A bicycle odometer (which measuredcuh 53xitjgk1n2 -j.:+chxiho . 0w zs distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle wit. 3+h0.:h2cjz do1witkc5x g hix-un jh 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rimb18uya.vtb2tu rh cv6+ z 8so+ have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, doesb. uusohb+2a+yv8tczr 6 v8t1 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 hqkatzfbut91a szz /,),6ooiyl( xe *wk 3*9xsingle value of the angular velocity $\omega$ Explain.

Can a small force ever fm7g mrnv40mk;bqh 5o(o o: 9nexert a greater 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 difficulxx69* bcxm )s qyr e2;38poyiwt to do a sit-up with your hands behind your head than when your arm 9qs8mo6yy;rp2wci e* x3x )bxs are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven l*a bu;:il,ah sprockets at the rear wheel and three at the pedal cranks. In which gear is it hard*ilu, :ah ;baler 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 fast4b:ko8y0r x sb 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 distributio8br4: yskb x0on of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) 9a+lc w 0y-yvk0tcc)z carry a long, narrow beam?

If the net force on a system is zero, is the neth+wodvh w818s(:oh .n6rmxaaeg0 +hs torque also zero? If the net torque on a system is zero, is the net forceh.e0 n:(xg8os6+wh+ wr8a dsvmhah o1 zero?

Two inclines have the same heighc,d ksgd/fj t s+3ta5;t but make different angles with the horizontal. The same steel ball is rolled dogkts/js;3d ta , cf+5dwn each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. Onertl y9mf..zdl/(zh p* sphere has twice the radius and twice the mass of the other. Which reaches the bottom of thery d /*mtzlzlp.h(. f9 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. T2l.nt0laa3fa:nl +w s hey 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 greater total kinetic energy at the bottom? Which has thenat+lsanl0:a f3l2.w greater rotational KE?

We claim that momentum and angular momentum are conserved. Ym us 9 ,gimt2eo643zpyet most moving or rotating objects eventually slow dowm9p4s23iut, yzoegm 6n and stop. Explain.

If there were a great migration of people toward the Earth’s equayhio(b- shy a(r 4a8s.tor, how would this affect the lengtsso-h(r a8(ybha4i.y h of the day?

Can the diver of Fig. 8–29 don r.0;xrh5y ow a somersault without having any initial rotation when she leav0; 5ywr orhnx.es the board?

The moment of inertia of a rotating solid disk about an axis through its cok:1zv mk5 qv10pk c0fenter 50zpovf cmv:kq0k11 kof mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstreb/u0p85gz lv*f 1 sszstched ha/ 58usbfpv ss0gz 1l*znd. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, o70tsvd/jbh03 i +o tpywcm4)kne is hollow and the other is solid. Describe an ho /v4sti0)y+w mj bp30 7ctkdexperiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal a a(cec5i2i6rlxle points west. In what direction is the linee l2 (a6c5iircar 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 increasing or decreasing?

Suppose you are standing on the edge of a large q0.p32i rqlye .ofow6uj/5mhfreely rotating turntable. What happow5 0fuq pemoi.hj2/qy3 r. 6lens if you walk toward the center?

A shortstop may leap into th uqi:r17v 1)qqfqx6ph e 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 di1q)1h:fq p 6xiqr7 vqurection (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum,0q yl q33io-xcmjn*a( discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the secoyqa* -cqn3(l io03mxjnd propeller can operate to keep the helicopter stable.

  Express the following angles in radi42cxyte+)+ ut6 isa ms.w3mf.g .daro ans: (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 En95yisg;r7 )vox wn/ carth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and tgo9 7cy5s vnw)/ir nx;he Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from pg;f1; (b4yh* apiiwr Earth. The beam diverges at an angle * i;f irabw4h1(gp; py$\theta$ (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 tu5lnl bpq1;waw+wjm 4 ao1- z;frned off during operation, the blades slow to rest wwl b1q5;wj1+mala;zp4 o n- fin 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 another child. Ifnstu3e6lu j/ a*e. /kb the ball makes 15.0 revolutions, what is its diame/ s*e3el6uj kt ubna/.ter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many nnl cdt/3 ia)d* tpc)j3i(r b/revolutions do the ) /i3tr/ jdtnbcdcp al3)n(*i wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diamete3vg7zna0gy/ n r rotates at 2500 rpm. Calculate its angular velocity 0a 7 gz/g3ynnvin $rad/s$ $\omega$ =    $rad/sec$
(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:e.cy l 6nd0bm+qp3f e (Fig. 8–38). (a) What is the linear spele0+nfd:byq6. e3mcp ed 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 theg+zl3cr9ip 6jok8um , Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speedwl5f;xxsd1.c 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 particle 7.0 cm from the axis o ,*h hklckc:5cf rotation is to el5h * chc,k:kcxperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm oo:gr38+ 3xocd/ a thato 280 rpm in xt3r +a 3:oca8hdo/og 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 radius 1s /ic3i/e3oenj p6vl$R_1$ 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 themselx)b-d5n pfzh -ves 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 interval. The spacecraft can z-)bhn -dpxf5be 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 bz; dm1wn85yb8dy h:g rest to 15,000 rpm in 220 s. Through how1wng yddm:;bzy8 58 bh many revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in npdm7:co: df.2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling “h r4,7h0eskxobgrc)d 8uman centrifuge,” which takes 1.0 min to turn througxr, kbedhos 8r g4c)70h 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 from 240 rpm to 360 rpm ic3gb y1g9l :pnn 6.5 s. How9l3n:g p1gc by far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turkalfz71grz9ph2. :r skd1rh/ 0/eg yp ns 1500 revolutions before it comes to a stop/h f1p/z 7zkl prer.:gd 9k r02yha1sg.
(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 they),4tw+iau yh car reduces its speed uniformly from 95km/h to 45km/h The tires have a diah)t a w4,iyyu+meter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed1 wxjsd l;,n:x uniformly from 95km/h to 45km/h The tires have a diameter of x,jdnl:x;1w s 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when cl5 to r5:4 ogdgsjzp--gk +ej*r4mlp8iimbing a hill. The pedals rotate in a circle of radir 4-+zjpki5j* 8o-odltrm p45se g g:gus 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 fl 7n,i;pg-ts -xflf : 0xvps6cm wide. What is the magn- g ixfpn6,sf ;lvp0l-7xt:sfitude of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the am( bu r9)xai2kxle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.4 2 xm)kr9ui(ab$m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod wqd0 p3xdyf,qwz84z t1hich pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. fdx01d 8z43q wtpqy,zCalculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tigh8u5c6 rugsw*vtening to a torque of 38 gsrcuv5 8 uw6*$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere os c7e n+ghxce-so5bs;8 s.pe ,f radius 0.648 m when the axis of rotation is throug xec,e+n87oe ; sb-sp sg5sh.ch its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle whfwec2yucq;zoad8 +: ;3+ keu da-+cbseel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hua8cuqfy:e-+e ;swuc +a;d +k 3z2obdcb can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin,/f s3umvb-1mc light rod is rotated in a horizontal circle of radius 1.c m/vb1uf-3 ms2 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 .vf d1sw.8zs - nnqm-ton a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force betwe.- vsmzw 1.n tqd8sn-fen 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 poar9zwob, *8c ,4fbki;jn1 )e2jzhupd int objects shown in Fig. 8–43edjn u) i jk*rpzb9hbf1z28a, 4,wc; o about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule con7lb1xsuw15 w p i)ap.qsists of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning 9 2rkdqsy)wizrss4-.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 satellite is to reach 32 rpm ind.i rq 2)s9s4yrks -wz 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unifo9u lc* r:llx)k71meffte*m w3rm cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calculat*)3l 7e9l*w k ume1fr flm:xcte
(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, iom ymp*/,5u laccelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentialjm kz2+iuq9rx ahz,b * z8im-.ly 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 of8.,ja 2zh9 ikxq-*uzbm + rzim 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 rotatil1gwu7*y-xdtx /ntq-j dmy-1 ng at 10,300 rpm is shut off and is eventually brought uniformly to dmj/x-t1y d-uwqg -ln71 yt *xrest 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 accelerates a 3.6-kgodyfv gf:rv )bkle5 7t,;6h5q 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 ob g91qbv llxis .m );wr-,/cdby the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is asv-1q9 cg xmo/lr)w bl,ibd. ;ccelerated 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. 8–49jeab4 5f1tvm 9g1 gam6. 5gfe1b94 av mtma9jg1
(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 mak4 t)sif(ee 7ksses, $m_1$ 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 thelthyo/ x( unb 3c32t(d hammer from rest within four full turns (revolutions) anhuytl(b n ( co33d2/txd 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 aw lopbyt*(r / ih yg;nw *rf71qc4h9o 9k6moh; moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine dkfdy1fh h1(nzto-yp.,x 5-x4 dmad j -evelops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radqjoh2 c8m 4s++hamntb 1md(n5ius 9.0 cm rolls without slipping down a lane bh+m4jn h adcqmot 21nsm+5( 8at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respe/x2jmwu7esm .x9*ei +h*x )droa l6 dect to the Sun as the sum of t7* d s*m6.le9m)/axi u x2 dheejrox+wwo 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 netw 1:5ju*e+g;u ha .+o qfevargnv-d 5h work is required to accelerate it from rest to a rotation rate of 1.00 revolution perao g;ue5*1 wd va. hjre+f+ 5:qhguvn- 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rol vpfony ylg5 y,ok-(97u3 hr7zls without slipping ukol3ygp(9o 57fr,-7vyyz n hdown a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall and4iy ,.t h0w-do uf;pei its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hinti0etow4f ,d.pyui-;h : Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the en3.zcbxilr 51mm) jys:czo:* vd of a thin string l:sri3bxzm1.5c yvz m c jo:*)in a circle 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;j b k+/lhb0s/ayjap1,mq,i:ctje m3 uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 c/j /a0;al p mhjqskbm1+b,:yei,jt 3rpm?    $kg \cdot m^2$
(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 roy;ag . lesn8ru( ,2wwktating at a rate of 1.3rev/s If he raises his arms eg2 kuaw,8s lynr;w.(to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of inertiarlqtod2 eb/ tl2/ xe3klrg+3 gnz k(:3 by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speedlo2 gb(/t/2tl3ze k+:xkr3 grqe 3dnl ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an iq0jglg 6 s*p*;fnb7ha6wc)v dnitial rate of 1.0 rev every 2.7 d0qpvch bn*);w6fg j 6*gsal0 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 vert5vo1 opef**py ical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws*o 1f5evpopy* 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 spinning at 3.qi /ic5ntl7z w,t 04n /w5rsik5 $rev/s$ 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 h60tjlnl,cc4 m 0yv2 vz3bpsyf:x 3n(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 cylindrical disk of:n +amre z(tx7 moment of inertia I is dropped onto an identical disk rotating at angular st7x:ea r+ z(nmpeed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at r+eoe 3jm c85 gbg;gp0lw2 p u6lqhhd 9hr:+s12.4 $rev/s$ 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 ce vbon1/+eiwn. nter of a rotating merry-go-round platform of radius 3.0 m and moment of inertia niwo+n1. evb/ 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-j t( 0cjk8f9dwround is rotating freely with an angular velocity of 0.8 08w(kfjjctd 9$rad/s$ 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, losinggzrz4 t;mmw46doi+w + about half its mass in the process, and wd w4w+tmir+m4o;6gzz inding 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 y+ b9q9nx,c/oeka1z/n94c w oif-5qih l(jwt 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 +dl3f6s 7f7hcfw,*s7fo h zrj$ 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, thasfxya.1h:lz f2(+e1 sp r n5bkt can rotate freely without friction. The moment of inertia of the person plus the platform is f1 kes +2yfzl xasp1(hnb5. :r$I_P$ 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 faao8r,a33jiio)+8srrb2snupa-s ;wn h3h (-go-round turntr283aapbw,oh8-sonsi a)u3a ijrf r(3h ;sn+able that 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 ground with the end of the rope utu4p1r nzz;6 lying on the top edge of the spool. A person grabs the end of the rope and walks at6 u4p;z rzn1u 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 sucwknjb3 ica9 i79 h-v0th that the same side always faces the Earth. Determine the rat 3wi-in9k9c7t0j ahb vio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate mjic-(vv;gw72 6;4gpobi yx;ikq xf* 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 r2z4e x9j : el r02fldwjl9:wnrwxn4(radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torqnw04le jfl42w w:n2:z(d 9e l9rrx xrjue delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg and di,9n/7te)lvy th)yhf c ameter 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 yv t ,f)lt9)7nhy/c ehof 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 reart;*hllw2/ r-hr* yk uo 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 k.z(j. fk2qadz ,vjm5 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 radius 11 km, losing three-quarters of its mass in the process, whatj 5.mfaj(v,2z qdzk. k 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,n7b 6ojxerm9a scf2)g88gfz for it to use energy stored in a heavy rotating flywheel. Suppose such a car hagfra ofs ,n98z m7cgxb6 8)e2js 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.”
(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 p6j6sqnk c871pm gi diav3) k;$H_2O$ 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 rolli7*dve6ew h z2tsl-i nf dv5b8+ng 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 masscn/ e0x,o4 mzlhm44fs M and length 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 the force of gravity acts at the centecl,m/sfo ez0n 444hxmr of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing v: 5yvzewdjt82:tstsd d m+-ryq w- 3m0g4 0uclertically on the floor, and we want to exert a horizontal force F at its axle so that it mtu:0v cz:ejd+wmwd8-34qt 5sryg d- 2tsly0will climb a step 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 with a9)qy0xdpuj0 m9n ,r7;a-jmp arel)oh radius The forces acting on7,da9 ahroj0)e9r-njq)u m; pxyl 0m p 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 0s20vp . ;//xjfvggagi bz8)bj.50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque re a /b g.2gv/f8vj)z;sb0g ijpxquired to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body7a6kaz vdn u5. 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 kd5z u76aan v.with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembl p buj6c.s*l; -*vtbzby which consists of two cylindrical plates, of massbpb-stbjv* .z u*lc;6 $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 geha-;c0ae djsq6 a.;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 sa -ad gqe60aj;h ;.cepoint of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assuar7b5ob0 fd w 9ueg1l,me $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car re*;d(nio h,l a9w +pzxa0 .ayqwduces its speed uniformly from 90km/h to 60km/h The tio0+w ail(pwah9z.,y na*; xdqres have a diameter of 0.90 m. (a) 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