:hb;*n jgb*kcqflb *a?

Can the diver of Fig. 8–29 do a somersault 9bf; ;jpqpyc; without having any initial rotation when she leaves the q9c;bpfy; j;pboard?

The moment of inertia of a rvo d8;tzg o x,*(r:e4kej l5rzotating solid disk about an axis through its center gelrer8*xo; jd(k4 v5:,zoz tof 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 rota,matp4k krw( er:4 o8oobo0q4ting stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, o,q oke0k4otr 44( wamb8rpo:or stay the same? Explain.

Two spheres look identical and haq q09kzobov7 )ve the same mass. However, one is hollow and the other is solid. Describvz)q907q o bkoe an experiment to determine which is which.

The angular velocity ofv)uvc6/m ck8 h a wheel rotating on a horizontal axle points west. In what direct8mv )vku/hc6 cion 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 the angular speed increasing or decreasing?

Suppose you are standing og7/j ie-re 3ct9pgem9 n the edge of a large freely rotating turntable. What h / g3jp97tecri e9mg-eappens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quicw/ce 7j t1;eknkly. As he throws the ball, the upper part of his body rotates. If you look quickly you will noticet/ j17en;wcke that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the lawnb c0a t5o)ep +iypv4) of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the heloytnp+e5pba0v i ))4cicopter stable.

  Express the following angles in radians: (a) z x ,)e1/e1r3 6*zfiwwp aabau30 $^{\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. Calculatee5rrk 7xf 94f5om8tzoy .fd( /sxyde 5, using the information inside the Front Cover, the angular diameters (in radians) of th95e/xsor .f 7tdx(yfkm4ryfze5d 58 oe Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed d1 -sg oerx*:kat the Moon, 380,000 km from Earth. The beam diverges at an angle :e rxdkos1 -*g$\theta$ (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. cxjzrf j updd080v. /+oht .(mWhen the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angula 8dp(0/ufx+ .jv0o. djtmzhrcr acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball makes j 9n- /c6d 4mmq5nihxl15.0 revo5l9xi cm-6nnqh j/4dmlutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 rusbsrt2:w ytg3 52*+ozgff-km. How many revolutions do the wh:brf+gzoyss 2rtft53 wu-*g 2eels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates wxs/ kl gv)zf9s*jn8 mg8 .b,wat 2500 rpm. Calculate its angular velocity iv, 8)bmk9. zgsg8/x*nw sw fljn $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolutise jyulh 8++fz9 2hm.kon in 4.0 s (Fig. 8–38). (a) What is the lineahyh j+. +eul82sk z9mfr 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 oru 3gy:*nwkga7bit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spee;g.; hgh 8 rv4.aizvqvd 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) mus84 uqczc cah+kjq1n azd1qeg27 +*7xwt a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration qk1cuhzgna x72qq7c 4a we*cd++1jz8 of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 ri4098pv1xmm bo ofh/mk 8cxf5pm to 280 rpm i1o k m4/i5b8fcvom8m x9fh 0xpn 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 radiu eg-cad)ejga7m7f7.j s $R_1$ 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, astronah goq7ao.+ -s;n0 msowuts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute durs ;gaom.qo07+ hn-wso ing 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 un,mnp;p c6* nwsiformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this;w 6*n,cpnsmp time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rwv t(n-2wyug,l ar.(tpm 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 jet j(r5ngsvs.w l.b5e7a s in a whirling “human centrifuge,” wh7wsje 5v ..(ns5br algich takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6rdq u g3zk-.a.rju wqd*1;1him /hiks1yh . f5.5 s. How far will a point on the edge of themsw5u;3gkhjq h1d z*kirf/qi a11y.hu. r d.- wheel have traveled in this time?    m

  A cooling fan is turned off when cj(,o.lt oymps8 det. -.g5ig it is running at 850rev/min It turns 1500 revolutions before it comes to aoce5s yg dt.i.,gtj(8mol-p. 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 revv x )/k4*2aa:s:jhq cdifhl y/olutions as the car reduces its speed uniformly from 95km/h to 45km/h :if 2a )sh /hy4vdca/j:klxq*The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the i 0,o1 )jx.1lh 1wvxabsd3wlncar reduces its speed uniformly from ,owl )1 x3.1sd0bhjlvawi1nx95km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight o;phogj4-f6 lm n each pedal when climbing a hill. The pedals rotate in a circle of radius 17 4f6h gj;mlo-p 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 y1d /: (+fwsu pddjm.r55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the forcr:umf(/j dpdw1 .+ys de 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 F4u0q) 23spcpar1 cl cuig. 8–39. Assume that a friction t0pq1 ac43lsc2uuc )rporque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of m*ztd;t1)tlh72tic *ic t2a edass m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal positiontcet i)7h1l; zc2t2i*ta *dtd and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinde)4h2hk j ;y.jwvdwy;hxsr (2d, e4y sbr head of an engine require tightening to a torque of 38ks4)dywh(djxj b.ey r; 4 shwh;,vy22 $m \cdot N$ 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 inertia of a 10.8-kg sphere of radius 0. 6jehu st5x+w4xneoj5 h5qz; ,mmg0, 1djfz n.648 m when the axis of rotation is througj5w5mjz6g4q;,x xo5 +ns 0zn fdemhehu, 1jt.h its center.    $kg \cdot m^2$

  Calculate the moment of inertia of ad 3facz ul+(gk;(nq;fi,usf7 kf*)w q bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hu( ufdg ;+qw3 );(cqlu ,7aikn*f fzkfsb can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thinanajokn:v 7-;f wze )6)lp; jqa*mx5c, light rod is rotated in a horizontal circle of rak v*l ;)j)az5;jn ocp7 aqnfw6-a xme:dius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s ; zmgvli ms)5(wheel rotating at constant angular speed (Fig. 8–42). The friction force b; migvm(5)lszetween 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 p4:+(j(.d udnxb yqs shoint objects shown in Fig. 8–43 abo .bu(ydjn xq:s+ds(4 hut
(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 *qnw-os-/(6pte n c qbtwo oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, engi0)w(iplx t6r bneers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the )wxp0i (ltb6r 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 f:7h3*:cphgwm sd ld2 mass of 0.583pdglfd:h:m72 * whsc0 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerat+nfqmd5oes .v0.o z4ging 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 tangentiawk r7ee 1g7(txfy (hn8lly on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two childke7 r8h1 7y(t( ewgxfnren (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 rpms :hslrm4g.1k is shut off and is eventually brought uniformly to re r ssg:kl.hm41st 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:gs ri6qrenw; 5g5:op 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 th9 o jyn/n4h8lu3b-yzq z98ocse forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–scn -u/o8lnzyqz3 48 byj9ho945. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be coow-u2y qdajxjx5s 5w 70a z+ s6*dkq-ensidered a long thin rod, as shown in Fig. 8–45 azxj-6j*-5sokaeswxdd 70+u q2 qyw 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 consists (b 1z5fk kl w1*yxpf4oof 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 thr+nevi m 3/occ(6yds 4e hammer from rest within four full turns (revolutions) and releases it at a vd3 syn/cm i4oe(r+6 cspeed 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 ezo. nd2l((*v)phcth 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 develops a torj;.h6z pzg mf2que of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 ev k41y)j,r ra4rt1.bp:smxn cm rolls without slipping down a lane at 3r)nkp4j xy.b4:r1t , rvems1a.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as th vrw+h45m vnltz(e -:ee sum of two te5zelwm4 -nv +:veh t(rrms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much nem sbgn: ,l w.,qw1.pnjt work is required to accelerate it from rest to a rotation rate of: smw.w.bp, lnnqjg,1 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.8owq5wu+ e,rsw 4qme sq;)b*+ b0 kg starts from rest and rolls without slipping dowmse,e+ qb wsbu4w;+r )5woq*qn 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 tip9j675j0s iycos/whvq4c d rt uu80 l2c. 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 groundoq4s/0j6h2 58wjidcu9 v7ls yct0 cr u? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thin sh b a.bbldkl3jktx 90r9en7: ,tring in a circle of radius 1.10 m at an angular sj b lxr alkbenthk 9,:0d739b.peed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cy) zslcg) *xc 1kr 6ecib9);r1p)rkxb glindrical grinding wheel of radius 18 cm when rotating at );pbz) 1r9ib6eg)ccr1k )gc xsxlr k* 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 sidf 2pmlb .t af ;8rz.c-y,svnlp) ;njl0e, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8lnp bf 2l)v8tl;pyra.n0sm j. ;f-cz, –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 zne(5v2.iav 6ggq jadq3dh1 ks:5h; y one shown 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 posit5nds1ykvgj.a (qveq;2z hgdh:3 a i 65ion. 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 frgjv f)o)- da,hom an initial rate of 1.0 rev every 2.0 s to a fj g,))hf a-vdoinal rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its ;uhfvdv.u7e* e4id1 z center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approxezf1vd* eu hd4i7u. v;imately 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.k8 1k)nyjfmtdy,60hp5 $rev/s$ 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 Earthfmb+plmzs)dy j/* w 9/
(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 I is dropped onto an 6zcif,ya i :+kidentical d i fz+ki6cy:,aisk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 wo3ep k(5uq;sn v(,qk $rev/s$ 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 kgev /wq (ohtu4/ stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia ehvw4qtu//o( 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 merrygi9d)mwmu. )ra u,r-s-go-round is rotating freely with an angular velocity of 0.8 -. sm,rgu9mr)i wdu)a $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about half its o0(um(0z-w2 vi dyv inmass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no inodmv0zy-0(wv u(2i 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 -k fzbk .yj.ysmbltf)r744(aof 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 t;5p4yd :ar:.e*o.kvj(ou; ncdy, cv zres3 t$ 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 wi 6/ptsrp3g q7u 5g izdfom,f+,thout friction. The moment of inertia of thpsmr6z f7 o+,5qu/dfgtp,i g3e 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 the edge of a 6.5-m diameter merry-g w 03m f, gn8jzppq:l8jh0tmx5o-round turntable that is mounted on frictionless bearings and has a moment of n,p mmx 8p3 zj5j:hqf 0wg8lt0inertia 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 grur3lhrro ,y5 kh5t* qm-hj m+)ound with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unw5)mt3- k5+lhru *hy h,o jrqrminds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side alnh5vq4kkobr-1w - m:a ways faces the Earth. Determine the ratio of the Moon’s spin angular momentum (abokbmv-rk1no4a -h5q w:ut 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 ftui8j 6 m6fp4p1nyc,brom rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape -sv jfz gawa s2v2o4bqp,w8*:of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rq :gjs 4zw, vf8sva 2-bpa*wo2est 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 disk ls q9g0kpym+;k,wt2ws, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of eners 9g+p2qm,;yt0wk kwlgy 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, howfccq.zbd)w,2dr5 ( 7g1fj qz v is the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.m8leb)oc rwy)l2.l g-0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform spl8 rc y-bw)gll .2o)mehere 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 storeaox,f ok o/ h2ziq9c048wst g)d 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 24sgo 0fiw94k/t cq,)8o oxh az20 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 anxs-a 9v zib s2 w*odn8*p4ej9n $H_2O$ 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) ib cu blor3nk0zc4mt0u-(67c j 8hzv0 ts rolling on a horizontal 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 (ix18/wqbw x84nu in;ft .e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravitub xwxq/ tiw81n8 ;nf4y 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 verticallvs sg:z ptph44vhp 2);y on the floor, and we want to exert a ho;v zt2phhspg:)4v ps 4rizontal 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 flat road is making asf:; :q+f35q b3j6 ij6 khjzihnkid (q turn with a radius The forces acting on the cycljf3+h qzb6:nk6 q shiqjjiidk;(:35fist 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 o-x-, 8jqmh nxmf length 1.5 m and begins whirling the rock in a nearly horizontal circle an8 -mmjx ,xh-qbove 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 armsj.+h jw6g*4zk4gz( bj0.kocvv. rvxx as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and withj v*x 6o jg(4 j.kr.zv4 vhc0xz+kw.gb arms held tightly against her body.   

  You are designing a clutch aso;hd/ 8mi( ebrsembly which consists of two cylindrical plates, of mas (iohm b;/red8s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 m4g.fumd - (sxr 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 m(x-4dsfmu g. to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assuy ie sl625nce9 9d0-fzlo4uoxme $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car r d9s o82zl+vw-zl0bzd ja4 obd4 r1j*ueduces its speed uniformly from 90km/h to 60km/h Thedds *u 2j0d+z-ro4jv18 a9 llbzwb4zo 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