A bicycle odometer (which measures distance tricdp l nerto+.q:j63 -aveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it-der 6qnc tpjo:3+i. l on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular ilvd;w0x 7guo hmx3u)h 5;2htvelocity. Does a point on the rim have radial and/or tangentihx iu5v3)xt hm g702 ;;wolduhal acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be kr9)v 0ibmp 0oc5,. l tv d5o4x0tyzsxdescribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force?ulmn1w:-k u6x mhiw,:agt f5) 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 behih vu/qq waw mb0h:,by;8x2(v7zxntt1nd your head than when your arms are stretched out in front of you? A diagram may help you to answer qvu21xzxt:y;qw,0b8(h7hnv tbma / wthis.

A 21-speed bicycle has seven sprockets at the rear wheel and three85vc,h4ix ez y ub/a5g at the pedal cranks.uev hz4 xi8 5b/yg,ca5 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 front sprocket? Why?

Mammals that depend on being able to run fas59 toj kcfs(9t (my1s61venj zt have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dyz om5t6vj ts9(kc(sn11j fy9e namics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) ca isxk,1r q9c6brry a long, narrow beam?

If the net force on a system fy c +( (,82txre-locgg)qaqo is zero, is the net torque also zero? If the net torque c)a gtl,(2-y+qq f (xg orco8eon a system is zero, is the net force zero?

Two inclines have the same height but make diffef m-gnx e*:wu cj5g53nrent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will thxjm 3wg5uc:n 5-eg*fne speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down a* bf*akd ;zd:fx;d +jtn incline. One daj;b;: *f+d*kd zt fxsphere 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 m v: (oi1sbjow(/kxq;)dr iuv3 ass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the grea(1ur w/db (voji:q)vo;3iks xter total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and an+ct;ta(:a rg pv ol +qsez:44fgular momentum are conserved. Yet most moving or rotating objects ae;ls:(q +f 4cpagtv+o 4tzr:eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equa- fp) )bp)6shlkzw9u 2zepsn*tor, how would this af*phnwsl)z6fb 9k2 ) -p)szepufect the length of the day?

Can the diver of Fig. 8–29 do a somersault wm t8b/yfi:m pk,7xv/- k)xi nuithout having any initial rotation whx7mm8:/in, ti /px k)bky-fvuen she leaves the board?

The moment of inertia of a rotating solid di bb 2pm5k2y.y hgml6(rsk about an axis through its center of yh25r(lm gp2m6 .kybbmass 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 j(xr .d ,f,d9wandoo4rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity incrdd49xj( ,, w.fr nooadease, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hnlme: dqbijti( 2wlljr 13/* 9ollow and the other is sol ln(2id3/9e* :mtjwl1ibrqjl id. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a hori/ r :uvwdtb1tbw3 fe.b wee:6 cs-,8sdzontal 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 increwbrusf 3,wc wed: bb 8e e:d/1stv.t-6asing or decreasing?

Suppose you are standing on the edge of a lagf*i ddd--* ,ei v. neto.-n3f- 6 xg7lgbnwxmrge freely rotating turntable. What happens if you walk toward the go-. mbf6i dvgd,n3f-gi*nx w*7xeen-ld. - tcenter?

A shortstop may leap nrj /khtx jr-c*9tl v2cv:h.5h ,ja)tinto 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 that his hips and legs rotate in the opposite direction (Fig. 8–36rnt cj/ 2 .)5ltjhk- xjh :h*,ravt9cv). Explain.

On the basis of the law of conservation olu avi35-bocvv 1 pk-0f angular momentum, discuss why a helico bvup0l-c vk-a15 3iovpter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following ang6 a8-ipf . wcnu/yd,9axy2frh les in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, usineoqvd gv4 (2c;vu1cp)g the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon,;v2d41vo p eq cgu()cv as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Eal: m8. /q8n bdotss3eprth. The beam diverges at a/m:p8e.sdq sn3blo8t n 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 mo sh/px 9qokj9 9c.qk5ltor is turned off during operation, the blades slow tokk9 js hp qxol99cq/5. 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 lef5pyuu* z huw-;3:(xz-ucy cd vel floor 3.5 m to another child. If the ball makes 15.0 revol hzp5;cu c3-z(uxufyu* w-d:yutions, what is its diameter?    m

  A bicycle with tires 68 cm in dia+k7g4vvrjn7 7y zw/:wy ia6bymeter travels 8.0 km. How many revolutions do the wheels makzvyyv7y + g6 b/wrak4w7:nij7e?    $rev$

  (a) A grinding wheel 0.35 m in dl76go/k qix*s iameter rotates at 2500 rpm. Calculate its angular velocity il qxi*g 7/sk6on $rad/s$ $\omega$ =    $rad/sec$
(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 revodw0 1aj4yd/ql gqv g0jfy(8-jlution in 4.0 s (Fig. 8–38). (a) Whatg j jyfy4d/gv(a 0l0dqq-1 8jw is the 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 0,dnumla9v 5 vEarth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sb gq1oqymqdk :+)f,f /peed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a partic8arbd/- ix0j sj4.:i yfdmx -dle 7.0 cm from the axis of rotation is to experiexxj s4 id--m0aidbj.dfy:r 8/nce an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from(5agrafkexz2gl6 3 -mi- t ka6 130 rpm to 280 rpita5( e-xlg6 ka32 gfrkaz6-m m 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 radiusgwl3lfxr a/y1tfhsj8y8hbw1ru: ( hr75(fq 4 $R_1$ 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 Moo0uo)pov1qu+ysv 6kr9 n, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.osvuyv6kr91)0p+uqo 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 acceler cyrv/4v5f: c/ r.vwi+nxj2lvates uniformly from rest to 15,000 rpm in 220 s. Through how mal+fx/yr2v:/iv 4rwnvc .v5c jny revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate4mp6(k8d8 uc tj6 rk12/ontpaguhf+9qxnw0 n
(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 ;cpbl4vj tuum,em.9/, ytt /o-ix8ddthe stresses of flying highspeed jets in a whirling “hum9j8 upmt,db t,d.uxl i;o- 4t/v/yceman centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates 4.rus6po ) qxoceeoo1;5x; xiuniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time; ui.)oo1sc6;oxx45oxep re q?    m

  A cooling fan is turned off when it is running at 850rev/min Isg21n a6rjt jx0jb;,-vgmx q4t turns 1500 revolutions before it com0j4jx6; qgg1sajtvbr-x, 2m nes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniform3pzk3t f* -+g :f5aoclv;rd bsly frdp3;g -z*a3b5 vfrl:fco+kst om 95km/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

  The tires of a car make 65 *s yiq/j)liy,gdo x; 8revolutions as the car reduces its speed uniformly from 95km/h to 45km/h Tyg)*j8sdy;o li,iq /x he 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 pup5gzbwraj7 l20k( ts 4 ) 4vb+uhwimo/ts all her weight on each pedal when climbing a hill. The pedak )4g(jb lta+240pv /zw7wihrbo us5m ls 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 forcev+tsdro pp75y0ijw5 ;-t q9 qm of 55 N on the end of a door 74 cm wide. What is the magnitude of the torquy o9p-t0+i vwm5 tqsqr7j 5d;pe 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 torq(m.l utk.zd0 iue about the axle of the wheel shown in Fig. 8–39. Assume klzu(. . dtim0that 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 o-t88c uwgk i5j9+b 1 j. zmlru8qiwv;ends of a massless rod which pivots as shown in Fig. 8–8t8+uvbu.9q1;o rjjw milgwi 5- 8c kz40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tigh ,h;l lr: lebe(nw5-qctening to a torque of 38elq l:nw-r5lb; (,ec h $m \cdot N$ 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 sp9,q q5ld.yux+klvmf+) yi ss +w4gc9 phere of radius 0.648 m when the axis of row v.ys +fq+ 9)ylqdigks+4uplm5c9x,tation is through its center.    $kg \cdot m^2$

  Calculate the moment 5 ba pv:wu(o5zz).nufof inertia of a bicycle wheel 66.7 cm in diameter. The rim and tiz.5 vf :ob5 )uuzw(panre have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light3p+xyv;z7zipq+ 8evl6mxy ,q rod is rotated in a horizontal circle of radius 1.2 m. Cal vxz86 ylq vm,yx+7+p3iz;pq eculate
(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 sc+y41q ehz) hwheel rotating at constant angular speed (Fig. 8–42). The frict41z c+ eh)sqyhion 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 objects6ou9yltq/w tf/*x1nwj9 k +py shown in Fig. 8–43 19//wy twyo9 k*f+nqj6ult xpabout
(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 f-9r ; 7hf 9kv-us* uz5a-vb5olw)ernjti8zhmass 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, engqyic yoe ;)a1u vx1w8:ineers 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 satei8 ;c )wy1oayx1:equvllite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm andz uvs.2yx7s dqextdj*p(i 6)3 a mass of 0.580 kg. qusv*) ixxz. s 2(6edt3yd7 jpCalculate
(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 4;v ein ,f45 rlrp,kkkfrom rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-roundz cs,vd3;)k7wsoyo)z8n+x6 . bdnxrl and is able to accelek r w8nnzvy s3z)xsbo.dd;7 ),+6 olcxrate 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 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 eventuahg*f+ e ;p/murk69a pdlly brought uniformly to rest by a ah/k ;rg*fm+ e 6p9updfrictional 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-j m(rz w4;pfm -f0cb3kkg 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 /)ei.7. ijappjekb836 vix m,pk ph2g is thrown solely by the action of the forearm, which j.ei7pi, 3kehig a p2v/8pbx)m6kj. protates 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 Fig. p3n8g287r y+wptlqld 9r0iyy 8–46 yw2 rrlni 089d+8gyytplq7 p3.
(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 td m+.+ k98b nuxl:i6cfnv8dbdt.ac 0kwo 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 acc bd kcar6m93x1elerates the hammer from rest within four full turns (revol1mxcb39d6r akutions) and 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 moment ox s;hy(ohz;y+f 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 torqfyj n(28.5c y zp/rwv fdzn*c-ue 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 dow 2e ;3n2htzz ncx(*kytn a lanetenk2hy*nt;(3c zx z2 at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun a jq4rfiw5z,/r* 5p sdss the sum of t5* 4wzd/5 jrpfsr, siqwo 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 mk- ldumy9.w 2a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it islyu9mdw-k2. m a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts fromjtd ni. w-sf.vuws(n12;3 afy rest and rolls without slipping down a 30.;da. -.2 n1 ytwfuwssnjiv( 3f0 $^{\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 verticaeh*4 liz/ su/qlly on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end o uq/*sh4iel /zf the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.2 r/;qh ei yrmb33+6bbud.;ow yb3ofy 510-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular sp3+by b 3;/y3 u mqfb6ywir5b;edhoor.eed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical g4iksi i /1qoo2rinding wheel of radius 18 cm when rotating at 154s k1q ii2ooi/00 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 :x u()vpx -8cjq;qo ccis rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decrea( x8):qccx-uo;cj pqv ses 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. 8–2xe:o292f :vjt7jgyt s9) can reduce her 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:gt eojfxvy9:27tsj2 .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 init * 9jto r18azw-do*lxcial rate of 1.0 rev every 2.0 s to a final rate-lo9jct 1 dorz*xw*8a 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 itgx o5d b.l6nsaegl+*jh:0: v .mhwl;d s center at a frequency of 1.5rev/s The wheel cagw b+5.o6dxjlhgl; e lnsmv:0 a*:h .dn be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center 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.4*7w.edxmua-9i qd 9 ry cmhj figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum ot /0qf wh/+oemf 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 cylindrical disk of moment of inexz,y;3 yro6 iqrtia I is dropped onto an identical di6 rqzo, xy;y3isk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ,l j)w xq073jd6ro,lfdom5yeat 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-gqqy2. d( ge;px/.biv 4lzqb,s o-round platform of radius 3.0 m an. xpg vqly. dq2/b(bie;4,zq sd 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 fre*yffxf* e8v v ukv54w/ely with an angular velocity of 0.8 ewffy/vxv*ku4f * v85$rad/s$ 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 whit5txm;l n/eo5w y4ai 3vqvy+r9 e 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 Sunytqnv ymiev9r x3wl4;5o /a+5’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 olana5,+mh-xk3 s5:z i) qbbklf 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 2bn;ln qvzo0v)ty9)d $ 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 freely wit ux ew6ye7/2swhout frictis2eu ye w76w/xon. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg persofrm7vvu2.k s 6n stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a momv.f rksv 2u76ment 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 ground5hjox-aa3.yr chl x7, 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 per,-5h.choar j7ay 3 xlxson without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Eao34b4do0ewbbp s+hd*s;d o sw )/(ieq rth 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 asso*3sb4w id)dbdeh pw4so bq(+0e/; o a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates frosd 3tg, e+h9d6-ld;h5ypb evv m rest 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 uniformtjl+nvoitn4(0l , m u9 cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the m+u,tm9vij(l notn l40otor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindr 67 vv22rrisydical 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 con2y7i srv62r dvservation 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 rt d5u+n mi9c0tear 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 uv p mgcw. m7uap4v;62with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of c4p72w mum;gp6v va .uradius 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-96 tsxck5 liz.pollution automobile 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 uniform cylindrical flywhee c6.st lxzk9i5l 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 a*1 28et of0fvvsl0oxt;np k+zn $H_2O$ 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 g p u3+0b)iyrwmd1p08alo t5b on a horizontal 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 pivo 5x2d xsl)1bvn :7jiult 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, detdl:u 2sv l1xx j7)5inbermine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertibi:a c5rpgg m4e,5h qrc:c29dcally on the floor, and we want to exert a horizontal force F at its axl:mpa2 e, g5i ccq5brr hdg49c:e so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4nx*r a ,2f;r n5y).okky nr)oq.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are 5 )kn,q)yry2*rxn;no. raof kthe normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begins w,rcd/v. y-oc:qpgk5p hirling 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 :dpqk g c/.vcpr5,y -othe 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 cy:hx8 n; hd3nb )fjbu ltv19zd2linder and her arms as thin rods, making reasonable estimates for the dimensions. Then calcul 1ndvx3) zdbh;ljthfn:2bu89 ate the ratio of 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 two cylindrihqy ,p.3guq lw+jos/7cal plates, of,lj.7+poq/qhw s3y gu mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 roug 5jp nvm;u-(vgk.t9 puh track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is gv(;uk.9ut njv -mp5p 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 nodp t twzu )/y6py.4d30 6 bpb*lhq9isot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unifor0,f9tbf tzbv mk9))td mly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) z)0v9tdt)9bftf,mbk 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