A bicycle odometer (which measures distance traveled) is attached near the i(o5ii u qwm/,m2p ly3e,d5fhwheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inc/2yihpuem5m,qiodwi 3 f5 l( ,h wheels?

Suppose a disk rotates at constant angular velocitb . aznj7rhq /r.qf ,7b,vokx.y. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly,vrbz,qn, rkj x7f../7boh.q a does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value ofsj .ishc 2:m3h the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explsqb em+)+ pap2ain.

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 aewofc 9l/a6d 2 sit-up with your hands behind your head than when your armsfac6 o/de9w2l are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and ;m9xs bx+*nt gthree 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 harde+ ;9mxsxtng*b r to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to w;i fozhpnem/ 6o: 0q2run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantagqnw/m h6:2ipoe z 0fo;eous.

Why do tightrope walkers (Fig. 8–35) carry a)8 td mspz2uj8 long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If ;nb*+ o+js):j9clu-x*c hhp m 4 rqlffthe net torque on a syst94hc+-*hmcbn *+jql )f uj lf;p:sxr oem is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontfdbw*h h04epx/vvh 96 al. The same steel ball is rolled down each incline. On0fx4w6* /h9 dhvhp bve which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inclqms b yk ,ed w+b6ueqy9*q7;-mine. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic e,7qm 9 by* -wsebkdq;+yu mq6energy at the bottom?

A sphere and a cylinse v36q.gj.x m)vu8po der have the 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? Ws v8.q6)ugvx3.jo pmehich has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum aret (xcv.; 7kqf*b v5zwo conserved. Yet most moving or rotating objects eventually slow down and stop. Explain.vt( 7cf*wq.ox z;5kvb

If there were a great mi2g-qutdu-8eb gration of people toward the Earth’s equator, how would thisd8be -u2qgu-t affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any i8bdg2u qe7-apd;k 0txnitial rotation when she leav2d8 tkgp-qa7 u0xe;bdes the board?

The moment of inertia l4j:)8yzlpjt of a rotating solid disk about an axis through its center yjp8 ljl)z:4t of 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 rotating stool holding a 2-kg mass in each ou24g)nsr;.e/do0 qlffdj k f(ftstretched hand. If you suddenly drop the masses, will your angular velocity increase, dec/dfn)fl;k 0oqsrj(2 4fe f. gdrease, or stay the same? Explain.

Two spheres look identicaldcj4o )/hw( be5j ve6b and have the same mass. However, one is hollow and the other is solid. Describe an experiment to det o4wv jec)d eb65hbj/(ermine which is which.

The angular velocity of a whexm,)/l reop(vokw t; h-s-m a;el rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tam /kl-h;)saxmwo eop-r tv(,;ngential 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 turntable. Whi sx5 x-hn1 lt;1k9rmd )g(rwaat happens if you walk5rx 1alsr1(tk9 ; ixmhw-dng) toward the center?

A shortstop may leap into the air to catch a ball and throw it o5che -fku- ,eonm86;gp qd 3fquickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (F-n;qefdo g-efkmh6uco 3, 85 pig. 8–36). Explain.

On the basis of the law of conservation of angular moment.mb,t6 v,a 2lilzg4bjk2 ;o ,rt a1ahrum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more waysb 2.b al1kio ; tr,v ama,64jhgrtz,l2 the second propeller can operate to keep the helicopter stable.

  Express the following anglzb30keg.8 2e.dh+k(hon) ai wdsgaj1es 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 coinn*(ht1vg27 fpr zu3r qcidence. Calculate, using the information inside the Front Cover, the angular diameters* n1hq(vp3ug 27rztfr (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed aty ,cpbl. 5-;sojsv/tj the Moon, 380,000 km from Earth. The beam diverges at ssvj,l-o/ b;p.jcy5t an 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 rpm. When the;su z;q0sk o*g motor is turned off qu*;o;0 kzssg during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball makiir y l;a4ul35es 15.0 revolutions, wy a3i 4;5rullihat is its diameter?    m

  A bicycle with tires 68 cm in diameter trak-b- vi5qvv(q .8qyo xvels 8.0 km. How many revolutions do the wheels make?(vvi y--.qxv q 5q8bko    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angh)tby ub/m9wen -4*erpv :+jvular velocity b*wy pn/vj 4eb+ h 9m)r-veu:tin $rad/s$ $\omega$ =    $rad/sec$
(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 (Fig. 8–38./xaq91gie.gkhw( 7qh( gllt ). (a) What is the linear s7wtxhagg.k1g9q (ihl ( l./qepeed 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 angularzv2ljg4.20 no-o (ikpvs,oa b velocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a,9z bjl5q a ),bj kr+pgelw6/e 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 a particle 7.0 cm from the axi( w/tad-yk0s ns of rotation is to experience an acceleration of 100,0s aw(dtny0k-/ 00 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates lq-ooq; p5gvq6/w:p xuniformly about its center from 130 rpm to 280 rpm in 4.0 wp;gq6ql5o/ :pv x-oq 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 radius zvo(7zty22m yzmuo 3 ;$R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apolljw0.o3 ft eq;dyo+oi:o spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. Atwyq;jo.ft3: i d0 oo+e 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 uniz/,;gxryc g i*formly from rest to 15,000 rpm in 220 s. Through how manyy z;/,*grcxg i revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rp0,x*(bay a )wrcjhqe* m 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 flk9mkxq )r-7yhf w(qq lf7 g1k;3nli.yying highspeed jets in a whirling “human centrifuge,” which takes 1.09q)1lf;-7k n7 y r y.k(km3fxqqlwh ig 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 diameter5vfb))y 2qxq 5i rnp(d accelerates uniformly from 240 rpm to 360 rpm in 6.5 s.)b qfdy(pvi2 r5x 5)nq How far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850retan po1 5d ;h0i*bnm.pv/min It turns 1500 revolutions beforeitn p1bd5ap 0hn.*o;m 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 revo1lb pk) z.qlg8tb9v. 1bc iz9llutions as the car reduces its speed uniformly frbc9lbpiz )qzt ..819 g1kblvlom 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 makegr yfr-;-bvhdv 976 sr 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires hrr 67g9-dvhr;-fsyvb ave 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 eachs n*,zyjekqa n ow;uek 1(:,t( pedal when climbing a hill. Thkyk no1zeu,jq; w(ae s n(,t*:e pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 7iqg*+a7zsn 3n4 cm wide. What is the magnitude of the torque if the gnn q3 a*z7is+force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Assume**bxn qhjxr va1gn+uvdw ib0+w6)7q; that a fricti1u07jwnv6hib+nqdvx) w*a g* xq; rb+on torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, argkwf6yv44-i r. 0 2hhy 8nmebfe attached 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 directio k442y8wm.gh -vyb fe0 rnh6ifn of the net torque on this system.

  The bolts on the cylinca :ch9jilxa w1(l 1*lder head of an engine require tightening to a torque of 38calc i( h1wj:1 9lxl*a $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m whewjv .c+ni/y ,t,+dt dbn the axis of rotation is through its ctnd/yj+dvb ,w c.t,+ienter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diamete7xrgnslp9lpwh3;:+al tp9 mk gr). 5tr. The rim and tire have a combined mass of 1.25 kg. The massp)tp5lshxlmg+9 ; 39atw:rplg. 7 k nr of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end oo03saq tzm80-(v .wz vt)wwy of a thin, light rod is rotated in a horizontal circle of raa- w.ms z(wo otytwz0) 0qvv38dius 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 rotatingg .; a;cw3yoma.:h uob5mmzp - at constant angular speed (Fig. 8–42). The friction force between her handsm- bmg wom5.y.z 3;u haop:;ca and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of po,b.+8 viel,fhsnv bhy 8(px/ sint objects shown in Fig. 8–43 a8svl /8ebiph nsh,fxb(y.+ , vbout
(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 twoeczk3/e 3j3m*5fby ak 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 cylindx +:)+qy( /bglvl rhtcrical satellite spinning at the correct rate, engineersrlq+x+yvtc lg: / )h(b 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 in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unifo ws.bkh5jz0 u)rm cylinder with a radius of 8.50 cm and a mass of 0.580u h b5jz0w)s.k kg. 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, accelerating it frouu l):2 +rpjal ,o(zmhm 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 an+mmhnlt4hqwg z 2.q( je//*osd 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 twj.4z g/*wqo nm 2+t/l(eqhh smo 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 b;whe(g av38 7lrt9w s0bqcr;grought uniformly to rest by a frictlr gws 73 8t(r9q 0hg;ewac;bvional 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 accelerates a 3.6-kg ball(l7ug yt6;)rhg i eyn, 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 6oe x9g2. twlazx3z 9faction of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniforml9x 6wfo zetal9gxz3 .2y 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 consider*o fkj89(lo wved a long thin rod, as shown in Fig. 8–4 jowkfv8lo(9* 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 con34 /wws )k8z lk ys4jcinax43gycve47 sists 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 1k(pxx6p* duki ,f,62 mpic yz from rest within four full turns (revolutions) and rele(2 yp6pfic, 1d,mk *xu6xipkzases 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 5pp.xzn8)tgo we4rs v4 elq3 1w f0.uh-pyw :tof 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 developiih5003 mw elrajowb 8)sq/j +le fo70s a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping dow4wayr v;ci2tnux x,:6n a la4 vw ,u26rxtx:; cainyne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with r5d-wyim)hfq vkvq p (l0+q36respect to the Sun as the sum of two terms, vd rp qqk3m0)lf(5iwvq6-yh+
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. epn9.8sv3y u s, enmc,How much net work is required v9.3pne8 m,,ysu c esnto accelerate it from rest to a rotation 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 wit-4q 36*o-f xbby4t oee1)zb 6 djsgcyzhout slipp6edzb34x1qte gfjz-c 6y*o4bbos-y) ing down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fa wd/6 -pyi uspalx3/8hlji)5all 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 conservation of/ji85)i/spldha 6 xywu-lap3 energy.]    $m/s$

  What is the angular momentum v ekn0dhj+)gs;zc;b/ of a 0.210-kg ball rotating on the end of a thin string in a circle ogh 0vc/+; d;nk )zjsbef 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 f/+g/yjc( yx-og ;exyuniform cylindrical grinding wheel of radius 18 cm when g+x-;(ocx g//y fjyeyrotating 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 cb igzox+0 (yo/ 9v3thside, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal pobgvic+o (hy/9 tozx 03sition, 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 Fg9 ,r:iz+ mgysig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tgg : +,9izrsymuck 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 fd48s 8hd :+cvzxzws y2snlv 8+rom an initial rate of 1.0 rev every 2. wzd+ld88ys2z4vhs c s:v+x8 n0 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 rotating around a vertical axis through its center aiq ckel5ir ,h5hk0 8qh2sup8 (t a frequency of 1.5rev/s The wheel can be considereq s5 0qpk8 ecu2iklr,h(i8h5hd 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 the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning ab4lp4 -tprj0fe,s a; gt 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 ;lu **x a/ ,r xihmync)-qnqw: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 moment of inertia I is dropped onto an idtb+;mh2 b mu29w i*lx4avp*l mentic*2v;li+lmpamxwhu4bbm 29 *tal disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns avffvqw.i)c n/zmsi q)b2f- -+t 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 mercrc/ sagk kn -.cn1i;:ry-go-round platform of radius 3.0 m and moment of inertia 920na cicg-kc:k.s n /1;r $kg \cdot m^2$ 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 rotatingl8d/nn )h.p5do4jxog xv3 n, c freely with an angular velocity of 0.8)pnhj8v/g d3.n,4ocxx 5lo dn $rad/s$ 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 hhrfr w-ie8 xwfu+ x607alf 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 new rotation rate be?(r68 fhr7ie-wu x0x+fwround to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 120, l, d5ypyw(4an:ppwu l3a9kb $km/h$ 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 kqdaaw3x;j(ckh 5xme604 iw7$ 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 fref16,b+oumvr)dj:7f t d1n7ag ci*mkz ely without friction. The moment of inertia of the person plus the platu, 1izodn1t :7+d gvajc7 *k)f6fbmmrform 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 m 6u9*bnlxs4wr r2r0o the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 0r6 sou 4*lbrxwrm2n9 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 endl890. z 6 gim* vv)zpmglkghc0 of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center zg0 0.p86* k9lzhcigglmvm )vof mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. Detw6r lrpn1b1)tbn-y 8or03x uc0a)f zw ermine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiu) rxp 381coabb0 n06l)rwy1z-tfr nwting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m m09 s l0:9q,xxbnylph/$s^2$ 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 in3 *8y*emlzpq*o-de g cs5iyw0 the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at cole**05c pyd-is gq8zmo3y ew*nstant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, wi+fc2zg* yy1al9m 2p 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 lin azpyc+*gi29 lm1y fw2ear 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 wheel m/nf8d bzrlb o(;m: 1x($\omega_R$) 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 o so+rdr** b/q p9n0vbeur Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of 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 bsn*rv p +0o/d9 *beqrall times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stk: 5o oaje+8ddored in a heavy rotating flywheel. Suppose such a8 djo5e+ oad:k car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without 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 illustrates an mnu7le nq he92gvqu,l7,j9 7 n$H_2O$ 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 surc +a9 (wewrc kk:6mil(face 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 frictiontv2+c*u6 xdl+2 t1r ;qnkf-8ucm pplv) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the uf +kx; u p62plt+qmn2lv-c*vtc1r8drod, 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 floo7ktc*svfedr);/x+qq fbe . u4r, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has heq7f*+k/ sx.c)d4 befev ut;qright h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn wit1e)96,o(fhexjn ft pn h a radius The forces acting on the cyclist and cycle o(fhx) 61n t,9ee jfnpare 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 begins whirli36croc 1:hr ys7jo0ux ng the rock in a nearly horizo so 7o:cy0 1x3jhurcr6ntal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cyli vvmo5w/h1ov :g+l3c/y i2fyhnder and her arms as thin rods, making reasonable estimates w fhvv5i1v o2c o3h my/g/+yl:for the 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 assem0oat8q m7drut5gnz. +kgjxhb1/,*:i w-kao cbly which consists of two cylindrical plates, of mazkkxaatcghbno/*g -5710ijt.m:wro 8 qd ,u +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 along the loop8 n)w3kmpn 8,sw3xu2k b 3)5h yfaz d2zr7dvtbed rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must dro z8fh)r7n 8t2m )dwxd 3,kpukbyv2bsz 3an5w3p 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 dj q gu 1e4avgbg2n/o 3m4(-d0hacbm b0o not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the oxqfi gcl9zfwd j coh (,q )6s7g16n*;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 acceleration of each tire?1hlc9wg*)66go, nfjx do fqi7sc;qz( $\approx$    $rad/s^2$(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