A bicycle odometer (which measures distance trkkjbj, x3 )p: n omk5*pv7mf/aaveled) is attached near the wheel hub and is designed for 27-inch wheels. What happexp:7j* oj kpmnk35f,b/ )kvm ans if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim h 00 wc7tzf)oecif8wy-lyg6j :ave radial and/or tangential acceleration? If the disk’s cy-f7ztg e l j6:fwc0)wo8y 0iangular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by5/78bx3nb iph 5bnewc a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a rl y qk6 npvjdkz/0-*,p)+ar-y djby7greater torque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands b/16 v*61 sdhb2md(g:r)w pzpadggq ghehind your head than whenagdw*s g:qbr)1gh md2( 1h6 zg 6/dpvp your arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets a7g1bw6gu. q d;ieap9 st the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large gb i7q9;wad6egups .1 front sprocket? Why?

Mammals that depend on being able toc;e:1-jo z6t kmkwsf7ldo,bej: yy 20 run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous2jfoy:,1:-0kb; jte cklw d ye mz7o6s.

Why do tightrope walkers (Fig. 8–35) carry 2hu892w nr nnwa long, narrow beam?

If the net force on a system is zero, is the net torque also zi qtn 3kp(ybl0)o)6br ero? If the net torque on a system is zero)otnyb0brk(pq3l6 i) , is the net force zero?

Two inclines have the 9 ) 2 cxgz:c+kxzij2gxsame 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 x zc2:)2 x9gcjxig kz+be greater? Explain.

Two solid spheres simxj.juju5.rdzklf) 5-7c.lylt6xg , qultaneously start rolling (from rest) down an incline. One sp)l7u rt6z.c xx.5fjdjj ly5,uk g-lq.here has twice the 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 starhh b*2a)7/gv1v0e mh 1fjz36s w7rib eemn+cet from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at/n)c7 fiehz e7v6v s0mhh1aeg wr*3 +2mejb b1 the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Ye cwwk9u8q2;cut most moving or rotating objects eventually slw;uq2wc ku8 c9ow down and stop. Explain.

If there were a great migration of people fmj(d -ttjk idt4 )q;/toward the Earth’s equator, how would this affect the length of th-k) tfmjtq 4(/jtidd;e day?

Can the diver of Fig. 8–29 do a somersault without having ang ))0cmbt n.d(og7b/a o2 drnhy initial rotation when she leave 0)br7n ggd2do.ctbo)a(/h nm s the board?

The moment of inertia of a rotating solid disk about an axis through it *me my)fn -g/)-dpklfs center of k)lm *n-y)de-p fmg/f 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 t/ q0bnf04ylx,yyxdcs.x ++ uv3e pa3 on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your ay.,fst+a0v+l b 0x/d3q4n xxyypue c 3ngular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one idf 5tecn/f(a*)c/p hqs hollow and the other is solid. Describe an experiment to dt *c adc/(ehn5) fp/qfetermine which is which.

The angular velocity of ai5hjglx z/1nd5+yxj/ wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasingghlz/ i1/5jx5 xdnjy + or decreasing?

Suppose you are standing onx6u)u0lj5pr tng5 o. n the edge of a large freely rotating turntable. What happens r0.xg6n5)lup o5ntu j if you walk toward the center?

A shortstop may leap into the air to catch :za6sv 8 ttkzmow9.qd6v7 i8da ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you loo6tsq78d zvkdtzi w8:o6mv 9. ak quickly 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 moy8c g, 1trlk06* apjtomentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can r8c*akt6o,1 ptgy 0l joperate to keep the helicopter stable.

  Express the following angles in radians: zznzj9 w5hm2 o1 v*t.ydi2bm5(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. Calculatet.9 *hi/gd awy, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earthtw 9gd/ia .y*h.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges ky(t4i3(l*qkce zy 2d akzi3tled*(ck4 (yq 2yt an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When t u*btw08)ltft he motor is turned off dufbu tl80w)tt *ring operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anotvv m8mho1n/)r*jh +d zher child. If the ball makes 15.0 revolutions, what is its diametej /)z hv8 nromm+v*dh1r?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions 5zpm esh. yy7)do the wheels mem7 y5yp)zhs.ake?    $rev$

  (a) A grinding wheel 0.35 m in d* q/j v:ct*jniiameter rotates at 2500 rpm. Calculate its angular velocitj c*j/v tiq:*ny 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 s (Fig. 8–3xc(.i u6lie gfvz2lm qs(441rwtg/1u; es nk88). (a) What is the linear speed oxklsgsg4nev;. 61z/(4m ucu21fi(8 q i rletwf 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) inje19ewuoc4d: its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of:p yo+g2p 5-wv21ussfjnib d7 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 c+:5 sppf9ywh nentrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an accel wpfhp5n9:+syeration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its cdw ;6rub2 ypoklt;f (2enter from 130 rpm to 280 rpm in 4.0lo pybud2k2tf(wr;6; 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 radius x x75pj8wx ;r jnh/ojmc3x+-wf/;lx l$R_1$ 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 Apollo spacecrafwzs 7pj8* a9skt 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 in w*kpzss7a8j9 terval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 r xz.4lkpkx( h(p3y+t4k ir tkl* p;e;bpm in 220 s. Through how many revolutions did it turn x + (b 3k t(pkkp;4*kyixh.rlpt;zle4in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. a+d(2rd 9ferdCalculate
(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 je sz.ua8 eu;wl iu +,wl n0ozb6e3fl*:*hdv(gdts in a whirling “human centrifuge,” which takes 1.0 min to turn throuvwz6iu o eefl 3bua.+,:lu*;8swg (zhdn l*0 dgh 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly fr r em2y3 t6x0:yjanp9gom 240 rpm to 360 rpm in 6.5 s. How far w erx0t2gnm36j: yy ap9ill a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it01 .yu iq1f t9d ozic+r8hy6mt is running at 850rev/min It turns 1500 revolutions beft9ortyifdz8m+0 q uhi6.1y 1 core 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 revolution,sz03 p 48;mqvayap pqef1b.hs as the car reduces its speed uniformly from 95km/h to 45km/h The tires aa p4y8ph10f3qm q. vpz,se b;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 b(l )a qgwoygz47p5 jd v73b,kits speed uniformly from 9oglb b7dpwya(43)k j7zv,5 gq5km/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 weightqiej9wy 2q2e o74p. uo lw5hp* on each pedal when climbing a hill.7eehu*q5w2yq9o p4pi2w olj. The 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 55a)ncnv5,6tv( ne d3vr N on the end of a door 74 cm wide. What is the magnitude of the tor)r( 3vn n entdvc56v,aque 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 ww lybu0aq acqz h82:3(heel shown in Fig. 8–39. Assume that a friction torque of 0.4y:q lau(z20 w8bhc q3a $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a masslesse3izo71t ipp- rod which pivots as shown in Fig. 8–40. Initially the rod is held in the h iezp1op -73tiorizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tighten:,p+sw; crvj+ci7uvuing to a torque of 38 cc+pj,7 s ;u uv+irv:w$m \cdot N$ 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 o1f4*9pt fyxu02ghicf bafylt w3ih aov5/0(8f a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its c0/ p2g b8y(cya h5w ui1l3t* 90hofxtfv4ff aienter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycl d ytt l151ipqav.q(1ze wheel 66.7 cm in diameter. The rim and 1t 1vqa yz.5q1l(pitdtire 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)uk97b-uks nocsh *-elzcs * , end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calc* s)9c,sh - o7uubzkkn*l-seculate
(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 bowlx(;ma f2h a9pfl yq;c2b 1nky1 on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction forl9p;h ;af nb2y2m11c(xkyfaqce 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 objects shown ca 1nctayp2;yci /(3xin Fig. 8–43 a;t2/1 acyxipyc( an3c bout
(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 2 ro:82vvxf.ze yk1rn8upxmwd ;7q(cis $5.3 \times10^{ -26}$ 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 spinq gngjlsj -;67yr0jpk9a6iu 2 ning 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 satelliirs2gy-qa9j0;nj ug 6p k67jlte is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cz5v 3xtyq2mlw, u5mt ;ylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calcul3 z,w5 umxm v2l;q5ttyate
(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 to 3 ,pu1y qfzo 8h8m vhxef3t ap757+hh /m$rev/s$ 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 andjx (kbdse;jf-i*nmhly 7;go ;i rp7* 1 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 rar -bif;(jjydpgk 1**; x7;eo snhi7mldius 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 dd)-;7tb(txxm33t: qbb qmz. (hopc b brought uniformly dbz(:t(q.ct xx )o3bq- btpdm m3;7bhto rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 ac+.s bs d84p/hy2fl howcelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, which 1dsov ( m9ude/rota9m ( 1odse/vudtes about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fi2lba4(4a qkdu g. 8–46 qk bl4ua(ad24.
(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 mafd l;v0dy ug kan7upaw+3*i89sses, $m_1$ 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 thehraurt )p-x(,3af 9 vrd lfm18 hammer from rest within four full turns (revolutions) and releases it at3vxt)18uf f- pr hrmr(, laad9 a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inert3ha7eg6*oqat6gr/ wl ia 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 ncx*z2ac;gxoxf0x*w s3wd() 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 rolls without slipping d5+ i t(pof;e hxnwvj. smr(:s.own a lane at 3(fs;i: xp.e( s+jnro5vh.wmt.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth w15 o3rlo *;4ruprszbwzci5 + tith respect to the Sun as the sum of tt*bzzowspuri;l 1+ r5o53 rc4wo terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much nhd5hp v iq30- +5hp6r0ac eqkdet work is required to accelerate pv0r dcq+ hqi5 - k36ha0dphe5it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from res hd-zwh3j3 k niyr3vs+p 8z9:rt and rolls without slipping dow3383zkz ri9hv nph-:wd y +jrsn 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 verty .nluxb9r11 gtdvj 12ically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper eynjx 11 rl91buv .2dgtnd 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 ball rotating on ;(uqgd7(dw* u iglf c0the end of a thin string in a circledu 70f((;gdu q *wcigl 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 clj,h cuyjw)g333oka61tnf ;gj 42ln n ylindrical grinding wheel of radius 1,j6lg yn4;ak j2j )lgu3nw fo331tch n8 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 at his side, on a platform that is vfixhbf:l/6b2f (z u 5rotating at a rate of 1.3rev/s If he raises his arms to a hor62 bhufbf 5ifl( /vz:xizontal 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 her moment(4gh)9idwx 1y 5 zlbnh3y+l ewbi+vf + of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rota il+4fgl1d++(h)bi5 ybv9hw xnezw3y tions in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial r3zkid7j y) 4lnate of 1.0 rev every 3 n47l ijdzyk)2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical i7k1dz, mz2agaxis 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 poti12d7zz a,mkgter 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 figure skater )rw*cnxj 4dg /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 momentucg 8)a s vnhg*.e0gcs(oxua0 lu:v-b/m of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindr0y1u.q;xeic 7 -+ct/ pcl/qq8lxs xhsical disk of moment of inertia I is dropped onto an identical disk rotatinx1y/ccl + .s78pu/x ic0sqtx- ;qqelh g at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.own2vnu- + uijp y0d,)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 aucho6v)06wac( d ix/ t rotating merry-go-round platform of radius 3.0 m and moment of/v c xd(6oucawt0 )6hi 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 wit38/44vjaqgs vpw koi7h an angular velocity of 0kow4g3vv7a jq / s48pi.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 coaww, fdrrwczp-q a. (ry)db*b 232+zzllapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate beafyzr2 d*zr +p.-a 2db3zw( bcwwqr) ,?(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 wio jer. nbk5gw/uw6lgh.z1;g8 nds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass j ,u4s thtk*um -x1iq zi-..bx$ 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 rotat/ c bd+4jsq,hke freely without friction. The mo/j k dsqh4bc,+ment 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 ofrwv3sz +np vj5pqn9 diuq+2++ a 6.5-m diameter merry-go-round turntable thatu+ +295pqz3rvd+vpsq+ nnij w is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the groundbfk 75vsm p4e3 with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What lengt pfk7bv3e5m 4sh 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 Earth. De343rzwbly*8ie , qtnye,ao ( gtermine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. 3tz,r ,nao 3g4 ely*bq8yiwe( (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from re xt.,rjhr0idp:va q4g+jf qm,l 53my /4p7ikrst 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 uniform cylinder of radius 0.20 mx6g/bi/oo7 lyy:uer1- n6jzyz:q)bb acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by t z/1ob6eyqyuni )yx :jl7bgr: ob/-6zhe motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg a0n 9vv x5u-vspnd diameteruv p0-59xvs nv 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-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 o wj5 p/3pbib4cf the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were rot+n tqnphf71/cs zpq//ating 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 c+f/ nqp/tz 1ns/phq 7is 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 use energy st ( *9r utnycydnvy33r(ored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”u cvn(3dnr9r 3y t(yy*
(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 le* 1vfwz34p1dxtdq9 $H_2O$ 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 sp2 - l 42cua08q plzj(gc1lxdkreed 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 lengthkz 7)+jjkvu3 i L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that thv u7i j)zk+jk3e 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 gnv 23(( e4 x-m1ddgcn zhwyi,standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a stepn i4(-3 x ewyd2, hmngg(vzd1c against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn wit *kmms8 wwmkee0ise,.r xnyeu6;- 7.qh a radius The forces acting on the cyclist an wk,m8 i sueee;m. -.km6q*swxy7er 0nd 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 )/ 403evzlcim z q+her1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating hmr/ze zlc0 +)e4vi3q it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater5ad8r7t ebjyo ;39 ve+qddt j*)ltm8j’s body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with armst8deq+)jd758ve l roy 3t9jma*d ;jb t held tightly against her body.   

  You are designing a clutch assemblqc+e;i) m/h;e*a0vdut(k qz ey which consists of two cylindrical plates, of mass k; m;cqt aedze(/+ihqv)*0 ue $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 x2clyey29t+h r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if2 eth2lycx 9y+ 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 assume 4 kl-voae wz1.1 idqlv1ztwn+a3-ha2 $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unyz-.gemdci-x6h-y /- z)vgse iformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a)g -/imy) d z6-x-egz-evh.sc y What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s