A bicycle odometer (which measures distance traveled) is attached near the vj:/ s5abfh w.pu6+nb-e6kj*f 2ndi q wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicswj*n6 u6vjiq bk5. -abp:hfef2d+ n /ycle with 24-inch wheels?

Suppose a disk rotat/97kfeve vtfd*i ;7 z7uyr4ofes 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 acceleration? For which cases would the magnitude yr t7 u4zevv97fe ff7*/dok; iof either component of linear acceleration change?

Could a nonrigid body be described by a single value of ba++* q ;p2m5hi1g3irdb4 df qe 6x)aeno 3fppthe angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? fs/h 7vt7/clgx/ e/uaExplain.

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 he+)utya y gy7dwm cf)0 reqm-0g* u3xb-ad than when your arms are stretcher 3 g+y7bm0 w)y-atc0mgx uq*yefd) -ud out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the reakpd ev 30. j4masqmk9-w5p:zwr wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprk-4j.sp pe0aqkz 9mwm wv53 :docket? 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 t;-lyo)( tk;/ wyod uwbo run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basistb ;w/yo yl k-;wod(u) of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (c a-zy/ q-9 n6tw5iv kpg2yfz(Fig. 8–35) carry a long, narrow beam?

If the net force on a systemw:o962op2i5ekoghf9- ix p vm is zero, is the net torque also zero? If the net torque on a s-h9k9ogo mo2i6e2pvf iwx :p5ystem is zero, is the net force zero?

Two inclines have the same height but-tul ;py 8rvn/ make different angles with the horizontal. The same steel ball is rolled down each incline. On whicn8;ryl/u-v p th incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from r0hfv e4w qfg,;, p3rzb m1ube3est) down an incline. One sphere has twice the radius and twice the mr1u4b3 z,;q0fvmewfgb hp ,e3ass 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 tf,yexj33q*csekf z 92.el4 clhe same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Whichk43cfs*e .lelqf2j , z9c3ex y has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserve3dedapm55c 20hrre 9b8q4nq ad. Yet most moving or rotating objects eventually slow down a8dnrhd2c e0q94aap e35r bm5qnd stop. Explain.

If there were a great migration of people toward tubdv;+q(rieh4z qu( h 1l*)rjhe Earth’s equator, how would this affect the length of the day(j1iu*lre (vbuqrqh4 h z;d+)?

Can the diver of Fig. 8–29 do a somersault without having any x(*ja2qz 0dcp initial rotation when she lead 2( pczxj*0qaves the board?

The moment of inertia of a rotating solid disk about an axis through i rbfwo l25 dvx.f7s7m;ts center of mar;x .w 7fo57ls2f vdbmss 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 outstrl:l405 swc quqetched hand. If you suddenly drop th4lwsqqu :c 05le masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howen*vh7gr( 3hod ver, one is hollow and the other is solid. Desgndo3 h7r(v*h cribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle poi9 m*du *-gy 7tuzpjjom(gyiv9m2 gf4 9(su0olnts west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this pointugstv49umgi97yd0yg9z (-mjuo(2jm*op *lf at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable.8zcv cf+msk .fo 96p (tge:b wez4pg+1 What happens if you wapw:eff1 m4zg v kcst.cgb(z+o8+pe 69lk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. m7k zb(8ob 4ytn m;i3zAs he throws the ball, the upper part of his body rotates. If you look quickly you willymn(o3ki47; tbmzzb8 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, discuss +pwimj o; k9c(qo19dkwhy a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the heliwd;qk9 k o9pio(cjm+1copter stable.

  Express the following angles in radianru46 qh+0oqcq s: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, z-yo31igfys5ctit.1 cr 4 cu, using the information inside the Front Cover, the angular diameters (inosczi u , i11-3rc.yf5 4cgtyt radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. Thvor oau4 16n82d*bzrde beam diverges at aubd6ra2 4o o1dzrn8*vn 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 rpmckqt)oq1tluh)-tdg8o+f- 1*jqv,h x. When the motor is turned off during operation, the blades slow to rest in 3tf-+qjx t,h g )ckt* odqvo)8-hl1u q1.0 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 .-/vo j rx7j(;zuecexto another child. If the ball makes 15.0 revolutioj/c( e.urjvo-;x 7xezns, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travelsc d 0w-(4rgzgs 8.0 km. How many revolutions do the whez4-rd 0wgsg(c els make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angul*.d;nz iu9as fsw8pq+ar ve. qp s+zsd*nw;f 89uailocity 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 makes one complete revolution in 4.0 s+yx6jh7l(s fs (Fig. 8–38). (a) What is the linear speed of a child seates 7h+y 6lsjx(fd 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 t k*-a jq3zz)m9wusyx+rm fe k. 5zen,-he Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poilnss 419bbkue zi8 hq 16vyr+2nt
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the)5esmz6j,asaet d)d3r2rx 3q axis of rotation is to experience a63r e,ams2xzjdet)r a5d )s 3qn acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly2s1 fu+od(ha j about its center from 130 rpm to 280 rpm in 4.0 s. De(o+us j21hadftermine
(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 ojx28ao (7*(oopjywfr -.1c nplqzf- $R_1$ 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 aboax(zyq/:9q g5pqx 74nj:x i ) vfry/mcurd the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. A4):yf /x:y(xv r un9p5xc/mzjqg 7iqq t 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 from rest to 15,0)6+q upwx9i9 icwh0 ct00 rpm in 220 s. Through how manxh upii w99t6 0+c)wqcy revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 qr-42rf7hlgos*:b k orpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets inx-q8 i*y y(s*v lw,fvd a whirling “human centrifuge,” which taki(f*8xly,ywvv*d q -ses 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniform,o4z72dfo 9plyh0 ,kqg cs2ks ly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have travehs7lk0 q29gocpdzf s,,k2 yo 4led in this time?    m

  A cooling fan is turned off when it is running at 850rev/min mx9cu n /;g9zdIt turns 1500 revolutions cgd/m;99 znxubefore 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 unaqfd+wyo(/ /)hg-yj+rd wa /kiformly froj/)/a f (gahr qw-d+yydk /+wom 95km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly +s/p pym9h;xel,0uprfrom 95km/h to 45km/h The tires have a diametu+x;y /rh p9,elpsp0mer 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 peexkq ;z 2srya4x4bjzj5 qq:5gvw3 -9 fdal when climbing a hill. The pedals rotate in5q44 gxykbf:zjr ;q-w2 j935szeq vax 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 m3hdu +4;-a zeakh)qh is the magnitude of the torque if the force is exe3 ;dk q-za+hu a)4ehmhrted
(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 j)/8ihom fr hd-2 u z9h(6puln jpham-+c21 lgFig. 8–39. Assume that a frmhz-jurl26-j( pni1h8cp) o 9l+ m f/ag 2dhhuiction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attachednw 51v.voo1t4j(r isa to the ends of a massless rod which pivots as shown in Fig. 8io( vtov w.5jna14 rs1–40. 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 ev j3p9 hlo11can engine require tightening to a torque of 38 cplvj3119 oeh$m \cdot N$ 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 h 1.pdf6ikr r70.648 m when the axis of rotation is through its center. dh7irfp k61r.   $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm-hvvesl y2br8m-w f :* in diameter. The rim and tire have a combined mass of 1.25 kg. The m wmb*le28-:-f ys vhvrass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is1/hg u )u9fiks rotated in a horizontal circle ufi/u9s hk)g 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 on a potter’s wheel rotating at constant anp r 6; t8:4;iaintaqfjgular speed (Fig. 8–42). The friction force between her hands and the claya ; q:aftpn8;tiri6 4j 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 ars mdzse5.m6tgbr0ba4 uis ym w.m1)() ray of point objects shown in Fig. 8–43 abom(5mi.e041ua.ms sb)sry z gwtmdb6)ut
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose to1 yt*zk. dczu8; bk;r2fowp; wtal 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 c9wvo;55v7emi p(u ohd 6-w8lgl9 ncgnylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If;oml(nlnv g 6g8 e-vpui95 579 whocwd 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 of 8.50 cm aw(fe- m(6phn znd a mass of 0.580 kg(h mnz-pfw (6e. 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, accelera;, -sdsxc wb*hting it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentia3mw j3al4ak f2lly 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 to produce the acceleration, neglecting frictiw3k 32m4aajflonal torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 ck,org:u:otxc/3 as iq)xj.)rpm is shut off and is eventually brought uniformly to rest by a frictqoxk3 )ca xujrco/,i ):.t:gsional 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 m3s7bo 5rpc4k--1 mpvvm dkd,accelerates 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 adnab eyjuqj w;(fui6q5(u5dw9p ,: nd259aflction of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly froj(:dwfaud y(q96 uu,fpli;wjq5endan b5 529m rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in3d hj v*lg;aosy yr5lc:45mj8 Fig. 8–4 jlyy: *4gojsrl55a38dvc mh ;6.
(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 c o5ec8.apcx3l onsists 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 acce. .pak bjzq0r5ec4p9qj 2i4 dsn g-u+qlerates the hammer from rest within four full turns (revolutions) and releases it at a speed op40 rq kj g-dsqijqbn .eap cz.5+2u94f 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 momhn mx*8k5 tx73b m1relent of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develop sa6s4 5goa+sps 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 masz)u g-9y wzyym9-*yc es 7.3 kg and radius 9.0 cm rolls without slipping down a lane at 3.3zy9zy)wc 9m ye -ygu*- $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sunsy v g k 2lcmh(:4/2/ffd5gmz k7xhz1r as the sum of two terms 7(2gklf/1y: dhz5mzkm / gcxf h42svr,
(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 an4t ; f*nx/o3lffk1b pqd a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution perp4fq*l;3on 1bkxt ff/ 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass mi 97msy6war(1.80 kg starts from rest and rolls without slipping down a 30.ayw9(i r76msm0 $^{\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 i;tb s0qvd13agc zn*+ ots tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hi*qna1+d0tsco g;zb 3vts the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball 7;0s sfei mp(rrotating on the end of a thin string 0;r sse7ip(m fin a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrj 7pjr;9akh4nical grinding wheel of radius 18 cm p a47jn;9jrhkwhen 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, hander o9yk++0qae s at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizo+oe q09 yra+ekntal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can)im:1,zehb5n mj 2 hpe reduce her moment of inertia by a factor of about 3.5 when changing from the straight position hjmpn)mb52z ,e:h i e1to 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 ini, r)ncfsa rt4t2w- ;jdtial rate of 1.0 wf, cts-da24jnr) t;rrev every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotat/qxkq/,2dq jking 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 rotqq j,kxk/2/qd ating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular cs9oppsx6,/ m-o(vj ymomentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Eartag y)xm,tu6 e5h
(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 inertia I ig8:qb8crj;d9p v ts4e s dropped onto an identical qeb tg4rvp:j9d 88 s;cdisk 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(n /ye3i 4vdoza,;((jhl h oiw.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a xnh .( gjk2p6av,rtq(6 amw+irotating merry-go-round platform of radius 3.0 m and moment of inertia 9hw6gn6 jt2(i,pmk +a.xr(q av20 $kg \cdot m^2$ 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-gof ejez97 pkg1xs7t 0k7-round is rotating freely with an angular velocity of 0.8 1t egs0 x7kj 7fkz7ep9$rad/s$ 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 about hui b)rwu 10eo.+t h6qhalf its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away w+qe60hhui.1b ru)o tno 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 excescl gyh3 v1dz02/p5 sdrs 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 0e- qzgrs,a9/km f+0bhk1y jf$ 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 at4be7cfhi* zhrli5u. 4 rest, that can rotate freely without friction.u. ch*bzl 4f4 i7h5ier 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 stands at the edge of a 6.5-m diameter m4xtk3d *: iz;yheym5terry-go-round turntable that is mod3 ;ktxm5t4iy*ye: hz unted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rol w/7ur6-uscav xd0 i4jls on 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. Whas-r0/7jcuxd v4 6wu iat length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that tm .y zl/2uuu4wyrhz++ he same side always faces the Earth. Determine the ratio of t.hwur +yu 2/lyz+um4z he Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 5f eqvd7r: +*q4 ww+og 0p8ot8qzhmpl1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape oc7:dw ewr/. xl 5ufuf r,pm*k3b /h;maf a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceler*.kh mldf:xw ua; m,c35u//eprb7w rfation. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050s;r0ba4 o bg;k-ofc2n( dd/sj kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diame ddsr /2nsfojbo; -a (gk;bc40ter 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 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 wheem (gcz6; ksar, + xp4 .a2bjzhx-ecw7- 1tgjvhl ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as t,5cf gqxa95jgreat, 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 th55,xc9gjatq f ree-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 fo5lwmifbfw7 /+ r it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to tral 5ifwb f7w/+mvel 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 illustratestjg v(9atf(pd9yots y 65;k1i 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 horizoncy1k391hoc ba: 1gcynv+f ; ajtal 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 anqs h.5.pk-hy ck)h1*lhl p-tnd length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, . cq)h-hh k5lnpkl1.- *yts hpas in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius cl wk(gq,4vwib ) *er a-e/g*aR. It is standing vertically on the floor, and we want to exert a horizontal force F at its ax*cv/ee-k iar g gw)b,*4lwa(q le 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=4.2vjl+1a ;9m s fjiir0n,m/s on a flat road is making a turn with a radius The forces acting on t1la nm0jv si9i+,f jr;he 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 rock into a sling of length 1.5 m and begins51a7d5 win1pu. ipc 9xn j. 8ywhhzdd9 whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a raiwp d.9x 7 d5nnjic1hh 1z.dp8wa59 uyte 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 cylindjn-hb ;)faf* ier and her arms as thin rods, making reasonable estimates for the dimensions. Then -fjbf;nih )*a calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a cl jrey3cw,ymi200y.o eutch assembly which consists of two cylindrical plates, of myj yw me,ycr0 0.oie23ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 .- 7s c6frsrqnalong the looped rough track of Fig. 8–58. What is the minimum value of7-6r s cq.frsn 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 asscflpg4 uu9p tom9,3b +ume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revoluth)bd ehv wwly;)e+(,b ions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (welhdv) +;hbw,be y )(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