A bicycle odometer (which measures distance traveled) is attached near the wheey1xxv,ia )oq. l hub and is designed for 27-inch wheels. What happens if .yqv,oi)xx1 a you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates atmvkj n198(ig.; m6o)yo 1pk fidbu2sv constant angular velocity. Does a point on the rim have radial and.y m)k2ko vmginsp8 udibo6;v 9(j 1f1/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value86njb2j 8rewm4euhbx a 1jyst0 1m)2g-*lz ue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than 0,y)d ty 2unm b,(erzva larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head d0bnh m+mnh. 3e/ej1u than when your arms are stretched out in fhe.0+31/be n jdmmu hnront of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the p 8x8/sv6ti08)cei p 4nmpe zfeedal cranks. In which gear is it harder to8n 4pz 8s0e )8cixfme/e6p vti 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 ab:cr.:*ro5rathr f )x fle to run fast have slender lower legs with flesh and )r:fx 5af:hotr .*rrc muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkep v9 h/v0t9rf*im/a l qzvgdj0-hm+:xrs (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque acn;qb.xpmch9be 64to0 )mk1llso zero? If the net torq;qn c04 x 6b)cehmbt1k9olmp.ue on a system is zero, is the net force zero?

Two inclines have the same height but make diffcce d4-g:k m4qerent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottomqd cgcme:4-4k be greater? Explain.

Two solid spheres simultaneously start rolling (from res;:cq;aiop) l et) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the glocp;eq a:i ;)reater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius an:en/p e d1h0g1 qjthp8d the same mass. They start from rest at the top ofe1q dpgh1hpj/: 0e8tn 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 the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most movinp0)eqg6n zjxr.u2)k lg or rotating objects epu6 0e.z )xnrj gk)2lqventually slow down and stop. Explain.

If there were a great migration of people to ra+6ho88t omi g-p8voward the Earth’s equator, how would this affect the lmoa +p 6oo8vhg8-8itrength of the day?

Can the diver of Fig. 8–29 do a somersaup )9nqsn 3kwy)lt without having any initial rotation when she leaves the boa) yqks3w9)npnrd?

The moment of inertia of) +o uxkjbh) whc.ar,* a rotating solid disk about an axis through its center of m,co)bu*ar ).k jhhx+wass 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 outstre072l gdlz, tg*jt6imntched hand. If you suddenly drop the masse g,tin2*gmdt7j0l lz6 s, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one xtqsp0 61l5zx-6v eku is hollow and the other is solid. Describe an experi5se k 1x0xlv 66-zquptment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points wnybnx8:cve j) 1l50u sest. 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 0uxyvb n 1c:j8)nl es5wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. +wr*pk2n 63)msxun t hWhat happens if you walk to hk6t3xunrmp s*n2)w+ward the center?

A shortstop may leap into4dhpo.g be ;s fv k68ahy9u 1ya8n+a+v the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite ya bh; v+kuhsog+a p 1e98 46fd8aynv.direction (Fig. 8–36). Explain.

On the basis of the law of conservation of a4rknk6ylh o92 6drx0b ngular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller c rbxdy6o6 k24 hkl90nran operate to keep the helicopter stable.

  Express the following ar .a9qu8dxvs1,oq ;p 16xzjzch -s(djngles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth bep; 38m7;gdt7th6j tooj : obqlcause 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 ol6qtog:3tbm78; 7pootjh j ;dn Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The qprvbj 3g(p 3qk1rp;/ beam diverges at an angpqb q3pprr vk;1/j3 (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 rot+d3 b pjl,dw9o*:tk jsate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the an,+k 3j:sd t*pbd9jl owgular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to1h:kq3j cwp ,(d3tedf another child. If the ball makes 15.0 h 3w3,:1cfk edq(pt djrevolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How maoxi gk,nmyin8 1u3 t26ny revolutions do thm3i8og2tynui 6 ,xn1k e wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter j1b rq/ 1d+qddrotates at 2500 rpm. Calculate its angular velocity +1jb / rq1qdddin $rad/s$ $\omega$ =    $rad/sec$
(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 rva0oej zg 18c9 .usr58d7j;ml5fgpzuevolution in 4.0 s (Fig. 8–38). (a) What ijdem5j o1.l zz;pru8 au0g 5vg 8sc97fs the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around t0umy :u3(h+)pbbb ah lhe Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pointna8g2jc4.o i i
(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 fro ci c,on:cu/fc egc2d-/p8dz)4lbifg9 5q;ixm the axis of rotation is to experience an acceleration of 100,000z8 cpiqgi2 ic;cl) :gf c,n4e/udxf /5dco-9b $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130wk ,36atna kz( rpm to 280 rpm in 4.0 s. Determinezk(a3tw,a n6 k
(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 fw 9 ;hc)cho. b zyyh6nr55g0j$R_1$ 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 spacec8nc;i 0v .*cny zqha)9w,hfkiraft 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 minu0c,yw9)v*zhf ; hcq 8.ia inknte during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Through h44f mzq8ue c6hf 8tzk4ow many revol8tc6f48 zm 4e4hk fqzuutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 t89zufyzmb -d5*ar+ yrs6yf2 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 highspe9v0g/ udxi(1kghj xb hl1d7g4 ed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 2lg d1udhvk b1xi(/4 x jg9h0g70 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 fr56vi vzh5uf(dom 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of uidzvf5( h5 v6the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turnsjnz8d; k./qja3me g. p 1500 revolutions befndjq.epm z j.ka/;3g8ore it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uni+ywzag xajza8yy9hb g,6+z * +formly from 95km/h to 45km/h The 6 a+8hwjgzzy ax+b+yzy9ga,*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 reduces ijcq r.kjf12fe2s3m be9)8 f.4 jth dxqts speed uniformly from 95km/h tkj2ce1rf2ejbh .s x4q 8fq3.t9) fdm jo 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 her weight on each pedal wh3u;;x. qak2i f 3pfzczen climbing a hill. The pedals rotate i 2fqzf3ic3k.auz px ;;n 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 or5 -ghb8u q8; j50 .qmoiqb6mljwl*crn the end of a door 74 cm wide. What is the magn bmll*0 qcog-5b8jijm6;.r5rq u8 qwhitude 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 shown in Fig. 8–39. Assumu ,(by. ..sycymfik:ze that a z:syk(bm.i,y. .yfuc friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass ff( si;td)i p8m, are attached to the ends of a massless rod which pivot; dpsif(i )ft8s as shown 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 to a t*e fty5w1h2nw3do sm 8nzn;-5on5qryo7j3rmorque of 38 jynre-f; n17wnm5*os t5 dhq zrn25ywo3m 8o3$m \cdot N$ 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 sphe0ya k 9xko*jl+re of radius 0.648 m when the axis of rot lk *kxa+yo9j0ation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The yr dr:.oeat +0k4n /vm:1mm korim and :omkore +.m y1 dvk0:r4mnt/atire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a ho cp-8hq)3udmp rizontal circle of radius 1.8)pc 3qum phd-2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant ang2-+x1 6 tbkqwa1ty 4sy6 xhdccular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N total. awkcy2dcbys4h6+tqxxt- 1 61
(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 ofo)wa gxccb3 3i/j7(q (v5kux a the array of point objects shown in Fig. 8–43 aboutx7xvjbaicq3(ou5g /(akw 3 )c
(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 two9;ocl br/ lk 5*brnln/.hc+eo 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 c,w+cgeg.nz +borrect rate, engineers fire four tangential rockets as shown in Fi ,be+z.cwn gg+g. 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 a radius. -dxlf fnd+o. of 8.50 cm and a mass of 0.580 kg. Calcuofn xd fl.d-+.late
(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 ld.x3 0 qhd*jx8ds5be 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 tangential- h/njeq47r ;ixkh;nb 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 of 760 kg, and two children (each with a mass of 25 xn7iqk;; hhre jbn-4/kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventuallkc(i: syc8+ypy brought uniformly ts8yyc (i+kc :po rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelj,)n yxc1qcc 0erates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forea )ey yz4r9aisuqy- :2pm-coq 8chor 2)rm, which rota8oceymq9c) 42:- oz)h ar2 rui- spqyytes about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as.z+nrbp*.l p wr6vx6bp8kh7p shown in Fig. 8–46.pl. nrp6zb6rkx+7 v. 8phb*pw
(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 consistsx-y;k6 + ;aefqujrnd ( 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 h5ct1t9e 5k8brr 3cljuammer from rest within four full turns (revolutions) and releakl18r crtb5j et5c93uses 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 inertia ofns/bn tb.ji1)/eh0u o $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine developscg6:.hj6: d5y8 1 w g 2ub2bhfh vw5j5bqtfvvl 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 radius 9.0 cmfz6d(qz f((+ht0o id p rolls without slipping down a ladz (p+(tiqzff(od6h 0ne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as theu t gi0tvo rlr:a)ex8;5a)k:b sum of two termsextrig:av 5oa0k l8);:)ubrt,
(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 vc3 9mfd.6f 7dcmh4na7ly h( rand a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation ratevy6 39nrhh adm.( 7dmf7lf4c c 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 rest and ro+ b dvz,pl.8(ydaqt 5glls without slipping down a 30t 8bqlay 5(+ddpz v.g,.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. 2 lp1js 01)dglgo9bjv It starts to fall and its lower end does not slip. What will be tjogpvj 02gl9sd)l 11 bhe speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular mome+58(+q y:he fu(k+bf cqvpr8lo hi:hintum of a 0.210-kg ball rotating on the end of a thin string in a circle of radiu5(8hfho( yrbe8v:u+i:f+q+ k c hlpiq s 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 uniform cylindrical grinding wu ojb;q+ap/50dmx(x aheel of radius 18 coa5 +(q0 mdbx/apux;j m when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a ra8 o 4nxho;z.mrte of 1.3rev/s If he raises his arms to a horizontal positir8.;xznh4om o on, 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 t1x+yc17 eeub of inertia by a factor of about 3.5 when changing from the straight position7 b+1exe c1yut to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate /wd-x8c4/+90qe iagl u yyn veof 1.0 rev every 2.0 s to a final rate ofu 4i nealw/-yx890ygv+/dqc e 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 vertai*gchb0.naz2 w1 3pb,hy rd- 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 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 frequchdzap,2by3gr.h a-01win*b ency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater ig, fbqx+uqyao8t,,w bt0m 00spinning 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 angulai z2hy:0jfq:s ay2z *tr momentum 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 momen4icw2wsex x431 9isrv t of inertia I is dropped onto an identical diskce4 324wvwii1srxs9x rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4zl (ryy0 (oak5cm.nx7 $rev/s$ 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 merr 8r k0.sa9bege.qv 4amy-go-round platform of radiuke . v.a4sqmeag0b89rs 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating free::ge sw.dy hh*ly with an angular velocity of 0shde y:w.h: g*.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 abo vm;m p*d87t)(*flzk9t tanadut half its mass in the process, and winding up with a radius 1.0 7azltk9m ;f)vadttd* *m(8pn % of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess omez,a.sraq ( xcz1,zr53lfy -f 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 xwr1+:2 mqq zoq9nq :b$ 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 aeo8;.ypg1 v (p.qdggbt rest, that can rotate freely without friction. The moment of inertia of the person plus theeppg.; gv. y8 d(b1goq platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diamewhu ygy7)4 ;pater merry-go-round turntable that is mounted on frictionless bahy 7p w)ygu;4earings 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 y/yh/zcu-lwdc tviq5s z l5i6p*72p( the 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 onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwindsyc/6ulw sli2p/5q yz *t-c p z75vhi(d from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side alwaysp,9fy hfa-u9qb(;( /cx o gmmq faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat thf;af yx9,hb( qpq/u9- o (mgmce Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerateklqw/yd2/1 dfhgrc8xxc1 5 r5s from rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone b m9zj se6c.3u2yj-iuin 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. Calculate the e zuis-b3y.j9 62cjmutorque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrid kgsjnsl:i *3+ x5pewjs--z3cal disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energyx -dsj-n3pw* +lksgs3ij 5 e:z to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed oz8*jgsb(t0;(em6cv- lg pki if the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the s(vv r-utl1vqs3xg5+cize 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 star of radiu 1xtqvrv g5-ls(c+3uv s 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 ener9m48c/fc9ftme zy) yigy stored 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 mmf)zmi 989y/4ecy ftcass 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 illustratesk ghio2u nx;5cs7ku ui-r4a99 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 /zyf;h qb tln6/5(uay+0lao hsurface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivo-d6+4l ikdtk: ft0 8so goy.aht freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54id68kt4lf .sdayo k0:h to+-g. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radi3j)xj;vq64e :kf+hxkddg+b.7 oy q d cus 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 step against which it rests (Fig. 8–5.+yb 3fj:e dhjxkgq+)vd6xo k4q;c d75). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat roau cp/v)1wjy 7wd is making a turn with a radius The forces acting on ty )w17uvc/ wpjhe cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg ro7 ,r eg n)xinw.lew11+ fczb*ock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circlxw,17) gzinno.*l+f wec er1be above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin ro v-i wb sqb6-7tnzd20xds, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly againdi -627znqx-wv0b sbt st her body.   

  You are designing a clutch assembly whicbq9 r x2s8 )y3rm.qozxh consists of two cylindrical plates, of mass oryq3mb9xxr8)q .2sz $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 Fig. 8–db;giwh )g0c /58. What is cbw0g /;g )hdithe minimum value of the vertical height h 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 assuf5xa4 eeki z71me $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unhwzkk5r. ux71iformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) W5rwk .7khx z1uhat 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