A bicycle odometer (which measures distance traveled) is attached near the whe d(1e3ulq tki:el hub and is designed for 27-inch wq3ke1:td liu( heels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotateddl-uo ; kp(jq q6ib.(s at constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleratiq (pj ;(.i-qd ludbo6kon? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body b*9nmuoh0v;iu q 5uix9 e described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than ,tioyxf-n*+cua 7 rn ,a larger force? Explain.

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

Why is it more difficult to do a sit-up w71pxzum;6owu g3kcxb-,j t0z. gzz 4fith your hands behind your head than when yuxu 6b,ok-xzzw7 z3m gfz;g.1p4j0 ctour arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheeli kn ei3soed 2;2*zj,uyo9ivoc4*s7e and three at the pedal cranks. In which gear is it harder to pedj3eec oyo;97odik2*vui 2z4i ,ssn *eal, 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 fast have slender lower legs wi-5:gl nhiy9njhx fu2mc0,4ngth flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distrigfc2n i0n9,5 u:hyx-hm4g nljbution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a (xvs7ddh:d g. long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net tog d+) uwjccib7m02u)brque on a system is z)dcb )j 20 ui+mcg7ubwero, is the net force zero?

Two inclines have the sz9sxex w,l3y/ u3we -92txm eqame height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bomx w,wz e3ux/932ts-eex ql9 yttom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. One0koij0v 4b,n b sphere has twice the radius and twiji0bn,kv40 o bce 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 samw ex/zelcy34n y)w.o1 e mass. 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 greater z yyw.oenl3 ex4c/)1w total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet moh0)zj 5psa xsk( s5u+.. 1l1pobylepxst moving or rotating o e.z+k l 1slh01pjsox)ays(x5p5 .bpubjects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how would;sn +n .kw9us;avo8x , qd2sbh this affect the ls2.u os h8;abws+;9 , xvqndnkength of the day?

Can the diver of Fig. 8–29 do antynw6j(; dli(n1p4r somersault without having any initial rotation when she learn64(;liytdw 1n(j pnves the board?

The moment of inertia of a rotating solid disk about an axrgsi1yc 0o,xo2/8wp dis through its center of xp1ds i/wc ,0o ry2g8omass 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 aoutymi an1: 14d7o3r+hr tc ymf7 -db eq65b:b 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase:ohe-b3: nfdmq t5b+dumytc 11b4 o r6yi77ra, decrease, or stay the same? Explain.

Two spheres look identical and*c.t2,jrmux u:q 9wd(2fes3+x f cxe v have the same mass. However, one is hollow and the other is solid. Describe an experiment to d cwmv*3sejq cu9fdx,x:r x 2 ue+tf(.2etermine which is which.

The angular velocity of a wheel rotating on a horizontal ,sd9b a0,xn(b ey 5lcuaxle 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 luxdbbas cn , ,5ye90l(inear 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 af vebsvn0-* o se*ur0* fplo6/ large freely rotating turntable. What happens if you walk toward tfvp-6ouoe n */ 00fsrl*vbes *he center?

A shortstop may leap into the air to catch a kyxh ir76ptpu+*j2onh5*sbw k 8 id 4,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 d 5i7 +k*o6n8htuxishj rb ,w*42d kyppirection (Fig. 8–36). Explain.

On the basis of the law of conservation of angular m4 xy7h*lozk: homentum, discuss why a helicopter must have more than one o l:* yhkxzh47rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles fk/k ew 1ld;6tin 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 amazn*29lou6x+o7g ej*-e rl:g ylf6 yy aying coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of thyorfo x76nyl9-ea*j *u el gg:2y y+6le Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Ma/4 carbidn8ia6)g;gk.w3fq2 x )ykeoon, 380,000 km from Earth. The beam diverges at an anifgkkd8)3.q/ycge;26r4w ) aina xa b gle $\theta$ (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 tknh oe7agjf8je669u66e *ogw he motor is turned off during operation, johuone*ag 66w6f k76j8e9e gthe 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 child.* bt +f a0z,zncver vze.n.u0*.im es9 If the ball makes 15.0 revolutions, what b 0vu9fazen.vre.c. ,tze** 0n+zmisis its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many)io0uy m ;rn-e revolutions do the wheelmu0)ione ;r-ys make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculatmixb*)qr;*np()-+v tz hxp qtsg kd4*e its angular velocityh tg q*pxz )4k-idb (x*+qr;spn)vm* t in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makpa q5jr:gp81v22 np kies one complete revolution in 4.0 s (Fig. 8–38). (a) What is the lina v 2rnkgpj5p8qi1:p 2ear 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 angula(q. 5o; gy)k(syw 9ii j (-zazjsl)vvkr velocity 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 sp5un) 3dv c e7x 7 upjhqa+jbfxrwe(os(z;- .w0eed 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 aq- /bh)w8 cgdzhu+7 g6qhqzl9 centrifuge rotate if a particle 7.0 cm from the axis ofb zhq6h lqu-gqc789d+zh)/ gw rotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel a85 ul,uq,c ,cy pd*bwu1z9rlj;nrva7ccelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determ8lc, jbrwqzd, r9c;,vl *1pnauuy75uine
(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 rp*nxh;wp;g /kts8w +s1 x5mj $R_1$ 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, astron1drdk ) ws0zq84o5 f5y bpvx-7 uq7cgsauts 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 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder wf-g b4)yd1zqqv0k8u sp 7wds5r 7x 5coith a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s.14mr46++dwonek ew93k bbgri Through how many revolutions did it turn in t3ko enbdg1kr m4+94b+r iwwe6his time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s.f 3e .+d .zddnl j,xakd-n0cu2 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 whirling30, kh,yax q8ob vtz4mcydq(6.* p nat “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutit,4m(.hq*y dtnczp ako3 60qa8vyx ,bons 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 accexs./l*ct rt1pq*ucv* 6a w7f dlerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on p1./c dct l ax*ftu*s v67w*qrthe edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revo1jc,lsd9 omm7 lutions before it l9oj ,7cmsdm1comes 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/ jnld-vaw,g,3 k6ow j speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.803aw-dk,jg wnvjl/o6 , 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 revol37o ;idb* chqlutions as the car reduces its speed uniformly from 95km/h to7 i3lqoh* db;c 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all zj,buex jga2l/6ao7- p jo4f7her weight on each pedal when climbing a hilluxl7 j 6peoj-7j4z/b2,faaog. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door npuj75 xa 4 v29o27/o cktivnf74 cm wide. What is the magnitude7o72fapinux5 k v 2/4toc9n vj 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 axle of the wheel shouftg5 67nq 1uoofq ucj: wvrbq+5n,4)wn in Fig. 8–39. Assume that a friction torque o , n76o+tq bfugu5u)q14qj fnow5: cvrf 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a rtco2);xqv t3wr).n an1qh,pt)d+u cmassless rod which pivots as s2.,vru;c a)3wntcqtd x +n1ht)qrpo )hown in Fig. 8–40. 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 tightening txnl++u..emip 9i h o/zo a torque of 38/ 9 +xh.m.pnoeziui+l $m \cdot N$ 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 of radius 0.648 m when trn+t- 8ofz*y gin6v1 w:rxkz 2he axi8kfrti 1x6ng-r wv2 z*n+o:zys of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diamete/gi: jx1lsyj3ily5,m r. The rim and tire haveg5msjjyyxli: l 3i/1, 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, light r 0b pozw,04jl4r kaau0 r* 3-cdiksl7god is rotated in a horizontal circle of radius 1.2 k0,kpl a wc0la3so7 ur dbrij* 4-gz04m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheelkj3p zui,g bhki-,k eg,,8(op rotating at constant angular speed (Fig. 8–ghz8,ko,pj ku, i (3-e ,bgikp42). The friction 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 pow6*fp9go) :v b ig;zvay a6zo2int objects shown in Fig. 8–43fo6*bw2zgzaa9y6v :iv; )g po 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 consiua5o,aetr sur3(9l v cr47d1n sts 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 saw*cw) p-atdd0)f5u ni tellite spinning at the correct rate, engineers fire four tangential rockets as shown pddcwua )fi-tn0 * w)5in 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 c k254u( v+-g/an 2; byc,jm onyl6lzg awczzf:ylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calculab+ wgfzl ojkmn-,;645y:czvan /ygucz 2(2la te
(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 restkun ls+w scr)y/2 f.e5 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 merrv(rkx2 / bx2vky-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( vkkb2rv2 x/x 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 ofxjzryg/ -c.: mf and is eventually brought uniformly to rest by a frictional torque ofg:xmy jr-z .c/ 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 ac spt.b. khdn5ts4/e:m celerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solelvrbuvz6cj;r(y j pfw wo8g p71q431b4y by the action of the forearm, which rotates about the elb3 vz(gw p6v;fowypu84rj bj71rq1b4c ow 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 thiv1y71f/k1v na l wl3wwt8 r9n)qq1jxln rod, as shown in Fig. 8–46wvf 1 l 1wq9j3klt)7q1r n1l x8yn/wav.
(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 j06si8u: q f6+fajtge 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 withinspb i8o -37vz4mtx0hu:h6ik 6.o yuvt four full turns (revolutions) and releases it at a sph -4v0vp:xyktosb tuhum iz68o73.6ieed 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 om+z-s4ijffi kr .9x6 ,; lt xes19ysgxf 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 torque lpbo6j,ewx.(; rpzl6of 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 v4mba +4cs zs.a u5aj+rolls without slipping down a lanem acb.+45sas4 zjvau+ at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sa b)-phin9zl .un as the sum of ti bzna)-h pl9.wo 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 mdlg kox:g1 6t3;:cec7.50 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 is a solid cylinder. ol m;:6cxct1:ek gd 3g   J

  A sphere of radius 20.0 cm and mass 1.80 kg starts , xgvhijt +isq(nwe :l0:o-m -from rest and rolls without s-h:esmij t-,go0il w+ nx(: qvlipping 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 fall and t1qj6q4c c-w5n9 r*x (d,egbc-q cepiits lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hinccc95nd j1qri x(*ebqtw,4 q-- pg6 cet: Use conservation of energy.]    $m/s$

  What is the angular momentiyr 4v +b)xuo1um of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 10x oi vbr1)+uy4.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the anguwd4 runb6 8b+ lhhwt17:zk5ok lar momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when ro hnkdr7w 8blkhz ow tu6b1:54+tating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at hi548dnm ivxpf*s side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal positiondn4xpf mv58 *i, 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 o*hb uz+k+-q enne shown in Fig. 8–29) 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 rotatiokeub +*h+nz- qns 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 0peomd88os y1 increase her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a f8dy8s 0o mope1inal rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its k.pki .ldg;:et9omkq( ,ck)xcenter 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(kexkd cl. .;:mqtk9kop,i)g 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 skae-ax2ep (dcvj 8l+g x/py41lfter spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Eare q.2r0s6(yl,l mzcxlth
(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 f0ux)ax/b de8m)cf) adisk of moment of inertia I is dropped onto an identical disk rotating at angular sx ) a)m0dafb ec/8)fxupeed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 l znd85 r8pwfb p45 oqlf*t)av+x/9 sc$rev/s$ 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-go-round plat*e2f bnk-5ueuform of radius 3.0 m unb*5 2 k-uefeand 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 dkm *7);iaje wtatx30is rotating freely with an angular velocity of 0 x3tj7)mwa*t;0 iad ke.8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing d e-dlsomop) ct**+u/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 momentuo+*m /*dctusod l)- epm, 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 winhqr 84dfv(kxv :6 en3gds 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 s:hx5 ww ei5*u7+seix$ 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 rota2m+2h1jcs ar ete freely without friction. The moment o2e1 m+hrj2cs af inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of u 0b2ldia:0er a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings ai0bde0r: l2 uand 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 thevkk(:zf+qg t/y ph+h/k 2wvw) ground 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 ont+/ h:/ tqvgwkkzy+p2( kf)vhwo it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always fac-bta/4 iy uab4es the Earth. Determine the ratio of the Moon’s spin angular momentum i4atba yu-b/ 4(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 o kblo(v; *guu7l9wh3m f 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 inw ; *vv/+wfv(;htay.cs o+ly u the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s intlv;ty* v;.wv f( u/o ysw+ha+cerval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0ahk*/ei yrq* b)fq62w5n g,cz .050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of ith g*wz rk6 2iaqn/)qyfb*e5,cs 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 rear wheels0k1f 2w u;eop* tv0p sy6rf/d ($\omega_R$) 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 p9.4oqq8lbldcjy (xq72 ufx * of our Sun, but with 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 sxqydcb f .xu( o2jp9*84q7l lqtar of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stored kozi,jhs5 r/*rmf2 m(in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without nizh(5ommrf,2rj /k* seeding 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 illustraten 5y 23a+*pora0x(2pzihdz ;pkmnkm-c7j rr 2s 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 rg0k /tgj5jjf: olling 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 pivot free1 )jck uf4o-iscdq ;++l;iejt jm(gb)ly (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 gra ;k4(mtie)g+bjclfj +j)i- 1o qcd;suvity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M hasg/jpeeztp 3rz5b. o0 il26f- x radius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a stergj56o.eb2x ftpz /pe-3z li0p 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 roawb 5*wn.7myn* h4o egid is making a turn with a radius The foynn7o.hbg**w5em i 4 wrces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg0tdk on o+v70.*vfq hc rock into a sling of length 1.5 m and begins whirling the r0 vq0o.f*cd tvn+ok 7hock 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 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 ;l(l bnh6zp2ulinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinnhllz; 6u(2bp ning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylif k6y zbxc /vj,r(l*y8ndrical plates, of mc *kvbf6yl/8rjzx,y( ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rough8u *cdf-qx)bvwk/i+/dl f1ajpc5,p p track of Fig. 8–58. What is the minimum value of the vertical height h)qujpc, w+xf/v b pciadl1/8-d5*pkf that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not apqr6 5 ,.zcdvkssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spdl; z95dpuo +kwa p2lrq,h7w8eed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular 75llawddr; 8o pqz9h+ ,2kpwuacceleration 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