A bicycle odometer (which me6- xxgog6 8ba;p9n7 cbo+ aexfasures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens iagb6;+feon- xox bg 76ax9c8pf you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Doesy1n;nqo+ tmj .ix8* nb a point on the rim have radial and/or tangential acceleration? In *q1m;x j .8+toinybnf 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 the angulaq5w.h9+fd; ncdt1ttk8eixw. zpzxw : n-*d; n r velocity $\omega$ Explain.

Can a small force ever exert a greatertxl/ p:s a k9(vsv tm)6qji/k8 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 with your hands behind ul,5ds1mk7j lial .l:your head than when your arms are stretched out in front of you? A diagram may helsd la ui:lk51.l, 7jlmp you to answer this.

A 21-speed bicycle has seven sprockets at the ret6ef b-r- dbibey4 ,k5ar wheel and three at the pedal cra5try b ke-,-ib e6bf4dnks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with fx 3gpm-z wf89c2e kz0slesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why thks-mcf0gp zxw93 2z8 eis distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a lot;vf db sv4z.6ng, narrow beam?

If the net force on a system is ;th: .;2gb)namnmob q7qv9tczero, is the net torque also zero? If the net torque on a system is 2t n cg;;m7qvnmtab.o9b :q) hzero, is the net force zero?

Two inclines have the same height bu*oih)iau opvl( 6.y8ot make different angles with the horizontal. The same steel ball is rolled down el.y i*o6 a(vhpuo 8)oiach incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from re *sky 4sr z28qzxo7a-zst) 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 h 4 *z8sa7s zok-2rxyzqas 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 im,0nmo6eg vt:-fbum h6q by6 8jg9*u same mass. They start 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 total kin6ubbh09 itvf6nqjy*e:, -6gmogu8mmetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angulamb)qn.z z1 *2 gmc0ysbr momentum are conserved. Yet most moving or rotating objects eve y0zzg. m c*2bb1)sqnmntually slow down and stop. Explain.

If there were a great migration of:2 5hqaov3pnfax8 yt(z e je:2 people toward the Earth’s equator, how would th8q5(2exny:vp3 a oaz et:j fh2is affect the length of the day?

Can the diver of Fig. 8–29 do a som-/si3f p2c bnl7vjq2mersault without having any initial rotation when she leaves ts3-/cbjq inf pl722vmhe board?

The moment of inertia of a rotatiz c; m,sxuif+*ng solid disk about an axis through its center of mass is ,fczs im;+ux*$\frac{1}{2}WR^2$ (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 sittingp2x rxja 7x9rb4 3); )wct)k1jh bzanm on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop3ax7j r4 mt;xwpka b9 bn) )1j)cxzrh2 the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow (68l2 tn mqvc 2y9ulrm0s2o ywand the other is solid. Describe an experiment to deter(qsl2o0 m 8wm6cn9l2t u2yryvmine which is which.

The angular velocity of a wheel rotating on a horizontaldbva9,l u4 dy6/ l/lm 0ythfy; axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angularfmday0 hy llu6yv b4ld,t /;9/ speed increasing or decreasing?

Suppose you are standing on the edge of a large f5d : n mxv+/go/zpk0qblhj:p d.nd,p3 reely rotating turntable. What happens if you walk toward +.qbjdpzp,k:dld5hox0/m3 p nn/:gvthe center?

A shortstop may leaptu s2ofpr, gfnh o); vx.,7.az)r8foh into the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the o .;fnasr) hox grfo8h7u,t.zv2f,)popposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, dii z:5rm;*q2 0erbnboy scuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the he:*;br 2nqo 5m zre0byilicopter stable.

  Express the following angles in radians: (amv8f8,ney p1 *w2ds6n/an rnb) 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 tl g-; ufdgjf46he information inside the Front Cover, the angular diameter;ldfu46fg- jgs (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diveloj,eozv4(1j n s.e1hrges at an anglej(ohee1 zv4 nj .s,lo1 $\theta$ (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 rp0b4 y,wd0*1hnkt e auxg9:faym. When the motor is turned off during operat*eyh9awku ay0x:4d 1 f gt,0nbion, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anot/.a93jko;q j wpnf2cuher child. If the ball makes 15.0 revolutions, what is its fou k w2.ja;q9cp3/njdiameter?    m

  A bicycle with tires xviqe.) ef3u/.m8 vs oxr yl9268 cm in diameter travels 8.0 km. How many revolutions do the whm.ei ofy28x3rxsevuv.q)9 / l eels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcubn:vf)a0 ht;9 drmja -late its angular velocit: a; vn0d)bfj 9mah-try 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-rou: )4zdtj mk6vb ekwp9 rk/0b37rfrvj6 nd makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a jr6zfr4w)6bk/ebvv0m9kk7 :r3dptjchild 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 angula- ax,+9b:ebhd1lr sd0.r3y pmxju(f sr velocity 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 of a po gc3n*v uo zkj,h+,*sbint
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm)1(x gjv*r ohsuvdie0ju1q;6r +,l6 p v rje3m from the axis of rotav ,j umpr(orls6 06 1j ;1+)g3hved*quveirxjtion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uni 2xxy/n8hfpl, formly about its center from 130 rpm to 280 rpm in ,y/fl8n 2xp xh4.0 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 ;d.h3wt9 ilk sb10tmys $R_1$ 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 Mzabzd2 pcbmpk *;+y+/ oon, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy eve mpbp*ba2 zzk+/;+ycdnly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. T )9)8:njq:wjlxm z ldmkr*xg3 tv, )xrhrough howj)gmq)x zdv 9w)j,k nt x3:8 l*lxrrm: many revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpswf5-s) cf1 h3zpcr: tm 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 j 5 *.uec*zb.bk xu9pvlets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions bexk.uc v b bup9*lz.5e*fore 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 : 3aje0qc ks)z6.5 s. How)0q3 z:ck ajes far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it et jod,ekpd7u-wb t+3tos6b0+9z;wc is running at 850rev/min It turns 1500 revolutions before it comes to t6bkwotz+p03 -jco,we bu7td e; +9dsa 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 revol, ,rzs2 8wp pzr+rhire5vj 1)qutions as the car reduces its speed uniformly from 95km/h to h85+erv2jz i ,1 pwqr, szp)rr45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its spee;21rb ep4wwkj d uniformly from 95km/h tp j4e 2kw;wr1bo 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 juf 2-g5fej70ed (rvflm*; l zwhen climbing a hill. The pedals rotate in a cvdfmj5ue7e;lz (0r fgl* f-j2ircle 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 m w2mrm- 2o5hkN on the end of a door 74 cm wide. What is the magnitude of the torque if the force 5-2rk mwohmm 2is 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 torquezvvtjks3: a 63 about the axle of the wheel shown in Fig. 8–39. Assume that a frictioas 336k:tv zjvn torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mas lzkou 3xbg6j7 30q1g2e*ztcysr)4se s m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held iqcgez o4l03k 6s sx u3gbr1t 2)j*ye7zn the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to ao ;6 v3kpzjk8m torque of 38vok8 j3kp;z6m $m \cdot N$ 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 momentnsx 1a4r6j)hnnskb)2 of inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is )hb)2n41x6n ksjra sn through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of ab01u e;jxbwukt ha0o6(ap39 p bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass o13abewk6 x;j0uubh09p ( poatf 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the 7 2 tb+jq0f6urf/jgeg7)dqou end of a thin, light rod is rotated in a horizontal circle of/j+j0 d gu27e q67ofg)fqtbru radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’sw3 f5k,wqm6rr wheel rotating at constant angular speed (Fig. 8–42). The friction force betww, rfq6w35 mkreen 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 inertiaqa-(7 a6r3 xrzb on/ou of the array of point objects shown in Fig. 8–43 aaquz/nr x-o3rb a 76(obout
(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 whose total mass:lss;* c p.bda,i:r4hj (njgm 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 cylindrin c6(4-2*qvsfwqv 1rub6 skbd6d mh3p cal satellite spinning at the correct rate, engineers 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 required steady force of ea1*- 3sw6rhmb( bu 6qd qn6vpcd2fv k4sch 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 wi4o3)ml iz7jcw th a radius of 8.50 cm and a mass of 0.580 kg. w7 )jczloi4 3mCalculate
(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, accelerating it from rest i+rg-g /gm) lhy 0,ragkle-. ito 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 and is ab nnp3f8 wppycqy 1;(h*le to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the (nph1w*y;yfqpn3c 8p acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually bro qvxc d;n8x)*vught uniformly to rest by a frvc;x *dnq 8)vxictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 4/hql/u khn(r 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 ghn-f5hubu 2 5bd -w0c:i7mu() rg odkis thrown solely by the action of the forearm, which rotates about the elbow joint under the acb-hwbku f( )-0d2 drm5c ngo5u:giu 7htion 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 can be considered a 5c bym).reoz 9vd+pwdfs;42x long thin rod, as shown in Fig. 8–46.5vw2o b9+dspyfz .x4) ;mredc
(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 consis ;tm,lx/2pv nlts 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 within foucyjum2 46i+c:b/ 1.9yhzh qzhm tv1 /qeg/tukr full turns (revolutions) and releases it at : myuet/tuhmb j zz /1h2q9kih c.6v1y /gc4q+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 inerbp8 af eyuq(8()d;xy 6i qh6crtia 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 develop/j+czbjee/91 kupv om6(8p was 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 radius 9. y/zpj8u km.l9+ohp)) r w7wek0 cm rolls without slipping down a lane at 3.3)hl8pkoukwr+e7jy p 9 )w/.zm $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earthx :dek*73vs 6fb9cdrr 8 sip7k with respect to the Sun as the sum of te7cvxs *8pf r :37br9kdik 6dswo 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)ie e-*wlc1 xecu4m s. of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume us1ewi.l*e4m x c)e-cit is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts frxbmmqn;0r)9 1ou.j p nom rest and rolls without slipping urbjom1)09mx np;q .ndown 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 verticqrv)i y: ei-,ltihq:6ally 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 poiqelv q-r,:iiht:6 y)le just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thin h8i c4op7j 1odstring in a circle of radius 1.10 m at an angular speed ofo78od jhip1 c4 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindr 8 t0ruzlx;)sw9 k/kdbical grinding wheel of radius 18 cm when rotating at 1500 rpm? )s 0 tkdk;wbl/r98 zxu    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his 6bze9uyh/8e k(ni h q*a+ysa7side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speedeka y6(/bzsyen897i +*ahqu h of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her momenbj* mcy/)gks) t 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 ijmg by)kc*)s/s her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase;dsl) dm( ) v uedr+/bpp, s+ft7gveg2 her spin rotation rate from an initial rate of 1.0 rev essb,); )mpl +dpdftggd rv7v+e2(/ uevery 2.0 s to a final 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 center at a ;exgln1 7g8g rfrequency og;1r 78gxel ngf 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 the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum ooopbf g ri*j4ww:f7et mk9* )5f a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of mb tgvmk7x-, mz e50(fb ,/igey(6dlsthe 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 inertiao9d++ (ded5 :da zp4msm2rexm I is dropped onto an identical disk rotating at angulde4da(d:m mm 9 +se5zr2xodp+ar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at e5q ,uq c;trqyq ,7)w:5djk o 3boge*n2.4 $rev/s$ 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 th tydxlhmq0iajl4v e7g 1.5 *p5e center of a rotating merry-go-round platform of radius 3.0 m and moment of in4* p 1x5qi la 0de5lthgv.myj7ertia 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+ya s:zgs 4-xp w8szn- freely with an angular velocity of 0.848gs +s -p-swn:zaxz y $rad/s$ 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 dwasi438v h ys9sgrf, 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 g84v isy9h3ss 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 in7j uz69v e9m+qv44nnzj lk. uirnx):s 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 qlgaq0v (tyr s,-w))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 x6 g(8rhzom 5tplatform, initially at rest, that can rotate freely without friction. The g5z6 xrh(8tmomoment 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 t/o91nkt8jzjva eau1kmj; r3) he edge of a 6.5-m diameter merry-go-round turntar1onaa1;v3 ze kj j9mtkju/)8ble that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope zlqkv62 d;+k2 ljam3 rrolls on the ground 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, hol d6a;2+l kmqj l2zv3krding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always fxne6bw2x wra, 7lg88a+bgy,h aces 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 a8 n brx67wah28+,gx,y gw lebparticle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 13z9yq;/ sijor;z wi/bys mj:d72ly q8 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 of a uniform cylinder j,icq+qkr) kjxhku.+.f5o w,s7xh-l of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivere,j7)qslh xcxwhfq+j kr+ ,.ku 5-ki.od by the motor.    $m \cdot N$

  (a) A yo-yo is made of tiuwz p5 tbm(fek3xs ))j+-k)cwo solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the -)) 3kfw ctmzk+ uib(px )jes5linear 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, hoqu/ixw10f8 pu9/fjl vw 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 8.0 times as great, werea,u dx+mei2; hv yo;i. 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 iaxueiovm;2diy+.,h ; ts 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 akku/7rw on9b9n -+xk6*xfx1wmdx9h jutomobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km wiwdn x69 1r79k-o 9fj+kxxnh/wbxumk* thout 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 ii+ xxg w7sg80elb3-tan $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speed v=3.3w mgums6 9/s,e $m/s$ 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 yyu i96hte5b9and 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) the 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, a9t5h e6ybyi9u s shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing ve+53ytxfbz1vw rtically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a sbwfx5 3zt+vy1tep against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling:3bly yg 4 yjz;2pvj5m with speed v=4.2m/s on a flat road is making a turn with a radp yb;5mlyz34gy2v j:jius 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 of length 1.5 m and begins )ygxgu5ss g+. b .2b4mmk26wpvix+fy agrp30whirling the rock in a nearly hxy5ggb ax.3kb0psv4 m +2g 2u6gs+imr) p.fyworizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as jff(x9siy7)oft+ib* gq:, z athin rods, making reasonable estimates x(9tfz:jaybfgo7f s)+i qi*, for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assem.xddz v12;/ bi891bij(rql q5vo pes bbly which consists of two cylindrical plates, of 1i/es l8o zd;bq di 25p1q9rvbbj(.v xmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rak.;; wlfeugvi goj3 sor8*p/ o79;pbw/kxjr +dius 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 dro.e sr/pk3;+wpbfiu ; g7g8 vk;9lox/ owr*jj op if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not agm +ioomilv/ug-9- 5f ssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its sdh x)m.wcfcw vk .)k+l /b(pk;peed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was thwh;)(.kk. wp fk+xcvmdc)/lbe 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