A bicycle odometer (which measures distance traveled) is attached b -fquij n291wqj:pb 0*goh1nnear the wheel hub and is designed for 27-inch wheels. What happens if you use it on a j qiqujwpn nbh1*:b02 fo-1g9 bicycle with 24-inch wheels?

Suppose a disk rotates at constant angulaui1vn*eg i7ynk/a5 g5ky578t sana5 sr velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocita8say u7/g 51s* k5 5intvne7yan5kg iy increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of thetm7nk a0g2bl: angular velocity $\omega$ Explain.

Can a small force ever exert a greater tor.ao0ppytn9k jq fq 3rk6b:0x 4que than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head thaydxf u2+t( k t37l oojxdxq/*-.sa)p bn when your arms are stretched out in front of you? A diagram may help you to answer thix a.(ul s/qko-2o*3bp+txtd )j7f dyx s.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pedaerl( f.jw63c4dcv i m7-e,uxfl 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 tfw 3eui(j-6cr7v le df.cxm,4o pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have a9r6 sev 3 ;kf; gy;atz7sr(qeslender 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 izs;;3sk r y6eaet7 (f9rv a;qgs advantageous.

Why do tightrope walkers (Fig.oy1gm3pr wc:.w)(yq*7fv r ng 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero ni fh) +c1vpgb8gje8+6hr vc.d7z2gs? If the net torque on a system is zero, is the rzhc8h+dj17f) ginv2c6e vg+ sb8g. pnet force zero?

Two inclines have the same height but make different angles with the horizontajjpc ;tf.4f ,x7pryu2l:v s1, qmkg/cb 4ai7yl. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greatesl jf7mgqk;4,tjiy uyf7c x p:p4, 2a/r1v.bcr? Explain.

Two solid spheres simultaneouuotvz(1z1a ,l*6+w hbr l;f6ky4kh+u e9epc n sly start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bot6 vlt6 eb1w;u h*4h zf1e9c( ++uzyn lop,kkratom?

A sphere and a cylinder have the same radiul;tp3f fmjr,bx-v /9p s and the same mass. They start from rest at the top of an incline. Which reachesl-x mjbf/3 vr;ppf9,t the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most mvgd/ mnf*/hi7gx2z 8 qoving or rotating objectshq/ *xni/78gd zf2gmv eventually slow down and stop. Explain.

If there were a great migration of people tol pb.v /o35zptward the Earth’s equator, how would this affec b53p.tvl pz/ot the length of the day?

Can the diver of Fig. srpsj)vfnm- e6 9wk*:k)b3hs8–29 do a somersault without having any initial rotation when she l 3r)ef6b)-9j hsmp*skn:wkvs eaves the board?

The moment of inertia of a rotati7z nfi+h; oju6ng solid disk about an axis through its center of mahu7o+n jz fi6;ss 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 0k31hjpit u67iyph: g on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masy0i upi13jpkt g7h6h: ses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, on0 nr1: -4b0ny9x1obfvw wwwtae is hollow and the other is solid. Describe an experiment to detet-yrv0w a1fwb94:wn ox0 b1wnrmine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. 7wzy -:4sfd d8mq//f ef0hcjt In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points eascm zhfs j fd0w4:-/eyt8d7f/qt, 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 k+cot:cg2* nia large freely rotating turntable. What happens if you wal*cctg :in2+okk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he:te k*y29 s 2j/trryoa throws the ball, srat/yytj:e*ko 9 2r2the upper part of his body rotates. 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 of conservation t p/m(72qdicy;1l bayof angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keqd/aiyp; 7 2yt(cml1 bep the helicopter stable.

  Express the following angles in radians: (a) 1et,)m tj5; zbugcny830 $^{\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 co c:se: -cuk:lz4pb5betd/0rbincidence. Calculate, using the inbrck:sepb-ed 40u zcl5t::/bformation inside the Front Cover, the angular diameters (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)8bcn3a vox/d5fi0yr Earth. The beam diverges at an x vc38 fiobna/d0r)y5 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 the motor is turned i/+n-g jrarm*ccy )a) 9i6, k0ai mxaeoff during operation, the blades slow to rest in 3.0 s. What is the angular accelerati-ca*ai i,xara/)riymj)c k g609n e+mon as the blades slow down?    $rad/s^2$

  A child rolls a ball 9-khsta 1e*mn :/tbgy on a level floor 3.5 m to another child. If the ball makes 15.0n /s9 :ytm1hgkeat b-* revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in d6ud)f+d,fp hv iameter travels 8.0 km. How many revolutions do the wheeddpf +vu6f),hls make?    $rev$

  (a) A grinding wheel 0.35 m in diameter ros kryjh 6gg4- *ydb.;states at 2500 rpm. Calculate its angular velg;gbdjshyk- r.y6* s4 ocity 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 l h.7mg,use. hrevolution in 4.0 s (Fig. 8–38). (a) What is the lineah ue.gmls, h.7r 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 (ams.//y2sv ,0jb ddncc 5fr4la) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ozrvn-9dkr)q )04m-mput ct(h1 to y1 sf 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 cent* f h9q r4ot(avg376k 2kfry:ny0wfooe)u*v drifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an accelerew dnh*y96yvu3(o k47vg:rfoo* t )ak2qf0fration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheuf6b f6jdl)bmwu pe z4*+gkq52z)e26j7qiq iel accelerates uniformly about its center from 130 rpm to 280 rpm)wlq j k jeq i2ui7z5q)6fp66*z4bd2bguf+ em 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 radiumbd+ t 0;q.bkds $R_1$ 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 spacecraft put themsc oozen 5(,(ykelves 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 revcoo(5(, kynezolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 22y3n8i/bwuj4kz aeo- k+ry bx vx*2,:e0 s. Through how many r2 , ebn/j y*zvwk4yb+k xeiu3o-x a:8revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1201 iqp:u)mulp9ajq (j10 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 streu .f y*ot-tp/zd4*r)u3vbz zvsses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to tvu 4 byr-)puf/3zv*t*d.zzo 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 uniformly fr wva7dn* x217jvbj9wbr.cyym, g7d s/om 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel hy/cb.7bdr7,mw7ywxgja n1v djs*9 2 vave traveled in this time?    m

  A cooling fan is turned off when it is running at f ow95s /g/yzlhw e+y(850rev/min It turns 1500 revolutions before it comes to yyfzes l o+(wwg//5h9a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed pu4 * )mwod5qfuniformly from 95km/h to 45km/h The tires hm)q w4 f*opud5ave 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 car48 p 4-axzcitzq2kn:31kp z9azmo5f h reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of z 81tz o fzqp 5ca9h344:ikmx-2k npaz0.80 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 wrtu(7 roari- /eight on each pedal when climbing a hill. The pedals rotate in a circle 7/ ourat rri-(of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is the magi+yspr 1 z+m11 pz( lvsba.o(xnitude of the torque if the for+p(o1z11 xi slyprbvza.+ms(ce 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. sv)jxivlf09a6,*a bw dx c8g38–39. Assume thfv la6ivbwx g*8 x3 0a)dc9,jsat a friction 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 ends of a massless ro; (kfxky,d(pud0j ui: d which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and t:k(xpd0;,ku(u j i fdyhen released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of aneg v7mf9tfx )nt5m hrp4pv+.) engine require tightening to a torque of 38. mffh 5t7vm) png xrvte94+)p $m \cdot N$ 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 os*st o:-(gi+m pcfx xld(py+ 8f a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its sis:ftlc yg(po+mx -+8 x*(d pcenter.    $kg \cdot m^2$

  Calculate the moment of inertia of awn (1bi1cww0b bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (wh(w01bwi c1nbwy?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is 7vlufa. f3t:)cl 6+:gmyyyk b rotated in a horizontal circle gumk.+7b 3v l)y:tfy6c:la yfof 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 rotagn2yl.( i tsrcb.xm5 :ting at constant angular speed (Fig. 8–42). The frictioim.bl:r.ns(2cgy x t5 n 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 objects shown k7ol7msq 0( rxin Fig. 8–43 abo 77 q0rsmk(xlout
(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 w- q 6 cjdzm9qk-t-gcd21-fjszb ryt:8a 7/nne hose 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, eng ufg:r5(wx0gj9q6k qk ineers fire four tangential roc6(ugq :0fk9gxrjwk5 q kets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform 0f+iire 0kub ;cylinder with a radius of 8.50 cm and a mass of 0.580 kb r iui;kef0+0g. 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 iw;;t /aymfu-owtfw 4 6;wkzrj1ai)6 n t 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 tanl+t4) 3niicrro )4wc) dil0f5yarjt 4gentially 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 c3yfcwidc n r))4+r)irijlot 0a54l 4thildren (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 eventvko2u0ufo7 07ziwgf1 yi6k ( aually brought uniformfugki6f(k1 2oy 7z 0vow0iua7ly to 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 accelerabu1p -+e :yb1xoh fo7vtes 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 fk z-:y/iy.yi eorearm, which rotates about the elbow joint under the action of the triceps mus:ey iik./y yz-cle, 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 tpsp5: bdh74,oe.:heqyvwih .hin rod, as shown in Fig. 8–46.qsb.wp.ho:ye57 d:h4hv e,ip
(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 consistzh6-- jp hdin(s 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 i60cqfj; 9uf0yyyz6uthe hammer from rest within four full turns (revolutions) andfqj y6yu9fy u0z06;ci releases 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 has a mdf zo: c,6scnm8;mi3x pf2q-doment 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 toi. 3*z k5ixv gfcds+zoz u7j*8rque 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 ranl0ehapbcxk xzuq p( 61a26qqsqn; +-7pc6 7gdius 9.0 cm rolls without slipping down a lane ahac(7nqup61ep-06z l+7;nqx xq 6c b2g qpskat 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun6 nyb3c) :fx)mml n:v22s oxew as the sum of two terms,:m3xfnlmn 6s 2) v )wbcox2ye:
(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 net wmety8 k74 m+zj)ncw* cork w t 8*yjcm+)74kze cmnis required to accelerate it 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 svt8 haj2grd5;)b kbz+ tarts from rest and rolls without slippi5h8rg2tjda vb +k);zbng down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It sti4nl b t2s4g+scaef79arts to fall and its lower end does not slip. What will be the speed of the uplsnefi c7b 42st4a+g9per 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 ball rotating on the end o2uaiy s:h l.0b-fwx0af a thin string in a circle of radius 1.10 m at an anhxa .0-0alw:ysu2ibf gular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular mome hyus*a h4x1s2ntum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when r sh*s1yh2 axu4otating 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 1jzqb ,vftb.xk 3 l q1.a(*pxnrotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. qt ,n 3 (jqkzfa1.vl1p .xx*bb8–48, 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 of inmm9 u5 6y qk*0,zhd.upqkm7)ft t 5tzkertia by a factor dh k7 5mkqut6y)q upz*.mz9 50 mtkf,tof about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can inctjgyfbz: 3epk2f3e 7 ;rease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a fina;et32 e:kjf fp3ygzb 7l rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its ce6l*z8q17j/ mi:cryt g+fpm gq yc11dtnter 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, onzcmt: 8r/ q17tp6l +mij1d1yggqy cf*to 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 figur(v0l.gbvteg o4v2+q ckuid/ 5e 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 th 8j j+ddq*6dnze Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of mome:q/c b (y p.zusb8(xom*2r+ jrq8rvpent of inertia I is dropped onto an identical disk .2bcj uropm8sye*r((:zvqbxp r8q / + rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4ivz /w1r7it.uci5d 4 y $rev/s$ 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 at1yi 2:;wob l0g;ij ythe center of a rotating merry-go-round platform of raiaotw j:10;l2gby; yidius 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 an7p w.xujep uv ftc2(27jywyev ,):7 shgular velocity of 02hv: 7 ycstp (j7evxuu2,.wef)wpy7j.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 about half its mt-te 7,em) pnpassm7eett n,pp)- 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 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 excess of 1 yds+yo73.mmekfi chto7s91:20 $km/h$ 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 vstpwu8f9bxvfvrsp3 h f27 /yt/ 4r20$ 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 a xj+y;p9 kzos -6hyhm+t rest, that can rotate freely without friction. The moment of inertia of the person plus hy+-mo 9 6+jhxypk;sz 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 diameter merry-0;m miuiljbj,5oo( cr/-uhp* go-round turntable that is mounted on fricti;iomuju0or/m(,5 *b hlj-c pionless 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 lyings*+ez;- adj q.iln: wg on the ela;d j zs:+n-w.qig*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 length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the sajq 4: jmsiq4l4me side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own444jqiq:jms l 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 rest at a rate ofsgy1 ; n-y5 fwxkdk16y 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* 6b m z5kitfdl.myde 1m+*nm4 cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constantz t+f1de . mmmyni6dlk4b5m** angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two 6sm2 pdfh5w o6kmz .k-solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released frok-.2d pzmfs5w6koh6mm rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, howvemyzxfnkt5h ;y:+ + 6 is the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the s9 n)pl7deqcn8* oeaf8ize of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 1npqd c e87e89 *)aofln2 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 carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stored n4-dqdx dhy8( in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindricad y4qd(dxh8 -nl 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 xa;.f(h xkk(u an $H_2O$ 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 vu occq6 3esx3h+q4 m,r=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 ignore fricteksct5yhfk p*. a k d29r;6y0iion) about a hinge attacep9 a; k02sc i 5rt.dhk6k*fyyhed to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radiugonqm-;b lvkoto+ ( 7/s R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so tha;bv /( g-kotqlo+7n mot it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2utevhap3 0( p(m/s on a flat road is making a turn with a radius (a3hvp(0tue p 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 l(3 f,sjtuk 4d)qmy p5of length 1.5 m and begins whirling the rock in a nearly hor)d(,m4uyj sqf3 p 5ktlizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her ar)d d37zb brmx:ms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretcherb) 3:md7 xzdbd arms, and with arms held tightly against her body.   

  You are designing a clutch f3ll s)z f8ba(e a6+ -ywzfmnv7au 55tassembly which consists of two cylindrical plates, of ma-e 8sa 67zutm az )lvlw+f5yf5n3a fb(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 radx1 vo xk6jj*uqsh9,3eius 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 if it is to reach the highest point 9jqo ,xueh1j6xs3k *vof the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not a:z el2g+ :svxissume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spe3/ej2iizo 8.m /emxwqed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the aq mx .8i/eie jowz2m3/ngular 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