A bicycle odometer (which meaiqm/eu iahp(;.a.bfso7, lj0)fmu er ,,,vp w sures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What faiirelu,w / ,0 b am.,qe,)v7.fp(u omsjh;phappens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angulo8dtqpiz2n/a/00 bo qar 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 of either component of linear acceleratio/0otqinz/odq802 bap n change?

Could a nonrigid body be described by a single value of the an h:s2dyya1)yl r2.h xegular velocity $\omega$ Explain.

Can a small force ever exert a greater torque t4y*wdh7- ucuj 4i(esa han 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 e: f4nfy 9jujk;ip)hsjg0 9 l*a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help youe: f ;lgk fs)9 jnuihp4j9*0yj to answer this.

A 21-speed bicycle has seven sprogewjp7 ;f*wtrgy+-4 lckets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small p+wefw4y7jgr;-t l* g 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,;lb: ayc0 s) 7q5k pub(bjstn fast have slender lower legs with flesh and muscle concentrated high, cl5s 0ytlnu7a,s b b(:);b pkcqjose to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, nar n:ni8 s-,hotsrow beam?

If the net force on a system is zero, is the net torque tcjuo so107/(em(j1 r ye9wdp also zero? If the net torque on a system is zero, is(ey 7prcdu(w/o1jjs0o91 tem the net force zero?

Two inclines have the same height but make different angles with the hori0l ch4j3:whnn zontal. The same steel ball is rolled down each incline. On which incline will the speed04w3c n ljh:hn of the ball at the bottom be greater? Explain.

Two solid spheres simulp q 4t2a5(a/n*y e qyn3cblcur2t)yb2taneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of t)ryay2natl4ep5t*n2yq/ qu( c2b 3 b che 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 anww 3w(b5u q5-gi du6yqd 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? Which d q5 g ybwu(i3wu-w65qhas the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum ahwf- )ku gts91n*e +hcnd angular momentum are conserved. Yet most moving or rotating objects eventually sl9c -eukghs t*nw1f+h)ow down and stop. Explain.

If there were a great migration of people toward the Earth’s xswdor2v+fr y:75v q3equator, how would this affectrdr:y 2v3s +qxo75 fvw the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rof+ ia .0fqlr( (yu+ 6aggx** jwombr2wtation when she leaves thelgwfm rf j oay(u2 6qgwa+.0+x*i*r(b board?

The moment of inertia of a rotating solid disk abou(5ef(z 4i p/sf*cb dmnt an axis through its center of mass z/f*sibn(5(4pf med c 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 eak9w)14 smbc9:lubpcb ch outstretched hand. If you sudden 4u) ck:wb lb9bsm91cply drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical anbe0iiuuf /7v(d 6a.vi5b xdb( d have the same mass. However, one is hollow and the other is solid. Describe an experi5a/xbfdi(b(60 ueiu viv. b7dment to determine which is which.

The angular velocity of a wheel ro v(2lh(tc n h /q//3a:hfjl*uwuarg8utating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the whee/8:vu(t*2aghu(lh rjc3u q ahnl f/w/l? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating tur.m uvzo:fu o4mvp4-u (ntable. What 4 -zvo: ( 4vum.pfomuuhappens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he )pyscnwm+8l,eyriwudj 1q (b j*7; 1gthrows the bajny b1c+s;e*,w)1g87irj (q pm duyl wll, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conserx3qg 0 ktczy-0gz/7 cpvation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep t 07 c ckpzyqz/03ggtx-he helicopter stable.

  Express the following angl:lz,.a s/bnv:oqa6yp es 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 because of an amazing coincidence. Calq*c*b bl+/hzgu l4b*fculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.z+ cb* b4fq/gl* lhub*
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Ear w7.m.b9fbj0gmun l w1 ;zotv/th. The beam diverges at an;jm 0b1n.ww t7. u/bgomzvl9f 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 (i(yr :bu6ull 6500 rpm. When the motor is turned off during operation, the blades slow y(ru bl(l u6:ito 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. pwx scsr23r42vdx3p3If the ball makes 15.0 revoluti2w33 3 rdrc2p4 xpxssvons, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutiov7- rqot58yxf3k di*s5mpb. i ns do the rxvfd3pbs7-5 y i.8*tik5qm owheels make?    $rev$

  (a) A grinding wheel 0.35 m in dv 9x*g+( zl hoc4hpegbigw7 zh15,w 8tiameter rotates at 2500 rpm. Calculate its angulacwhp9 1t8 i*7bz(e4lwg,5zx+ohhvg gr velocity 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 revolutio3n brc (2 *u,lzev9qfjn in 4.0 s (Fig. 8–38). (a) W2 vnu, elrz(*f3bqcj 9hat is 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 1 zd)xt0jogs(7lcn+oe4t rf0) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pointx df+y3egk0xn w:ax5q86 4mqh
(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+o,g0)pych l k cm from the axis of rotation is to experience an acceleration of 10),kl+h yop 0cg0,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel cyql(w+(h;s+3 g esb maccelerates uniformly about its center from 130 rpm to 280 rpm in 4g+s+bmy (;s qe3 lc(hw.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiu:;nbnh:z cdf5 s $R_1$ 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 a9yov h*qr.1 wrboard 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 revr*v1 9 roy.hqwolution 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 fro x-zo)q5u od/fp-vdw +jl;.ukm rest to 15,000 rpm in 220 s. Through how many revolutions did it turn i; f -/o5dk.- )dql+z jwvpuxoun this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s.nnrt-l x;) 6ft 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 7:m 7hwxgmz8 m* u,ub7dck6qk highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete rev,bzgd7:7qk u7 c m8w6hxmumk*olutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 f6imj +1tkvk, bm38vg rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in 8, v6m1jg i3ktmvfb+k this time?    m

  A cooling fan is turned off c )i7kwwdb8i0 p,h)ni when it is running at 850rev/min It turns 1500 revolutions before it comes to ai ih,w )0n8)p 7ibdwck 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 thezy*he8 mh yl 1t6z1xzg./+ct e car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter *hytc1eh68 xy ztz+.eg1lm/zof 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 co l(/, 3,lwzotbr b*wkar reduces its speed uniformly from 95km/h to 45km/h The tires hal z3rolb*/bt wk,wo (,ve 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 ;z.l-2ol -apif(qs saputs all her weight on each pedal when climbing a hill. Tz-.2 pssif(l;a-lq aohe 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 s,ta)3ea81f.t jfpcp a door 74 cm wide. What is the magnitude of the torf38 c,.tat)pa 1jefpsque 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 shownu pfda/b,k -g) w-1ahs6 h8m wzn+ktr1 in Fig. 8–39. Assume that a friction torg )z kp8 -,mnthua1 +/s1 d6wbkah-fwrque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to thgexi f0*h5 5irie+,rm e ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal positioi*0 ,e5mghr +5er fiixn and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an enu* k ;xxe3 (sphpo5a*cgine require tightening to a torque of 38 h(p axp**x53sec ;o ku$m \cdot N$ 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 inerti.4hwu b/xk: )wq5 pfp:c ls/gy3ak-kma of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is 4pyk- g5kqc/ p: kxabww/m l.hf:)s u3through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicyclo/:c di)b:viv tu dv,q).9ntxe wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of thet:)d, vcbo 9t/di:vi) xqvnu . hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotateeol2q(ii cq76k (p9ymd in a horizontal circle of radius 1.2 m. Calculat p26qi9 ycq(il(moe7ke
(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 cdur5ilu9k;4 1;i fu+d nb/xgwonstant angular speed (Fig. 8–42). The frictdl; x1;u9w/kbu +f n digriu54ion 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 ofrnf ca29nm i1oc67dj8sp;fm: inertia of the array of point objects shown in Fig. 8–43 abouo pa: 9j7nfsfc1mri2c8 n dm;6t
(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 oxygen4szmyq3.u*da 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 correct ra:xr;66a mk t(mtwyf bg b:fewr5n 9i;4te, engineers fire four tangential rockets as shown intt:f5x rg;i;m k6:m6a b9wfrn(b y4we Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a 5ktht6 4(ki ga(m4j du5eky 4pmass of 0.580 kg. Calculatkj44y64idu(kkpam5 e h(5tgte
(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, accelerat)n2/g vw /cwswing 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 tangentially on a small hand-driven merry-go-round and isg(b0 b7eh)ob kd.a5j t 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, a5j.dkebbh(ag)t 70 ob nd two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually br 4y,q bncm02b3cw tg,fought uniformly to rest by a frictional torque bq t320yb,, gcwmf cn4of 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 fah3 fg 71hh+faccelerates 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 /fax;10qsx oi- rru h5the action of the forearm, which rotates about the elbow joint under the ac r5r0;xsaqi1/ uxfh o-tion 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 c8 6xuufswi ;)tan be considered a long thin rod, as shown in Fig. 8–46xut) ;f i6su8w.
(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 tl)mdzp :u)v* ywo 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 wl2my 3y0vg95l(vg hfn ithin four full turns (revolutions) a052gvnlmyy 3l9f( vhg nd releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia of *:df6*nf bj0t scxt b8$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 28us,9pr q -ncr.( ylo4q0 $m \cdot N$ 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 rdd0:ptzu /x. l 1ssiw04 zz2feolls without slipping down a lane a uftp/sewi sz4ddx 10.0z2 zl:t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic n xf ;5jjm+5eoenergy of the Earth with respect to the Sun as the sum of two termsf;+emx o55jn j,
(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 of2vx1yl *wtd 8s 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotat*lw d1vx2y8 stion rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls wt.mgp* f7yv 1hithout slipping do*fmgt. hv 17ypwn 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 balv* p(fwhhj5c4l8 v gh,w-+ra zanced vertically on its tip. It starts to fall and its lower end does not slip. What will(*vjr-+ hwf45hg, z awv8chpl be the 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 momentum of a 0.210-kg ball rotating on thl sq 9fcha42o/d6hxrj bg2 ;t7e end of a thin stringa g/xhso drbj7h9q242t 6cl; f in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding w r7kom i+c(pg8kdlx,3heel of radius 18 cmgr,ilcp o+k7( 8kxmd3 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 royth w r(-axh.dty5( v/tating at a rate of 1.(dwa5r hh.y -/ttxvy(3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig..trurfnu 75 (yvr6ia) 8–29) can reduce her moment of inertia by a factor of about 3.5 irtf6( yv5ruu7)n .arwhen changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial 8psx.o )q* mqyi;j+bx rate of 1.0 rev every 2.0 s to ay)o*.xbji8;smq+qp x 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 rot8u jg opnk jszg04t 2necdcu+( (+98qa/r 1oqpating around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after thk89to+n gqje4nz+d8j0pr1/cpg us coq u(2a (e clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at9 acxn;k jm2zjx2 q81tx l1(y+o hhdq5 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 angularugi4-o.rjipc2*u 2 o d 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 momenh z;w ysnn72b:t of inertia I is dropped onto an identical di:w;y bh72nzns sk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns t n;3ocz;og;vtxy;q6 at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merr h.jlj1pku* h+y-go-round platform of radius 3.0 m and moment of inertiphhu1l+kj *j.a 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merr9s8cd9-l*v yy.m -j (nir grwpy-go-round is rotating freely with an angular velocity of 0.8dryg rc99v- sj(mi wlp*.8y -n $rad/s$ 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 whue9g 88jm(grt(qwcf,f) t-bv+jj r9*wvt qc; ite dwarf, losing about half its mass in t b,j)q ;*8gg(cw9f8( -rtrj vttw uvc e+jqm9fhe process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve w7bh fve m51dri.;2b,mcl zltv r9 a2.yinds 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 m 7qsnhd e9mi x1ybbt;3 vk-0 6a,vcl1$ 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 rotate freely wims.nqh r+) 5egthout friction. The moment of inertia of sg.)mehnq r+5the 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 d- f u ,ayut(3f0zbuu8merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia z,ay0fut bd-8 (fuuu 3of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the grou rj6ms cytye+:.)mw3 and 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, Fimyj3eayr:w+m). st6c g. 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 sde ,7vpl*jc0m t3cix/uch that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbivjx t,l3d7m p0ec*/ci tal angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rywr3 k 9 f::eiy5(acgeate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius n ,jhic9j7 c(1 yy ufs)9eqc9p0.20 m acquires a rotational rate of from rest over a 6.0-s intervcc9j 9h nyjcp,s)1ef(qiy 97ual at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid4ybg wl 6e( haq,/g(ld cylindrical 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 energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it isb,(hdqy wa(4g/el6 gl released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is thce,prn/*h* (j )wo omhe angular speed of 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 size of our Sun, but wg:j-4.ngi 9go6mmi,t2 bmwq g mog2b;ith 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 neutrbmgg,9 g-g: 2q6 im.tgiwbj on4m mo2;on star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use en ;np33etwdo/yxz: stm* ;/dbu9vn v fm6is4o.ergy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, use93o/p*di./z6smd m veyxu nst4t ;3fvwno;b:s a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrate l99)bfd-jbsmzbc*.1,lv h (ve6a wm 8/chrals 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 surface at sphsw:b 63+qw uj n+-0mp3 lwewyeed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we 4szq 4onr/ l)mignore friction) about a hinge attached to a wall, as in Fig. 8–54. T4 4 mnszlr/o)qhe 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 R. It is standing vertically on the floor, e0eddyvrg*fr 89j n2a1 o,he ;o 7 5zvxe2m:hgand we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, wher x8f a z*ev9e yh2;1njgeg :h5d0rd2oe,v7mroe h

  A bicyclist traveling w /o5 rnbrhn8 :dib-uw/ca87xo ith speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycl-5h7 bn8r ba8woui/ dr/ noc:xe 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 xe cib)s hjaqg0*b; 46begins whirling the rock in a nearly horizontal circle above his head, ac4aqbeb js;hx6 *)ig0ccelerating 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 rods, m(rgz fd:sn//q aking reasonable estimates for thezq:dfg/s /r(n dimensions. Then 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 clutch assembly which consists of two cylindr1x1dpih59 xipical plates, of i ih119x5dpx pmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 bvv3q. q dk 76p1ly.zaradius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to re6y.kqb3. z vvdpla17 qach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but . *mhp p ..dehks;g2ljdo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions 3;klww2 l3 mhvas the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular accelerationmkl2;h l33v ww 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