A bicycle odometer (which measures distance travp 43 8a0uh hwm /;/znlb)hmsjweled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle witmwhuh4 zw /n30;ls apbhmj8/)h 24-inch wheels?

Suppose a disk rotates at constant ang7 e +iura00nl gepfe1+ular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration chan e pi++en7rf0u l1ge0age?

Could a nonrigid body be described by a single yum y)gc/8ezd6c1ki9value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a lark. ( 30qe*9zx2 wu fvaradw;jbger force? Explain.

If a force $\overrightarrow{F}$ 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 diffik,g(8 mgq;c5 -h8n i 1qjbnbnmcult to do a sit-up with your hands behind your head than when your arms ar qkn g 8n qn5i1m8j,bmch(gb-;e 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 the pedalhqskge,lu;0rd-6 r3 fy03o fp cranks. In which gq,s0 f dhor63 e-ulky; rg0fp3ear 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 witx fpagxo 91q2j6/kz 4ph flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why thi1qozf2ka/xxg69jp4p s distribution of mass is advantageous.

Why do tightrope walkers (Fig. y1d4mm ,+f/ hnpg0vyb8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque ale3*ohqyi6i x b8;k.7apjk6y x2 8cowy so zero? If the net torque on a system is zero, isy38ka6q ow2yc 78y*ipke. x ;xb jhoi6 the net force zero?

Two inclines have the same height but make different angles withr73)arlik x/w b9fqq(t qm9u / the horizontal. The same steel ball is tq7uxfr)9w iaq q9k/r/l( 3bmrolled 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) down ane ih; q sza8q(9osy2/u incline. One sphere has twice the radius and twic8iuz9q;ya sho(qe2s/ e the mass of the other. Which 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 cylinder have the same radius and the sa. b/mtpq*rfqid3,3t jme mass. They start from rest at the top of an incline. Which b,3/it tdqm*rq3pf.jreaches 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 angular momentum are conserved. Yet m e s(fcewnnyl 0zf,nhzd+(7;ge :7x6qost moving or rotating ob sgdqn7y z7e0nf6,c(:l+ w ne z;xhe(fjects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, hcj6pj)j:b ,+ya:o kez ow would this affect the length of the d:jzj c ,k o:)6+abeyjpay?

Can the diver of Fig. 8–29 do a somersault without having any initial rotati3wnsf fju(*q 6on when she leavewunsf (*fq j63s the board?

The moment of inertia of a roy4tbgf lby) 6eu+ 8:5mrxv7qftating solid disk about an axis through its center of mass is+ :y8u6tlffb q7xbe 4)vg5ymr $\frac{1}{2}W{R}^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outst 0dxftxzz5(*gp)2hmn*i/bi d retched hand. If you suddtx)d*n m *2zfzx0ih/ i5(gdpb enly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howeverisesxr -z5*uss mxs) 4*8*oqs , one is hollow and the o s4 zo8rxi*5m*suxs*sse -)qsther is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west./:ex ir13wyzh l d)keh1(am3 e In what direction is the linear velo)zd3ie m y1hk rx(:l w1ha3ee/city 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 on the edge of a largei857 ce9hac* u )epurt freely rotating turntable. What happens if you walk toward thuh u8)t pece9ar5i*c7 e center?

A shortstop may leap into the air to catch a ball aim m0 ck3:5o(nip5 efg hod2e.nd throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quick 0:(m kpnm ei3e.hi5 c2og5dofly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss w6m.,cqp9o oqnhy a helicopter must have more than on.o cqpm,6nqo9 e rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angl/zsepuj2vb/o kfu4w5/ij*i- es in radians: (a) 30 ${}^{\circ }$, (b) 57 ${}^{\circ }$, (c) 90 ${}^{\circ }$, (d) 360 ${}^{\circ }$, and (e) 420 ${}^{\circ }$. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. spj 1x28 9uqshgogwri*h2 u(u8 y3b;s Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on 2sps;o8q (b y389uu gj2i1s whxu ghr*Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km f qmyzjkg j b/2)3s ;2qq(plgix7b5zt cujy)/9rom Earth. The beam diverges atu g)zj5z2yj2x7(q;lbyc//b q9p m)3ijsg tkq an angle $\theta$ (Fig. 8–37) of $1.4\times {10}^{-5}$ 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 is turned 5 0:w0 f.bpvlu0*9b /bqvs7dx kovbw9x v3slpoff during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as t*l0b3f5s wl pvxp:7vs0vudvb. bo xb9w/9k q0he blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball gj- it.lis6*ymakes 15.0 revolutions, what is its diamet js6i-i.y l*tger?    m

  A bicycle with tires 68 cm in diameter y4 4vnn7hwx)g6) ubwvm42 m vvtravels 8.0 km. How many revolutions do thw 42hbv)nvx76n)4gm uvy4vmw e wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 07 jo05 9zlchunt5tb: zye.umrpm. Calculate its angular velocity tm5z07che50b. z : y n9uuljtoin $rad/s$ $\omega$ =    $rad/sec$
(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 revolution in 4.0 s (Fig. 8–38). (bn+ .c0lakt5ia) What is the linear speed of a child seateda nt ilbk05c.+ 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 (o hdia8 b+ltpl9 l;b6velocity of the Earth (a) in its orbit around the Sun    $\times {10}^{-7}$ $rad/s$
(b) about its axis.    $\times {10}^{-5}$ $rad/s$

  What is the linear speed of a pokk:t96leyi:a int
(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 dya7 bdw7 4n,yrotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,000 n7ya,yb dw 47d$g^{\prime }s$?    $rpm$

  A 70-cm-diameter wheel accelerates un,cab lnou5d vne5h 59sup 0-0diformly about its center from 130 rpm to 280 rpm in 4.0 h9evbd0nc u5pl , unos- 0a5d5s. 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 radiusom81/otlt li.+* g4gkyr 9 pgf $R_1$ 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, as5:eft(q91a42 9est r u vmhtlytronauts 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 during a 12-min time interval. The spacecraft cany4l:ste9ttuf vhmqa59 e 12r( 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. $a_{tan}$ =    $\times {10}^{-4}$ $m/s^2$ $a_{rad}$ =    $\times {10}^{-3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm is :mcxf8 b7f+e8lugh,n 220 s. Through how many revolutionb:e7g 8f xls8 ,hfmc+us did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1h )au2st-(d :t7 5t*ntzl vthc200 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 edrtko yxwn--1b *:s.jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete rews k: nrt--e* .byox1dvolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/mi{n}^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniform2gbu po1mof;o7.ufe, vg- t v-ly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time? ugbvo-op;2fu- .ft m gv,7 o1e    m

  A cooling fan is turned off when it is running at 850rev/min It tuekj.x2alf7t)j4 k-k:qhx vlwx7;mh . rns 1500 revolutions before xxk wj e;mhl.v7a)f t4q:kj2-lx7 k.hit comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unij1cpc(2q( wj 2yj y6kfx8:tol3fyy5c formly from 95km/h to 45km/h The tires have a diameter of 0.80 m. k2t2f:flqjc3y681(pyjyj w cc5(xyo
(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 spe6ku ma.jef90g +8n qried uniformly from 95km/h trf+.u0q8e 6iam g k9njo 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 put .mmi h(x15o(4upcwhls all her weight on each pedal when climbing a hill. T (l 5uhxcho.i1pm(m4w he pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m\cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is theb b w*9k7f laqc k)o-,(jre,mv magnitude of the torque qmkaw ve7,o)jcbb *(, fkrl-9 if the force is exerted
(a) perpendicular to the door    $m\cdot N$
(b) at a 45 ${}^{\circ }$ angle to the face of the door?    $m\cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Assume*,tqb xjk b1m4y((uikrl nrfh b7dw;:a88j 8 e that a friction torl;qkiytf d8(majern8uw jbbh,4r:7*1 (8k bxque of 0.4 $m\cdot N$ opposes the motion.    $m\cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are /xn0q bx9*:u;dcpta aattached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then rele cx:;x*d tn ap90uqb/aased. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an en n) bjs0 e6l/tghyry v1j0)gnn0v7fw(gine require tightening to a torque of 38 y00eg(7whv)jn)gv /0r 6 ftnnybl js1 $m\cdot N$ 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 0.648 m when theap z(9lzf+ p-k axis of rota( l-+ 9fppzakztion is through its center.    $kg\cdot m^2$

  Calculate the moment of inerti1szza55wwak5(kb 3 l ra of a bicycle wheel 66.7 cm in diameter. The rim and tirk5w(3bl sa 1r5zkzaw 5e have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg\cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizontaly6(ym8w pm fk+ circle of radius 1.2 m. Calculatmy8+p 6ykfwm (e
(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 4m)0xrufda- i3 rq/qg aq2vv*potter’s wheel rotating at constant angular speed (F4vv2ag u r*-dai) /qrq0fx 3qmig. 8–42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m\cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg\cdot m^2$.    s

  Calculate the moment o,m 1rz9qs.wt9 1nabvy f inertia of the array of point objects shown in Fig. 8–43n9r ,1b.wq91v y tzmsa about
(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 at9;n zeu5 xrz (h g.mj8eeo)6pfoms whose total mass is $5.3\times {10}^{-26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $1.9\times {10}^{-46}$ $kg\cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times {10}^{-10}$ m

  To get a flat, uniform cylindrlib a k.pg*z48pq c).u 4kyl1,2 isbdqical 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 each rocket if the satellite is to reacbqgkld z yb ,4..*8q)cp 1asil2upi4kh 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 mdjp wlf4m7/i gqd 1iy/+v o pe4ydr12(ass of 0.580 kg. Calcula2m4/yfovl1 i7+r(/4q y1dj igppdewdte
(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 5 h o;r doek5bo-vxk:/mea6xi,(2z(-cxdxbuing 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 merr25i5ssgwme h0y-go-round and is able to accelerate it fi mg25s0h esw5rom 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 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 broughthoip0ev4 7sodr-:c 8q n /t8kt uniformly to rest by ani kcqhrvsto7/ t:dp-4808eo 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 accelerates a 3.6-kg ballyzy- ,:v9455fs r*zoqdh cjp: .txzxl at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m\cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the f*4 dl*qbe y.xgl-q, +)w7d0bhjaoch o orearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–0w *ladx7d+o)h o4-c *.gb ,ljyhqqeb45. 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 long thin rod, as shown in Fig. 8–4s9so* )sittg,e3ir kgfc m9356.ts93 tk 5)mecgf3 oiisr,9s *g
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg\cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m\cdot N$

An Atwood’s machine consists of two masses, 0 4(d ib,wnevcmngg)2q gpg( 5$m_1$ 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 four full gjt6,as +fq4b turns (revolutions) and releases it at a stq gj,as +46fbpeed 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 iner *ozs 1rvi(/lnje7rp8 tia of $3.75\times {10}^{-2}$ $kg\cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a tm y 5eirn8w*7mk3f 2k +qla;wtorque 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 cm rz ur dmcl)55 thgw ;.-k05lz0tle4b iuolls without slipping down a lane at-b5l .5e;h)4k tgz0rul tim5dlw0 c zu 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth hh2am rrl -0dj6lpv+r.qu-s1 with respect to the Sun as the sum of two terj vhqmhr2l6rp d1l-+ ur a.s0-ms,
(a) that due to its daily rotation about its axis,$K{E}_{daily}$=    $\times {10}^{29}$ J
(b) that due to its yearly revolution about the Sun. $K{E}_{yearly}$+    $\times {10}^{33}$ J [Assume the Earth is a uniform sphere with $6\times {10}^{24}$ kg and $6.4\times {10}^6$ m and is $1.5\times {10}^8$ km from the Sun.]$K{E}_{daily}$ + $K{E}_{yearly}$ =    $\times {10}^{33}$ J

  A merry-go-round has a3) +ki7j/sctfj(u*7vz+m odg5oqert mass 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 it is a solid cylindt o7ocz3+j5ji(ru+f * qk t/m gvd7)seer.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and* f55 )kzzij4pb g*bxjoi+*gr rolls without slipping4*ri* gfz 5)ijkx +bz5*b gjpo down a 30.0 ${}^{\circ }$ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall and it sz 9wmlay(h;3s 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 energy3 zhm9w;y sla(.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thin s-sb1z .e so, z3qx8dzitring i8 .s b s1zz,oie3zd-qxn 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 uniform cylindrical gri9y:f hek*l.fr3 sb d1:n3s yqknding wheel of radius 183 fq h yern3. by1ksl*:dfs9k: 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 azr+7a atw*; uxt his side, 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 speed of rotation decreases totu +zaa;w7*xr 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 moment ol9 ew5/c m4 6zheywks +il tb(8,aq4jhf inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she make8( eyl4 65zjbae4k h,tcws9 whi m/q+ls 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 spinnd2 g 246zxy6qunw8yo,+j+ 5hugaei y rotation rate from an initial rate of 1.0 rev every 2.0 s to a 6ehyn6uu+a42xn wg2, d+ g5yqj8oiyz 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 ogd i)k5i; 2d+vdue/ kaxis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg ugo/kvde)i2k ;d+id5and 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 of a d+k gv ;nysg54figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg\cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m\cdot N$

  Determine the angular momentum of the Earqrwn4,d;ioy5; , vkwsth
(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.    $\times {10}^{40}kg\cdot m^2$

A nonrotating cylindrical diskdnic8npa6)vt53gc)k f1y3endia vg 4 a-1ek; of moment of inertia I is dropped onto an identical disk rotating at angular speed nfkaed -1 84)en6vpkd5icgvi1) ayc3ga;n t3$\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at :mz-6r2egr9s wjyc 9g 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 center of a rotating merry-go-roundr7i:h jofzv;9 platform of radi jzo;:i79hvfr us 3.0 m and 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.$K{E}_i$ =    J $K{E}_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely ww qm 5tk0;-sj da0 )yrcewm:l4ith an angular velocity of 0yajd 0cls k4r-;w:e twm5)qm0.8 $rad/s$ Its total moment of inertia is 1760 $kg\cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a wpoyey26*7 lbhjx,; y 9+yeam z8ya /oihite dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing *ex6/e2y yy+,9z8a 7 jylh ;oyibomapradius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$K{E}_f$=    $K{E}_i$

  Hurricanes can involve winds in excep4i)xhv e)hbs)j o- :k qxf7)pss of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $\times {10}^{16}$ 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.    $\times {10}^{20}$ $kg\cdot m^2$

  An asteroid of mass tdtjgehb- m6(; fwo)e j5 ;wk3$1.0\times {10}^5$ 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.    $\times {10}^{-16}$ %

A person stands on a 1 - r-jxt/gaqoplatform, initially at rest, that can rotate freely without friction. The moment of/g jaqxr o1t-- 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 the edge of a 6.5 w5xw4f-lobs6 -m diameter merry-go-round turntable that is mounted on frictionless bearings and has lsx -6w4wobf5a 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 rolls on the ground with the end of thfy;iu,(3 nt ck cigj hh238:doe 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 slip n2ifiuk: ot3c;hydg c3h,(j 8ping. 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 faces the Earthjq 2d )bc,ih(jy pq5o)o* tf1q. 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 particle orbiting the,2qq5)*tbj1qoj(p f) ho ydci Earth.)    $\times {10}^{-6}$

  A cyclist accelerates from rest at a rate of wnoy)c 8mkxa2 m 73+un1 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 c qci5s (uj9oq.s q ,p n7ht94ayxf,ve7ylinder 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 delivered by the hp,y7 9qxs (49 u qcvetais. q,o75njfmotor.    $m\cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg andrpt8.+kdhb( jtn dp: /3ntl-myeh9 p ; 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 linear speed of the yo-yo when it reaches the end of its 1.0-m-longt 3h;hp98d+ .-t t(yp :lnjr bedn/pmk string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how 9ou t fb p+qp3v5qig+,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 8zn;n ) 7wpxwd-.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 sphere at all times, and -wx; zwpdnn7) that the lost mass carries off no angular momentum.    $\times {10}^9$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy storedtw4ya*+ zlhlcb:vi 43 in a heavy rotating flywheel. Suppose such ba* +ywclti4v z4hl 3:a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without 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 $1.7\times {10}^8$J.    $\times {10}^8$ 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