A bicycle odometer (which measures distance traveled) is x k, yrk72-9 mesjzjy6attached near the wheel hub and is designed for 27-inch wheels. What ,6 7xjjk9eskr 2y-zmy happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angu8z2i.g/a+ owh5 onehb,;akhz lar 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? Forzg/5 eha8 2 .wo ;ai,bknz+ohh which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of ) ,dhx6iftmhg d,s4.uthe angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than ajn3wz u2ph,h. 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 siwsv3 gqr/ vo+rw(v-qi bye7;2t-up with your hands behind your head than when your arms are stretch+(7s yro v3wbr- /qvv iwg;2eqed 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 p 31q1)xsko8xp o o:et(dqi i5h0fd5rnedal cranks. In which gear is it harder to 5 )fx5tod0s:kxr11(ope8qo d3qh iinpedal, 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 lowe30sdt r1 n.2bdv)i *e56/wxxe k2 esnevibur4r legs with flesh and muscle concentrated high, close to the b1d wse0 .v)e/x*bxn6e i24k stv3nrurbdie52ody (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkerc4s 5c ghrg* 1p/.mgays (Fig. 8–35) carry a long, narrow beam?

If the net force on abk y6i+bjh6d3x 8,c dp system is zero, is the net torque also zero? If the net torque on a system is zero, is the net force zerid cp836+bd6hkybx,j o?

Two inclines have the same height but qxh;a1us3 ms+y4 x*u zmake different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the q zs4uauhmxxs13;+ y* ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inclinem)b2rbs o31q p c0 dxcf)pk2r5. One sphere has twice the radius and twice the mass of the or)1sfbbo r d)k5 20x2 qp3pcmcther. 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 tp) qv.pkg5 jk(he same mass. They start from rest at the top of an incline. Which reapvp(k.k 5)j qgches 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.yyh5by .uyk6 -bzo td1wj,8*uvyra/ momentum are conserved. Yet most moving or rotating objects eventually slow down and6.yv/*,bykzt d81y hyawo. rubyu j-5 stop. Explain.

If there were a great migration o;ap,8une o)b h(tehn 8f people toward the Earth’s equator, how would this affect the length of the;nupt() 8h,beo neah 8 day?

Can the diver of Fig. 8–29w9b,w;-6nqive *.)r 5jtno7a txtxm sf hsf1 ; do a somersault without having any initial rotation when she leaves t j -sh mt,q5bfr;se.7tv xa fwwn6;oxn9i*1)the board?

The moment of inertia of a rotating solid disk about an axis throm2ba( ywcvz;hx 16w ww:kx4wc l60k* lugh its center 6wlxkw;ch10k4 6c( w*lyv x 2:bwwamz of mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstretix .lese)/e3tfyenh c()h,z :ched hand. If you suddenly drop t.3t ee)h(c/,xefsn)zi:l yhe he masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one igj0 /h9dj(kp/ wpg f.ws hollow and the other is solid. Describe an experiment to determine w phwfw/jpj( 90d/ gg.khich is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In7gu*4 cjymc.w 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 angular speecc m*u.y7w4j gd increasing or decreasing?

Suppose you are standing on the edge of a large freelyao,9*j7pmpl.u/uls ,pf- bg a rotating turntable. What happens ifl9bo*ajg-usl7.mp,p,a pf/ u you walk toward the center?

A shortstop may leap 6-i2ol( otdmq 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 l i2modqo(6t-that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation o87ewh fxv5fb2khzl -zf m ;)6ef angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the sf;8)z mf65- wkbh7vhl2fz ee xecond propeller can operate to keep the helicopter stable.

  Express the following ang zg*+p:7r: )m g*cuucekzz cw1les 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 aciao jxkr) 6y2 9 3rf3xn4zg;y;yyfbvp 6 e./ln amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moonyzvop3k9;2; j3b y y. f64)err6i nfyxl/xgac, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed5 e s e-z4jr,3qvxxw2v at the Moon, 380,000 km from Earth. The beam diverges at an anglexv ejws42rv e,5zx3 -q $\theta$ (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 gsd+ tnr4.nw.j5k t7i rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the bladd5nt +ns .gtjkrw4 7.ies slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another,-*(mzye50x y(a xkgfseg c,b child. If the ball makes 15.0 revolutionsgb (,( zxf ey-cgax*5k0yms ,e, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions don6gpb hmgig+;rgm ,92 the whemgn9p g2 ;mhg+,6i rbgels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter+z1cn1,) zmpm3gkjb z rotates at 2500 rpm. Calculate its angular velocit13bm kzc gn+pm )jz1z,y in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 slk7s 44gue.wz- h xu(cx 8j8ef (Fig. 8–38). (a) What is t 7 jc8s xwgeulxhu8(4-k. fez4he linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in 0imr/ p*tdp4uunnv6e(z z q,4its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a ) gcbf r0wvtl7*+; wifpoint
(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 cm7-0zxao 7hq-uixkcz0. l w2ol from the axis of rotation x zluloo07 qhc-z.7 -0iwkax2is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerate bd x,s:(/z(q(flmiwds uniformly about its center from 130 rpm to 280 rdlm( d(/b fw, siq:xz(pm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiuisp.f vt570 pq0b, ct/iw4eq as $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollhc .cg 4f yg/cw0we;;yo spacecraft put themselves into a slow rotation to distribute the Sun’c0wg eych;wyc.;4f/ gs 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 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 refg304db mu60vpw+sqp6rg ;y7 mz -loust to 15,000 rpm in 220 s. Through how many revolut3 p6y46uums+flov0 bzw7qm;pdr 0gg- ions did it turn in this time?    $rev$

  An automobile enginelk /ny1vmdv : l5frc;/uo)g 3t slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying him m)apnlw:dbb(f(7v7 ghspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutiofm: 7mv(7np bl(wbd )ans 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 unifo*ii0z2 ,6bpz 8pwi vs* cge.0ewc5u rxrmly from 240 rpm to 360 rpm in 6.5 s. How far will a point rp .b v8iizxc* *0,60iuzg5epsww ce2on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runningqtw6+0 cl:8a o;cbbwht*) jrn at 850rev/min It turns 1500 revolutions befc+w8lt hbqa ; :njt ocrw06*b)ore it 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 redu5n 8 eqtvlc)ma7 y)g5nces its speed uniformly from 95km/h to 45km/h The ag n y57ecq)5)nvml8t 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 v4jl)2dd,yv+2lj myrg.:yw nspeed uniformly from 95l2:,d.mjygjw 2rd +) vl n4vyykm/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal u9p c0hw180pl 2 asfx9ytke* owhen climbing a hill. The pedals rotate in a circle8 *oxu1k pl w09yf 20chtesp9a 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 ofmz2pk. 4uq ex- a door 74 cm wide. What is the magnitude 2x4-puze q.kmof 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 wheel shown in Fig.)prs9s h6lqv 1 8–39. Assume that a fr)1h6vsl ps9r qiction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attachebg q 7e5alr/f-xd8/oh d 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 released. Calculx5go b q//hlre-8 da7fate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightenin epps)i 99o.jhg to a torque of 38 9i pso)phej.9 $m \cdot N$ 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 mlwi2vz ,d+m. (kukhh ( when the axis of(hhi.ul v ,zmk+w2d(k rotation is through its center.    $kg \cdot m^2$

  Calculate the momentiy2-fgj mw* ,drd-6 bhaq*eh, of inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The ma6fm ,qdab hw- ey2*-igjdr* h,ss 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 v3 w:xq;zx 3sthorizontal circle of ra3w3 s:xqv t;xzdius 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 pln jw*.5*xgr f ow.jj/bb1+x a potter’s wheel rotating at constant angular speed (Fig. 8–42).woj5 j./l*xj fbr nwxgp*b+.1 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 of inertia of the array of point objectssc9m bz60tc rc f2gjd404u a7e agac2; shown in Fig. 8–43abfgsc2c0 ;ua g6ezt2jr m04 794acdc 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 atoms whose total mass im0wc(0 owtc6 cj7 t7n bl 7xq2uw:adf:s $5.3 \times10^{ -26}$ 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 k+y(l u v :tcuf9bc/o;c(sf,fsatellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 36:y9 sl ktoc v /;bfc(fuf,+uc(00 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniforg slg-8ms8 bw9/dav5rps7oi;m cylinder with a radius of 8.50 cm and a mass of 0.i 75 o asw;d-p8vmrb9g8 slgs/580 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest -us,ao:u ku,rvzj 7r3 to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and is able4vzwid0 ;moe*+jr emo k;, un9 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 require;du onm r;m*i+ w4ok0,jev 9zed to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating e)0a*6 8qvh(mak obdt at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictionae6a *(v8q) bkdmoha t0l 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 ball -h *jjgjrh8 g1gy9d 5hat 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 solepncrh8tio- 8*ly by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated un88 chi*rno-t piformly 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 cckb hv-u.c0uy *9d2 aktyjb 5;onsidered a long thin rod, as shown in Fig. 8–46.0kh 2 *dy .9;b-ujtyacbv5kcu
(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 uax *gpsb+5 ,lsmiz30bs qd2(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 four f o0+1w;j8.jep.g gmfgrsn8dlull turns (revolutions) and releases it at a spg +ew0fj 1.so8rp j.g;nd8glmeed 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 momenp lp17 i5bg ddg9wm4+xt of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 2807s.l vps f3tq0 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radib m( 8zzys5v7 mt)b iayo:or7ji3+nx4us 9.0 cm rolls without slipping down a lane at 3.3)vz 8s3nxtb zyyo4bir m7(7j+ :oa5mi $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with res 1gx 1bnh+ aylu(wp*w.pect to the Sun as the sum of two term1+lb auwwg1h .p* ny(xs,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7rl x0eehiw 99q5mdw; 9.50 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 iswd95e9m r qxhi;e 9lw0 a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest andgqov) del, :: fo:qu*y rolls without slipping dow*q :yqvodu,l: o)fe:gn 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 anc ljr0( 8bgxe4d its lower end does not slip. What will be the speed of the upper end of the pole just before it hits th j (ebl08r4cgxe ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotav/ eg)v;jk7elting on the end of a thin string in a circle of radius 1.10 m at an angula; /levvkg 7je)r speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheel; ;3h:rdrv/ fm *wjeik of radius 18 cm w/fr ek;:r*i;3dj hvm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a rate o :r*lhz,ma w:;gpa/fzf 1.3rev/s If he raises his arm wgmfa:l:p, ha r/z;z*s to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce hebr/rkl ygpc6rv,:9j i 6 tdt52r moment 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 positi 9rrrg:kt,l6j py t2icd/6v5bon, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin d) qmk zxwcui-z9 k(;1rotation rate from an initial rate of 1.0 rev every 2.)-m dc kqiu1;x(zz9kw0 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 throug)ljg sukng7uze91 z:/h 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, g1/:z gu nsuz97klje)onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater;fif olcx:j a.fs bx+ )z(vl86 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 Eart vy32t t2j5fvj6a1 fhnh
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia hvqgb6vkogi dgszs)5.1 v) .-I is dropped onto an identical disk rotating atvovih gsqkz).6sg) d1b- vg.5 angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 24u vclo*ps n*0.4 $rev/s$ 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 9p(f3ut:e i6*odxd 0j6aok 1szcuj h+stands at the center of a rotating merry-go-round platform of radius 3.0 m ju x jpdiho166eo0u3+(* akcs 9dtz:f 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 freehr,6jpqduunwr l1*); r:fef i93 lm g*ly with an angular velocity of 0.wmfurdi pj*6 3* ;hqne9 ruf1l:) rgl,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 white dwarf, losing abou+mghs-x,uuk7l t+m7kkudu .:t half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries am.hs+udm7kg-x :u l7+tu,ukkway 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 e v(bfby/uy 59sob/to5ap) q4excess 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 mg-7xj8 wzzl* $ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freel.q ldt7)fih/q - .hmqr0ut9jey without friction. Tj mt.rq./ i7hud )-fq tq09helhe 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 the edge of a 6.5-m diameter7c)l0c brhwh1 merry-go-round turntable that is mounted on f)hc10lc 7 brwhrictionless 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 with the end of the rope lying on x ,deq1q*hz:7*fdag/ ll*ztb 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 person7 a/* e*dfqbzdxhql ,zg 1*tl: without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Ear j0*f*gc.mxreth such that the same side always faces 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 particle orbi. x0m*er cgf*jting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rat v ccpzi::aj58kp j8a+e 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 uni63g;2p ysxparform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s xrp6;ys32 agpinterval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.0508k/( / jl-. wjssjonkoda7 ;jb kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hjk/;j7 bs.o8 o/j (ns-jwkld aub 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 rea2dcp +n( pv0ib;o1 iiwr 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 tiemeet1cfl ) jwam-; j/fc1 5h-mes 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 that the lost mass-ec)fjt 1hc -e m;5m j/elfa1w carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution asib+f-9p0piey52yhrm . oku/5j z4svutomobile 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 ps zm/oshe i505r -yu b4pj9 fvyi2k+.uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an vw7kd ss)8gz-) . s(q2uinont$H_2O$ 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 horizontt3vw5v 0sdn y7al surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignoreyfb kse1 do4o*m+75yr 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 y+r 5f1 kodmbe 4osy7*the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor,5j)s7ctb5*uorc,a i t and we want 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 he, at)cui5so jtrc57b*ight h, where h

  A bicyclist traveling with speed v=4.2m lvrz1h; -; 4hxvlzx;t/s on a flat road is making a turn with a radius The forces acting on the c1lxv;v h;-;t h4xzzlryclist 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 b5ol b3yle v.6uca d:3into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque requbl y .lcvu3a35bode6:ired 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 thin rods, maki1l4w. biwgq +sfo+g:ing reasonable estimates for the dimensions. Then calculate the ratio ofof4wi+ g: giqwl.s+1b the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of )0ip 5s4*-6pfbbykuk fd9 h gjtwo cylindrical plates, of ma hfp 69ibkspd )jf k*g40b5uy-ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 looped rouj 5a:vc g (q1d vc3ahcdpen/w.td4m*:gh track of Fig. 8–58. What is the minimum valued(q g14pd*5jh ceaa cvd:mt vw:/.3nc of the 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 not a ,9qwhra k h8xqf:y8p(ssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as 3 uml0m,m oe,u4tyv,uthe car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was l0,t yov,3mu 4uumem,the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s