A bicycle odometer (which measures distance traveled) + oh bg1mcxb (1+wlq6uis attached near the wheel hub and is designed for 27-inqx(hmobgbc 6 w+ ul11+ch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poin8i8ujo g 5azf33jh;vjt 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 acceleratio83;zoavjj jh 3 5gui8fn change?

Could a nonrigid body be desc7p*qp*-cupz,0mem9 r xe1ax zfvt 0a 1ribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert afj82xxd1 tyl0 ;k4r rt greater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hand yr6 c/z/pcgv)s behind your head than when your arms are stretched out in front of yo)gprc6 zc/vy/ u? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear 9j4;j r9zs *g3rwytu: cxn1bvwheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small fz9 rgjb*r3;4 tvnj9y:ucxws1 ront sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have sctbr /)jpot ;7lender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis o/tr)p;ct jb7of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. ;hf h;yr9 +nhl8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the n46 dmwyzs v,xqi887ag/ d4avdet torque on a syste 68xymwdi7d daa8/v ,4qs4zgvm is zero, is the net force zero?

Two inclines have the same height but make different an64c bsez9ngn)steg 57gles with the horizontal. The same steel ball is rolled down each incline. On which incline w)ge9zbs s6en tnc g574ill the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start r)yc14:y u d5naq )gcfzolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom offaqy1u5 czg4d yn):c) the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and 9 w1n z-vpiaa1au 3zu)the same mass. They start from reav3 nz-ua zu1iwa91) pst at the top of 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. bc+nz-k* e6mux pbd ux )s,0m8Yet most moving or rotating o+m*d-k ze, b68 ) sncpxmu0buxbjects eventually slow down and stop. Explain.

If there were a great m69yonyof/ 1f d7nobv +igration of people toward the Earth’s equator, how would this affect the length ofy d6o7 9ybfn/fvn+o1o the day?

Can the diver of Fig. 8–29 do a somersault withoutmw4 j 7f*rc6vk having any initial rotation when she leaverjc kw v6m*f74s the board?

The moment of inertia of dfk).b9ebvaa 5 :5zcx a rotating solid disk about an axis through its center ovbbzf :9 5ca5)ekdxa .f mass 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 rotatinggq 9lp.5wur(jwpj+ * v stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the maswu qv(p jwj 5*r.9+lpgses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mas8xo 0k3 pwxnms(av:k( s. However, one is hollow and the other is solwpks x 0xm83(nkova(:id. Describe an experiment to determine which is which.

The angular velocity of a wheel rotatp+j ev:2kp*t 4l oq 1p-.hkjlfing on a horizontal axle points west. In what direction is the linear velocity of a p*t-hqj l4e lf jok:p.12p kpv+oint 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 wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turn(am / syw (rb.7*mcy spj*j-ymtable. What happens if you walk toward the cente(mjj*/mwy* p.b syr (ay7c -smr?

A shortstop may leap into the air to catch a ball and throw it quickly. As he thsigx)z6p(qz(2 ej:3mfwlpk4rows the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotas) xwgkp(6zm :4p(eijzflq32te in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angulaa qx5nsg ra):5r momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more :5rq5s )nxa gaways the second propeller can operate to keep the helicopter stable.

  Express the following angm/ydc./,6x p+tchu aw les 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 amack49mclvami9 l: ;/nfzing coincidence. Calculate, using the information inside the Front Cover, the angcf /ml 9 ni4l9:;ckvmaular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is direcusfu5l0s+-zuz k 2.mirct+ (fjj eo-8 ted at the Moon, 380,000 km from Earth. The beam diverges at an anzke- 2i85s+c suotful0. jjzr- uf+(mgle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is turned bu.qm s *k*) fauchsfs062dz 0off during operation, the blades slow to rest in 3.0 s. What ish .as6 u*0kusffm2s*dcqz0b) the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a ag*rqv*+nv g i6w fm.6g;ll f/level floor 3.5 m to another child. If the ball makes 15.0 revoluv6+.nq lgwfim; lggra * /6v*ftions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels y*:*g4 :(u+ke jdo /hjcitusy8.0 km. How many revolutions do the wheels ma:ys*yteuj(k+od ih 4gc*/ j:u ke?    $rev$

  (a) A grinding wheel 0gor 6d(ozswfl*:m+s ta2 ,qh).35 m in diameter rotates at 2500 rpm. Calculate its angulrsf +ah,w(d2 )sztq6o mgol *:ar 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 revolutk,m6y a3:n wx/0ttfy jion in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m y6f k:nwtjmx /,3ayt0from 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 Eae k,n hsromt(k/:/dr. t4gnl/rth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ox8-) 7 gyuyp9qm*awnvf a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if 2+2hx6g*nh fu r5/gzor:lvc s *if3zy+dg : ysa particle 7.0 cm from the axis of rotation is to experience angsy/6 +zd:zr :h*ovsigylg+5* 232rf uh nxcf acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about itses. e6z:tp: sb center from 130 rpm to 280 rpm in 4.0 s6t:es:e bpz. 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 radiuca.pps1av 3t/. tuze yui b)4 zy4pmp og/)*o7s $R_1$ 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, as-ec7o2mua5 m utronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s en7mcmeouu5-2a ergy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 1 30if s2 njccvcp6mb465,000 rpm in 220 s. Through how many rj4s66m p cf bvni02c3cevolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Cih+.x 4wceyw:n, k d;dc 4nci(alculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling “hj9zgz0 3c,gkn ggr,h0uman centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final spzn 0 gj9ggghz03,,kr ceed.
(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 24(lxk2tu(0hr5,c q k ez0 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel haet0hk2qr ,(xl uzc5 k(ve traveled in this time?    m

  A cooling fan is turned off when it is run0 0e asimmw5xd .(y2kining at 850rev/min It turns 1500 revolutions before it c w s2i0aky.xdm5e(m i0omes 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 rw5gx(q q 0rf/eeduces its speed uniformly from 95kmf0q/(r 5xg ewq/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 revoluo/zg8u,q4i* lt ofpvg4b ,2c utions as the car reduces its speed uniformly from 95km/h ufc 82qv,tp*g o 4,zbli/u4ogto 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 eachi3;l qaxosj4 o*r3 .mh pedal when climbing a hil h*s.4j3mix 3l o;raqol. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 59pky /us x;s:dd p+o- mmo/w8r5 N on the end of a door 74 cm wide. What is the magnitude 8o-m/p w9x; +sds/km odurp:y 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 shln5eymp0adn)l avgamvv9m. 5 1 6z v71own in Fig. 8–39. Assume that a fric510m lma.ey5lpvad9n anv)61 zvm7gvtion torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attacheh7,cw55cclwsg /9k l uuz e/:qd to the ends of a massless rod which pivots 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 nq w 7:5 lcleg5 /ckuu9h/,sczwet torque on this system.

  The bolts on the cylina+ea2lrthq 8l8+bsp 0jo*6)t u/ zurtder head of an engine require tightening to a torque of 388a)0 qap+2 *+otur j6r/ztlth8l sue b $m \cdot N$ 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 1i kp:ph r67d9b 2ftyq.0.8-kg sphere of radius 0.648 m when the afi6 d th.kprp:27 q9byxis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in d(g0b no/40wdqhcc * k6wa w4irrc* 9ln wt3yr1iameter. The rim and tire have a combined mh/3y nw(w*c bnicw 49lgtr6k4c r0adrw oq0*1 ass 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 auk zedn2f; :r8 thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculat ne;2 ufd:8rzke
(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 bow ayclh:qs+w*8 l on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is l scqwa+h :y8*1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown1t28, tc.rvjcu h)uzi in Fig. 8–43 a)ti tucz1uv.j, c8rh2bout
(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 co 0g1j vjqtp,)3af+h gxnsists of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindric w/08rte .jsoxal satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm inr8ojt 0. w/esx 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 mass of 5pz f;14/qm+ 9cmi6c hmlknc/l pr4bw0.580 kg. Calculalwli+m 6/mcfbqcz49 ;h51pk4n m/prcte
(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 bam g/4fq ,oyns.7 rh+hwt, accelerating 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 is ablpb l f9vzbf/jcmcep9p7* 9ro5v u-)d;e to accelerate it from rest to a frequency of 15 e ;f ovb b- 9zcuj*prf/v)l9p9 cm5pd7rpm 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 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 brought i.y,(cq4fet0opyp i (uniformly to rest by a frictional tortoi epi(c0p(, yf4q y.que 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 )q )l 8pr3xvue krk58faccelerates 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 ba*x4) f6(;r(d jgemz uj3:nbclmg8emjll is thrown solely by the action of the forearm, which rotates about the elbow joiezj( 3*l fmn:m(6;xugcd) ejgb8 mr 4jnt 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 shown in Fig. 4 m7z1l;s3gfnp/ak;gto-1- cnbpt wz8–46. o; kg-f3 gz14spcpma- lnw ;tnzb1t7/
(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 consiseqad y8)o(+ fkc6 ljg,ts of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (revob ,(0)oyn w zz)nlq+ullutions) a l)wuz+,bnqn0)zl y(ond 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 in n-*pc jqsu+ dft*zvb.*+f,-der ) ssvertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of wc g11ue)n3p u280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls a cmv+tr *,ui2without slipping down a lane at 3.3 tca im+,r*2 vu$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth wit,k 1p1qrv)g)p/r dthph respect to the Sun as the sum of two ter p)r1qgpk,p rvhd/)t1 ms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a ct+qx/sx0 aebdg. ach3+dm +jkxv g0:h.+2zyradius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 rev bxvct0 h:kxc.q/s+ .ah+e ax3d+zgjy0+gm d2olution 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 reswk 01k 3pzj;ygh/ca8 xt and rolls without slipping down 0 x kkyj81a;pzwc/3g ha 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts tor2hl9(3peq7jn szw t / fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conser/p3l7 jzshqre ( w29ntvation of energy.]    $m/s$

  What is the angular moment4wce* e:q0eo4c/ y bwmrine03 um of a 0.210-kg ball rotating on the end of a thin string in a circle of r* 4n eywbeo:wmi3eq0 4/0ercc adius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momenkuh86 i evau94 xid)m*4h yp(wj:u+wgtum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rph :p xvu8g4 uamh iwk*jidy) 4(weu96+m?    $kg \cdot m^2$
(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 pla 9 bwa .lwg-+8;)pkxv wwuwl(atform that is rotating at a rate of 1.3rev/s If he raises hvw-+ll 89 . wwb()auwwaxpgk;is 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 Fzkt2a js 9zo6-ig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her an 6o2zk- zsat9jgular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation ratq/ n 2e1rzlsfpos t6(:e from an initial rate of 1.0 rev every 2.0 s to16sr estfp(loz:n/2 q 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 rotating around a vertical axis through its center at0wbk 7l9z8htz 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 claztz0b8 wkl 7h9y, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at df6i.2jyopx7 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 qe)-dv9 nk9m j) 7kpwfEarth
(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 is drn6.zjb4iil1) z,lo rd opped onto an identical disk rotadznj.1b,rz l64 li) ioting at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at w.w. 1 zmd;22tppcgadx o3:ur2.4 $rev/s$ 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 rotatinfxk p3+bj:f k2g merry-go-round platform of radiu:jbkxfp+3k2 f s 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 freely with an angular velocittyxd7)eq m a7w p2/o7my of 0.teo yd m/a 7mxp)77wq28 $rad/s$ 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 eventual v8/weyps8iz 8f,(as mka0j3 yly collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s n yz k0p3je fs/8ys(mvaw,88 iaew 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 involzpt3 -h zv8ca/ve winds 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 gc/.g i1i y06i1 qz)dt:i:zoy(egbd s$ 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 wink9*k4kz qz9 ythout friction. The moment ofqk9* 4zkzn9y k 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 m+ 3nlanu)ty .u*3wwwrerry-go-round turntable that is mwnuu3w3lya. t )+wr* nounted 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 rolls on the ground with the end of the oq58 q7p tifzs* t fr4k/jtvtl50ty3 0rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holdin lffr 5ttqt i* 4tp5k7zjs8 tyv/0oq03g onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. v/byq r+ ikw4cb62 r c9ioic1.Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case,v iicc q.r 1ro49+yb icb6kw/2 treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of4 .b.4kv hby4eu e nnl5ui*c)x 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 +0zb 2kda0q *zunliu6of radius 0.20 m acquires a rotational rate a2 0zl*uiq dzbun60+k of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg and cn tm7b4f h;iv3of 0c j6d(rt(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-y7i c(jtvotm; cfb0 4 n6h3rd(fo 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 rearj x(ztwh6 ;0sl v9o4ql wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as grea0 )jxmpb1dke 6pryck335n*+f dd ci u3t, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its massxc33+ fc*5)dnb1ujk0r36 yp dpidke m 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 automobilp++p;xn s dlh4e is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a un l4pdhs xp++;niform 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 illustrate0tkwk )3/bgies 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 suomnf27 y;l(.s jl ah.yrface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore fricti852be0ks)9 dq or 2r-rw ncntbon) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular asr n-2r9dktc)0w2enob 8qbr 5cceleration 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 vacmg)bwv:(e . ertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against eca )v: (.bmgwwhich it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is makinem ;j-y ow zy5r nd*xdy76*ix8g a turn with a radius The forces acting on the cycli-d*wrzoj e*yx ;n i5 7mx8yy6dst 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 o kw z:3z,la:g*jo8aa77fwpkinto a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelepjk,77faow8a:lz o:kag 3zw* rating 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’zma8 2q)sz+vts body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Tht8as mz 2)zvq+en 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 j6fd 2t.2uo jaof two cylindrical plates, of ma22ot ujj fda6.ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ahy1 kl7dxt9x: long 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 td9kthx 1xl: 7yo 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 assume:f jvtrde6)n8qjfz ,wk 0oc17 $r\ll R$ h =    (R-r)

  The tires of a car md9cwk02)i/mehn, :d uh b(gb h:fbbg+ake 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) Whgh bnu),( g : eb:9hbhm/20k+bwicfddat 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