A bicycle odometer (which mesm*(fgn 4;mfc4/ 7orvb0l u1sm ql yk;asures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicyclem;g*(l kr1l b40syf4v/ o;qusn7mm fc with 24-inch wheels?

Suppose a disk rotates at constant angulazxk2msi718; +.im 2namv zhm vr velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velnm.m ;i m+ h1vv zz2i27sk8amxocity 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 sing7e q5jdc)4cqo le value of the angular velocity $\omega$ Explain.

Can a small force ever exert a great1pjfm a*es+2k00b zhner 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 az(-x (2vkndz z sit-up with your hands behind your head than when your arms are stretched o(2z z(nd-zxv kut 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 de z617+,yfi mz)giixthe pedal cranks. In whi giezd+ i, mf)1xy7iz6ch 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 hadi5cus5 pa t 4b+lwe 8.*de+ps5ksyr1ve slender lower legs with flesh and muscle concentrates.uis y s 5a+b1w e+5epkcpl5*d48trdd high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry yg18f iica(rbl 65 tj(mcr;h, a long, narrow beam?

If the net force on a system is zero, is the net torque alsfavg, ju:zvfv) zwwm5 +uud/*+4-o yr o zero? If the net torque on a system is zero, is the net force zer+:ydw zwvmg* vuj5off+a z)u v,/-r4u o?

Two inclines have the suig/-4 rdni*my2 3 ixeame height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater2m ri-4xuie/din 3*gy? Explain.

Two solid spheres simultaneously start rolling (from rest) down anq6 mdfce( 56xv(i quxnp *6e n3keg8:q incline. One sphere has twice thdx3fe( 8i5e(q kmxpq q nen v:u6c*g66e radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They star/6,q7c pal7w p ctxy0qt from resq7 0wxpyp laq7t,6c/ct at the top of an incline. Which 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 angular momentum are cqkn m b o5juq6dxt9h+s7.2/ lj*rv0 gmonserved. Yet most moving or rotating objects eventually slow down and stop. Explaqjmrgdh9xms +0 u2lt756*k .qnbovj/ in.

If there were a great migration of people toward the8/,gfpqal megf6mz c2/* . rzjzz1z8r Earth’s equator, how would this affect the1fqjzr6./2 pfmecm8z/*arg z,zl8zg length of the day?

Can the diver of Fig. 8–29 do a somersault without having anzp-pzrd l6a,d 2 jr23ty initial rotation when she 2rdar2j,tpl z d-6 z3pleaves the board?

The moment of inertia of a rotating solid disk about acuwv:t y*x(*,lyjiy/ n axis through its center of mass i:u tcj*/w *xilyy(,vys $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holdi wl5;lsadhz+xkl g61wkar4 *7ng a 2-kg mass in each outstretched hand. If you suddaha 1w; 5k4gkzr*lxl 6wl7+sd enly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same v fyg6,pl7- lxlj cez4rw5u +.mass. However, one is hollow and the other is seplj- ygl. 47zrc, 6fvxu5wl+ olid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points westwfhg,3 km zgp - hl,2imiu6/h*. In what direction is the linear velocity of a point on the top of the wheel? If the angulawli26g h3i*ukhf,hg/p -,mmz r acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freelyqorho46uf1 (u rotating turntable. What happu1fho(ro4u6 qens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it qui0e)o 7qty8dmc5ghqp, ckly. As he throws the ball, the upper part of his body rotated 5etcpymo7qh,0)8q g s. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law+k d) bre39gde of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss e 9rd+ed) 3kbgone or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles i/+-tm.ze zzuo n 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. Caenkk6t .9nx( klculate, using the information inside the Front Cover, the angular dxkkn9.etn(k6 iameters (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 yp:jayhz)epf ljbo8 v0cg c) n6:a-/)Earth. The beam diverges at an an) ) eabjz8 py):j6-fa0lvh :cpg/ycnogle $\theta$ (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 66n jkg6hc4ytn 2 y7 cqf(*2rte500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is thy6(qet2*ykjcrc62 fg7 4nthn e angular 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 g5hdt+ 0o7smi1b ahu+ball makes 15.0 revolutions, what is its diameter? hdumhi o07b5gsa +1 +t   m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revos3 c+l 50xqbrblutions do the wheels mqr35 c+sl0bxb ake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. C xs gyxv9z gf;3h/3 u*i+j6umgalculate its angular velocity inu9y+xsjm ; v h*/gxg iu6g33fz $rad/s$ $\omega$ =    $rad/sec$
(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 comple30q*pp4eu af y -gpc,zte revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated au-0gqz 4p c 3y*fp,pe1.2 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 ofs. awtz7l z7j6 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 iqx2is3 cdw h/25l4+cbgzx2j a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rmpcbaa84/ j+g.nfgl8otate if a particle 7.0 cm from the axis of rotation is to experience an accelerat/cma+ 4fan8.jl8pbggion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acceleratiy2wz1y2 f+v r ggj0h0es uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determinev0w zi1jygg0y+2f2r h
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius .*+- lwetdspq5lo8we4zn. n w$R_1$ 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 Moof 46r;k0xqh;n1c.f)zd 7nahnnv5asa n, astronauts 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 ; sah1)4fhnzvdnf0. rn q6a;a cnkx75a 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 m- j5k1g3en9jdd5 g:je ivv4z from rest to 15,000 rpm in 220 s. Through how many revolutions did it tuzj-4ij5 nevm1 k5je:v3g d dg9rn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. C.cuuku7;1,bm /: jypvmq-en,u deim-alculate
(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 foot-z-tjn vos/ 8 .m2ud5tthj,r the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1ts2 .v,-o nd t /ju5otmzthj8-.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 unifokobh(ahpo,p 2 3hg-:v rmly from 240 rpm to 360 rpm in 6.5 s. How far will a poin h:2-p vgha3op,h b(kot on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/minidfc *sps8wr**vp hymv51;;dfo*k maf2sx 1 * It turns 1500 revolutions before it comes to a sto2 rs;*xdi5py*1h c pwfms1 v*amf**kf;od 8svp.
(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 unifo3jjt, p 2d.miormly from 95km/h to 3j,.mt 2pj iod45km/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 speed uniforp1he btzk.0xd8z,7p f mly from 95kpb.,zeftkdzp8x h 70 1m/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 wcro/ogujf;la( 1hz0 * eight on each pedal when climbing a hill. The pedals rotate in a circle of gr ;0f (/h*ouzojalc 1radius 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 the +sagv/ l99g xnuf 9w,imagnitude ofv,n9+g u9 swg/ilx9af the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wu3i d/*f4zxebjsa bwcc ,)h3 .heel shown in Fig. 8–39. Assume that a frictiu/b adf4bzhsw,i.xc) 33c*je on torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the e /,:8pzjpiftt nds of a massless rod which pivots as 8,/t:zpfpitj shown in Fig. 8–40. Initially the rod is held in 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 engil2bg ;azdg 9i)a/5qto ne require tightening to a torque of 38 )gtl;/2oadiz5q b9a g $m \cdot N$ 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 4dbpww nnk)j 5; 6ao3rwhen the axis of rotation is through its center. w;r5wb jk 4)a odn63np   $kg \cdot m^2$

  Calculate the moment of h7kty ko0 mz0 v+5y6cainertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a ca+kmzc7v 6oyh0y0 5 tkombined 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 tt wo hakw87a/o j1c n1bt.rn u65s.hu8hin, light rod is rotated in a horizontal circlu bs85k.o/wh168cohut wj.aart7n1n e of 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’s wheel rotating at constant an31e-ii5y/yat0k yc mxgular speed (Fig. 8–42). The friction force between her/ki0eiyt3ma c y y51-x hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fig. 8–4+n(/h*tu rvjof9 vy0i,vl js63 abou(vj+nyvjuv6 9 lsi*0ro/,tf ht
(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 7ptv6y)njb6 nf 0nee 7o,e*lk 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, v6 abobwq -9-j.qdol(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 stead( qw --boj.q9bdol6vay 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 o4z o.o,plo80*e ehtwpf 8.50 cm and a mass of 0.580 kg 8e,otp0*h.z4lpo owe. 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, accelerattbh ho3771ln ting 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 taib 2gqq24e8f;v* fhwu d4bxo*ngentially 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 children (each with a mass of 25 kg) sit opposite each other on the edge. Calc2e4 og4q bx2i;*huvwf* 8 qfbdulate 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 iqfo.qn 50k; -o3pai29nmfeix s shut off and is eventually brought uniformly to rest by a frictional torque p5neoqaqf -2i03 .9oif mnx;kof 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 a9/;( deqa z9kdyi *asi 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 byzy9d-v e qx14w the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is acceleredwx4z qvy19 -ated 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 bf j zw1z2*,zljlade can be considered a long thin rod, as shown in Fig. 8–46. wzz l1*zj2jf ,
(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 consw fd2e/q e uq*f5,fnb*5h sbd,ists 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 fourzqaq6d m26 pq8 full turns (revolutions) and relea6qaq m8 zdp2q6ses it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor hak0 t3 y(ob,8rognb1e(f7n tous 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 a5vpckxpf1 evoo9 e2.f7 3 eg2(ddir1t 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 kg4 ts;0 x xbgubklm84l8 and radius 9.0 cm rolls without slipping down a lane a 8ktulgbxl m08 xb4;s4t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of-(:h6 v ygkjsc two terms, gyhv-ckj:6s (
(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 ofpqo 3dh 5hp0izkl: *;k 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? Ass 0:l k3z5p;di phhq*koume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls withouts1r4pg4fr l0wu30d9 v8c nw;j iu0pzo slipping d 1nzrd4iu0jgfpos4u 80 lw3;9r wp0cvown 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 balance+ dc)pqc5 s(9dloupcrzz3-c 5 d vertically on its tip. It starts to fall and its lower end does not 5uosc ) q(r5dd plc+c-cp39zzslip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg bal9dyf -yw8w8:qu3 rxb cl rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 8w -q wc3frb:8ydyxu 910.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momerd*0mb j a*3ztus.6l z jpu..0uf7kxxntum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpmz6lu x.sf.a7zux0u.j jpm*br*t0 d3 k?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his smhjh6,6-ml/3o y4i5 3pznr m6mspo gnide, 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 decreas 6ml hs5om33pzn4/n jro6gmim6-hp,yes 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 mz tdc8t5c 8jpx::( (qf5xu jzreduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she (jz5 :c8 pqfxc85xtuzd j( mt: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 spp n;smflt*+/jq mnv0;(3okqz in rotation rate from an initial rate of 1.0 rev0j(momnqv /; t*z p+s;3qlk fn every 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 aro - u;v7j4njd-bi wb i7, gje98v4ujgxyund a vertical axis through its 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, approximately shaped as a flat disk of radius 8.0 cm, onto the center ofuu4ve;,n77-x gijjg8 bj9db i vy-4jw the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentu 8purs8yp hrmkh 6 7l()jn(f)um of 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 the xtyd zspq8r,4r3;ew 6Earth
(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 diskj) lj 5dbtl (iaem5 3m0*9yfri of moment of inertia I is dropped onto an identical disk rotating atd(bm 9j*5fr3 ajli iml0)e y5t angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at +-amfad0jn k;ljs3ai 7r8p 7a2.4 $rev/s$ 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 sy/c:0rp* ix.1nmex rrtands at the center of a rotating merry-go-round platform of ra:x.c/ rm yi1rn0epxr* dius 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.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity , e j2.x9uun,idrxqt6 of 0.8 2i 6u,j9.n uxqr,e txd$rad/s$ 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 hu0kp t5,bsx1 t4 n-a1wtqd.iqalf its mass in the process, and winding up with a radius 1.tbqu1ait4, xk tsn w 0p.-dq510% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excessti4;wygy )* ed 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 9p 0mn/m9x ujaae9 io5(hn f6x$ 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, initialr:cxj 3 iqp(do/s 2j0uly at rest, that can rotate freely without frictio 0u djo3rxjs:/ci q2(pn. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at thov 1*c) kixa0de edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictkda)o i*0vx1 cionless 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 rolls on the ground zn)v(3lp j ,w,h3)mkt( esxsis/mia2with 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 wits v,nk()3)si2/ swjhxz imlma( 3 e,pthout 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 g zu9c-sz5torzh, -8f +b5fdr the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its ou+ -ob9szd85 fz5fc,hrzr-t g wn axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rehjpuv5 h+5( g1b o:p qy3ag8yoe1uwv:st 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 of a unif kk,eumr1d0f6+e knj (orm cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0,rk0m 6(u+ ke1 ejnkfd-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 cylindricaln zg(t8wok95 l disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) think(lt5g9zno w8 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-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the iok+l,:. tbxhr2o vnx 7v*v9g 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 tispr4cr8 vt r)x uxn*lwn6tx)1 d.wd0j9 p h8t5mes 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 19jrtwc6 vutxs8prr 1 4d* 5ld))w80x tnp .nhx1 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to us 1kmyxtx (h/:ke 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/k1xm :h y(xtk 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 an -c l8ubwd( / zzu5e/ko$H_2O$ 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=3.3 kwq:fem1xf s)h -+cd een2c:.$m/s$ 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 / hy-y x:c iw,na)wjwxe k8z43length 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. Awh4j3wziex 8, )/nkyya -wx:ct 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, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. Itqd8f/ed )/:uf)nnh js is standing vertically on the floor, and we wantdnjdqe : )n/f/uhs8 f) to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speem,o:clpc5 mfhtbe9qeoe 06--d v=4.2m/s on a flat road is making a turn with a radius -o :fpmo6- 0t,ec95hlq cmebe 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 1.54gm snpuof6fpq,1 (x2p l7nn* gf r0t4 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from? n fpofrx,qm*nt04(7g2 s4n f 1 6lupgp   $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thi6rcmqv5nv : hj8ac+s. n rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretch8mc.6r vavh s+5cj q:ned arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates,5;gjqhghs45 i m1k s*3q;3srvq f7xsz of * ;fqrqgss 7z;xv1hki 33sj sqh5 5m4gmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the loop9ydt2*9ri93 m5 up-gxcvvz czed rough track of Fig. 8–58. What is the minimum value of trzg yuz92i *39p5 mc9cd vx-tvhe vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do no3t2/ld1dkc +nwih85p bfag5 dt assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car .7hu- qaunvahy:4v. jreduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each 7 u-qvhahyj.4u va.:n 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