A bicycle odometer (which measures distadolx4m;ntf 11 nce traveled) is attached near the wheel hub and is designed for 27-inc d1x o;tlf41nmh wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim +wyj z 1lvj.-mhave radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the poiw v.l jj1m+y-znt 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 the angular velocity4g,+2l hi ntjb $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explain. hkj.:lt4 kt36s 8nona

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 * p:t8s(o9ywb5/1nm zrzj mqoto do a sit-up with your hands behind your head than when your arms are stretched out in front of youmm y9b pzq15zo: n/(w*trs8jo? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheelsk 3ohc5m e;,l and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In who3 kse,5m lh;cich gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with flejmhy c, l7*tr/sh and muscle concentrated high, close to the body (Fig. 8–34). On the basis o/*m7tjrl,ch y f rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (x ei5ru6iqikz )5c).n Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If :uso2rz str.n / d+)qzthe net torque otzq.zusn2d )/s+r:ron a system is zero, is the net force zero?

Two inclines have the same height but make different angles with thei)/: 9tympt 3nyh*w fj horizontal. The same stehtyntmpy) 39ij*w :/fel ball is rolled down 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 zqgyi gr+.depcwi5vf9s5x6:61 p ea 2 an incline. One sphere has twice the radius and twice the m1i95iy2ezrepx :p5fsgd w .+g 6cv6q aass 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 tzmx8;.)ygd a*;esbwv m1, vemass. They start from rest at the top of an incline. Whgm*yb;)sa8xw.v d1emvez ;t,ich reaches 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 vrh3c/,h. 9)ihg9sbl u)yhfuconserved. Yet most moving or rotating objects eventually slow d39h)9s vc)lgb uhh. y /hi,urfown and stop. Explain.

If there were a great migration of people toward the Earth’s equator, ;vt6o40hxghmyd*sco 4i1w 5 ahow would this affectyx1m6ho* hwg0dc4 ;a4 ov5tis the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any ly m;r7l a9dnzu goh9o90k;*r : zof-pinitial rotation wheo;hda n979mr l-okgfl zp;0o*y :u 9zrn she leaves the board?

The moment of inertia of a rotating solid disk about an axis through 6 *y)i ylibo*zfj.t2qi* p 0uxy h6)ruits center of massjl*y0i6h *ub 2ft)q i.) uixyoy6r p*z 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 rota c/ 0n6hugng(yting stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses,c 0g6un/gy (nh will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical aq 8 ;ggygh7-j+pwd6ecnd have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine whic;d+y gjg7 h q-cwe8g6ph is which.

The angular velocity of a wheel rotating on a horizontal axle points wesrj9stht 6+f/t t. 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 whees6r +tf/th t9jl. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turn. 8hx s+bdvth0table. What happens 8s+ h0.dtbhvxif you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As h df+3m6p4.iwwz 0uvx be throws the ball, the upper part of his body rot bw4fv3xpz .m+6w0udiates. 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 of angular momentum, 9hb5utlj36 zy; 1yqgndiscuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propelle3juzy1h;9gtn y q5l6b r can operate to keep the helicopter stable.

  Express the following angles in radians 7k*re;ld.;rd;qj qq: 8cz *was5ylkg: (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 Ear,m3vz3 nbyrtv0m f+ u*, yth-hth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earmrzbnf ,3ht t3yyv+hmu,-* v0 th.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam dive 6u)q :tbvar:6.p5xh fhh/lipf j+;l prges atvh) /;a 6l :p+r.phfu f6ib: txj5hpql an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. Whe yhephs:3r* 5s(xmc3in the motor is turned off during operation, thsr mx(y3 ehhi:pcs53*e blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another childq;i;3fakx )t e. If the ball makes 15.0 revolu)3a q; fk;xiettions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travelsh- 3q/as: qd/gfqk: 5jtm:dvn 8.0 km. How many revolutions do the q:3jq -g5:d tn/dhm:qsva /fk wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate icxfhe ,,sz8n- k)vkxt rm) b/,ts angular velocity in /zx,,t-fsxer hmv,b)8k k)cn$rad/s$ $\omega$ =    $rad/sec$
(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 rer807 u oxpxq3;gkbk2i 99njf ; srhbs;volution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 mrsk3;ibk8xx7n9sjp2ou ; 0 rfg;9hbq from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular veloci2d-dei) p vyaw;m; kx;ty of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spgzx0mwxx8 ; 1heed 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 pahw +ld7omgk96fiy 05article 7.0 cm from the axis of rotatio07y l df9wh+ia5g6mokn is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about ifohfbw+fh z;vz. 12r8ts center from 130 rpm to 280 rpm in 4.0 8h ;1hfvw+bfr.2zfz o 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 radius5vz2yk )) 8trqipk2byp wkf my1v1-*h $R_1$ 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 themselvxs2p m:g(fhi c3 vt0k,es into a slow rotation to d(hmvfs02g,x:ipt 3kcistribute 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 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 9 +cl3g5 qq+ida fj0mn:6lrugfrom rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this tiq539:uld cfgj ml++0raq6ng ime?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculavfsi* e1,c-8+yz q gjpte
(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 whirl.4ga rn)11hyvqtl /;7lu1uh7twjwja ing “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching hr.wnjv74 ;u)1t1 uhlg7 qa1 jla wyt/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 3,qr: mc9xh,bh*lugwqw 6 -n1q60 rpm in 6.5 s. How far will a point on the edge of the wheel have trab , lqqw :6u*xhg1cq-9rh,mwnveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min Itq4n 1erml*rb 3 i/d );zh4zifq turns 1500 revolutions before it comes to enz/ril qm d;h4b ir*)z4 fq13a 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 spevoak,.x 0-p:c jak 7owyk)q x:(ynwk1ed uniformly from 95km/h to 45km/h The1xy :ojc.-aw0,w q7p(kav nxk :k)oky tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reducesi)fh x .le.yu) its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 my )ueil. x.fh).
(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 wei nemm.(j17a0 yd0ppu cght on each pedal when climbing a hill. The pedalp7d num00 pcaem .y(1js rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is vujpq7zdc m;yza+o;h4aj,c 6z q/8 ,othe magnitude o,z cjm,j7zdv/;+qq cy;uao4 oha6 z8p f the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39k0x)jk5hup / o*6x tiw. Assume that a frict0)hx /5 kkw6*i oujtpxion 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 en)6u6mu fr2j9pu bha/a ds of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in theuh p)fmbjr 96/6aa2 uu 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 tightening to a torque of 387q eq-fndx7;k tc +*ydx 1xm6ia:s (xtian sdx*qd-71q ex:xx;yf76mtk (tc + $m \cdot N$ 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 o:h0biib ri . 3yy*px/10.8-kg sphere of radius 0.648 m when the axis of rotation 3.xyib pho0 i/i ybr*:is through its center.    $kg \cdot m^2$

  Calculate the moment of inert(qa* cecyjj ;atc16qyg961 kkia of a bicycle wheel 66.7 cm in diameter. The rim and tire *16cckjy 619 aaqkect(;gyqj 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 x)iejw .m:+ lm+1 y7hryr5tazend of a thin, light rod is rotated in a horizontal circle yhme.m+ra+j t)r:z 7liywx5 1of 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 dlbpje+6 2i:s on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands andiels +:62 bjpd 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 poin46n kj 3wl a.i41adjc bt :5c(zjkia.dt objects shown in Fig. 8–43 abj : c b.3nawda.1zjlak4 i54cj(tdk6i out
(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 j vkirh ;5enp+1b, i/btwo 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 at the couj :p s 1 sgx2tr;62njg2(dpbirrect rate, engineers fire four tangential rockets as s pxg;bt:2 1gisjp2n 26(u rjdshown 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 cylinder with aj,3ido7n: vlhsn.j 9 v radius of 8.50 cm and a mass of 0.580h9vinnv.7, dlo3: jsj kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest to 3 gb(f5 ipxddo +62oh 9r$rev/s$ 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 tangent3e 2oml+(cxfox-jgn7o rn 86xially 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 children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required trjfn -8( o+73og26lx xmcnoxeo 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 obk w9 7-6x. rmbt7g ewjso*8joff and is eventually brought uniformly to rest by a frictional torque mjwj-rb o9bkesotwxg867 *.7of 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-kgx1eqen6fxd )bl* xa2 ( ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, whicha6vxlz24**fq p apr++pcmh/ i rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from mcxf pi+pp/q2 h**aa6+ zr4lvrest 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 l4 0jrm,). iulg)ewttin Fig. 8–4 .gl) 4,l i0t)meuwrjt6.
(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 consdzxiga/ 3s k5g;)-er jists 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 the hammer from rest withingi gin)z 99xehjv(*8y2cw 2sq four full turns (revoluti *2g2hgyin8j ) zw9ev9x(cs iqons) 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 of inerti ,,femram6qe29oa5p i a of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 28ha0d:eq. /1w khn +gah0 $m \cdot N$ 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- hqnq.)- eh icuavgo(el6s,.* hgu5 n slipping down a lane at *-u5hhevlea).,nh gug. i 6(snq-qo c 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic ep30/a o 7soqmz1q)+2obx vsdenergy of the Earth with respect to the Sun as the sum of t mqss qa oz1d2+ o3v7bo)e/x0pwo 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 l+ n a 80eaz rcz7-)znqcz:g-lradius of 7.50 m. How much net work is required to accelerate it from rest to a rotatiola rn z +gqc)a:l0nzc -e7-z8zn rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rie0wy ; b 7s7d;pg4uxqest and rolls without slippeygbdu 0 s7x 7qw4i;p;ing 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 starts to fk nkwmy0r-,9m all and its lower end does not slip. What will be the speed of the upper end of the pole just befoykw-n,km rm9 0re it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotatif 0kyz cxouen2+.lse( hcf(.)ng on the end of a thin string in a circle of radius 1.10 m at an angular speed o 0k2)f(c u.efeh+czyl.xo (ns f 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg unn *0i(qiy :y s ekz)o*rh vi;jxuy9/e)iform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm? rn*eyy:z9;k)vh*( s ix0 o/iyqie) u j   $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating wwc1wrhs3); mz 8)afu at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decrease; mwau)c 8hwws r3zf1)s 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 inbic/e ub27 ) pfsd;)v6x bny-bertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 byunxf7) 6s)be -b;pd/v 2bic 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 increase her spin rotm a- qi1i(a7h jig9 +kzifa+t+ation rate from an initial rate of 1.0 rev every 2.0 s to a iia7 tk hg+am-iq+jz1a9f (+i 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 rotap 0cbhe2 1u5rrqk 33h-mvjkf. ting around a vertical 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 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 5.-c pkj1vkrh 32r30u mhqebf frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinninb zu 8ul*0s)l*z,xgl zg at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the a54q;fmx sy9yEarth
(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 li9us,25o5pggag3 d8x dmjz :inertia I is dropped onto an identical disk rotating at angulal jsg8g23 5m ,5d9dguzaopi:xr speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns 1 qm.gwua5zh hw 2:i-mat 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 oc.:v s(, :g,wj myzctaf a rotating merry-go-round platform of radius 3.0 m and moment of inertictzg,wva m s.c(::jy,a 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 rotatp8b iruqc:sy( phvc22 x.0.y xing freely with an angular velocity of 0.8 : 2c.us2 yvxhxyppi0c(r b8q.$rad/s$ 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 event -r ilf/xi;9hzually collapses into a white dwarf, losing about half its mass in the process, and 9;-lhif/xri zwinding 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 windss4 r kjzvi z r4+0)eq4 ruyfj9 4u++gos,rml1t 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 8gsqjgm r.y(-faxb ) 6 t9 sb,j*mf,or$ 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, in k ar6 np0rn, gu2kea:;l+lby4p:ilo*itially at rest, that can rotate freely without bn;4 irlg o+al2 l, prp:6kky u0na*:efriction. 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 person ) mqui3n(bq0j 6npqg2 stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted onb 0q3 jg6qnpi2unmq) ( 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 tzy zv1umw,.r. he rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slippinymw z,r1v zu..g. 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 same side always facw k0p(.mi j(h i1zg0tsje3 vs7es the Earth. Determine the ratio of t01 jpm 7sgikhiej. vt(0sw3 (zhe 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 x99(5tjc. kc5ofzvlqyo9 ye 1 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 i il deyi.+)vxnn2(+,6 spzpian the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculanpayvp, ni+x6.sl)2i dez(i+te the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg t6b2frrf23nq b* l 2imand 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 fronl3*qf6m22tb birr f2m rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the vr gl;kl1) h,zrear 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 8xw;fuw )iqlj( d ,sw93.0 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 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 qd;x( wf)siw3j luw9,no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a l mh,52zw3* z9bheoqw poysc14ow-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a,c3s2wwo 4phmqhz51e9o* byz car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(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 illustrad4dyl (ps648voeax0 rtes 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 sg/op wb: 3ex5zy k8/vyurface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we igns*nx .zh8v /xrore 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, determinez 8/ xrs.*nhxv (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 standi 5,,sph 8j4qgj8q +-dyfe (rprl c*4 psth.sqkng vertically on the floor, and we want to exert a horizontal fsh ds ,8qr*crpse t 8lqk4-hf+jqy .,gj(54pporce F at its axle 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=4.2m/s on a flat 1,qcan +iuuh) road is making a turn with a radius The forces acting on the cyclist and cycleh nu+q cau1i), are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begins whisky 6 k:)i7d)f2cl,b zcmz9 vyvm j6y.rling the rock in a nearly horizontal circle above his head, accelerating it from rest to a ratembyiz7v)f vd 6ycyc6k2s 9l:)z .mk,j 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 hg+q6:+/8anxr1kxcehsh lrx ,er arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched ke,:rx nqhr lh+ 6/8cg x1sx+aarms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consis ;p *79bl8gtl*x 9c gnatg9pocts of two cylindrical plates, of mass a8gp9*tt9og9l nc*xl7b;p gc $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rough track of Figgyjcy/ bi-4)v5fr:xd . 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 of the loop /yvcxj yr5df 4ig-:)b without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not ahm x ,l:7l 8jp4yy4; cryj0ysrssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 rev0zuk7p- wvz8cno/ a)b olutions as the car reduces its speed uniformly from 90km/h t70)z/8-aokwu pz cbvno 60km/h The tires 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