A bicycle odometer (which measures distance traveled) is attached near the wheelttv v4prkl3)52d mj:t03 tjl r.cjz k2 hub and is designed for 27-tlm5 4vkjr3 jd.0lt z tjkv3c2t:) 2rpinch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on th:7r h:n5 wgknie 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 wg5 ri:hnw: n7khich cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value oa i cb1 pb2 :40f*ud8j3tsnbprf the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque gsp/qhj))a+ pthan 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 si*am6m 6ve9 au,v1moix t-up with your hands behind your head than when your arms are stretched out in front of you? A,v6v *ai mexma96o 1mu diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at,taw2bp gvinp 5rnw*; an1u9 7 the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocketgr,7;5vup *a n1nn2w9itab wp 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 g.54m3kbq 3zxjs7i wrfast have slender lower legs with flesh ans 3zw53 qibgm.4rj7x kd muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walk+iiec94 *wgztpfa 23+ohgl; o ers (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zp dwj *f(lxfgtz 8662gero? If the net torque on a syste6g( wgzj d*lft xf826pm is zero, is the net force zero?

Two inclines have the same height but make different angles with the c wa 8kno9z4-s he+d*thorizontal. The same steel ball is rolled down each incline. On which -se zh okctn *d+wa489incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling o xi4eyl5e1d6nt -k2 p(from rest) down an incline. One sphere has twice the radius and twkn4lo5die1- t 2 px6yeice 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 energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start frozs -c dw) u,9ageb-q9vm rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has thze, v)c-9uwad qgsb -9e greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum arrir3tl v(suv2w )fc z9+1pt) fe conserved. Yet most moving or rotat1crt3)rzifswup2 tv)v lf+( 9ing objects eventually slow down and stop. Explain.

If there were a great migration of peoplejrt*hli;2.qja acb6 * toward the Earth’s equator, how would this affecach6j iqtl*b*;2a jr.t the length of the day?

Can the diver of Fig. 8–29 do a somers* sev:a7;,p kpkf 5nhhault without having any initial rotation when she leaves the ;pk kshfve5 *p:hn 7a,board?

The moment of inertia of a rotating solid disk about an axis throughb6f:g ( o3/zk-p,hnpfn h epy5p,xsc5 its center of mass n:n(3g/p ,6hfpkz 55bepo xyf sc-,hpis $\frac{1}{2}WR^2$ (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 y wzq6w c91;bwa 2-kg mass in each outstretched hand. If you suddenly dr y;zw96bwwq1c op the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow m h44 uwioyb.5and the other is solid. Describe an experiment to determine m 454uyibwh.o which is which.

The angular velocity of a wheel rotatin -hq2pmt5pmq(g on a horizontal axle points west. In what direction istpp2h(m5qmq- the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rot 4 l7 f6y y)f ex/m:))j yshd+,bzdakewtbej2*ating turntable. What happens if youbmb )4+jdke ef xhst*,l/y d aez7: fjy62y))w walk toward the center?

A shortstop may leap xdys64 j 64yj6c20ptd 5tqtuxinto the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If yotu6tj4y062tyxpd5 4sj xd6q cu 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 conservation of angular momentum, discuss why a helicle *ie/:wc(qu dq 8ti1opter must have more tuqcd:w iq/ile*( 81ethan one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angleg*)x9 y (hy9w ypt8ziks 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 becaul *r;ya w2et.dse of an amazing coincidence. Calculate, using the information inside the Front Cover, the angulalea dry.; w2t*r diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km fr7qo8,8u jd7v4ep 4xh ggo9xn*k ghfw290yvqv om Earth. The beam diverges at an anuo044 qogyp fj8 hvnwd7*x98 92gkhevx7q g,v gle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 65001las-k+reg.h6 ut4vv rpm. When the motor is turned off during operation, the blades s1s t6vl+v4gau. r ekh-low 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 balg 6 :vu*qky4 dp a2kx aq3t.vltd2;glg,r/oh/l makes 15.0 revolutions, what tarq vgkp 2dt:;k gua2vlh,/y dq g4.6o3xl/* is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How macpw -tn2+ ,hlt tn)a7mny revolutions do the wheetwhct7-)pn2t ,a ml+n ls make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 pwxj(9l awro9 g/v,y+ rpm. Calculate its angular velocity in,9p9w a /y+xljo rwgv( $rad/s$ $\omega$ =    $rad/sec$
(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). ;+ 9gtz ddpbi*swe j48(a) What is the linear speed of a child seated 1.z9 dbsg i ;w*8tjd+pe42 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 s gf4wu6n 70v,h zdym)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 speedj iv)rel.4h1 c of 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 a parxlsc,0 wv:utgh ; 0nt5ticle 7.0 cm from the axis of rotation is to exp: t05swtn lghu;,c0vxerience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acceler*g.k3xek . ra vj1tcr +rev)h5ates uniformly about its center from 130 rpm to 280 rpm in 4+5aer*g .rrc3. 1 )jth xvkevk.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 radius ectp9q/q .c 9p$R_1$ 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 Apol2.go9gwa c nk2lo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, theyk22ogc. wga9n accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Throws*0awuopdp7b,d s4pu7q r*s *o . v6augh how many revolutions did it a poso,q4 .6*0sw* pu dwb*7drv7asupturn in this time?    $rev$

  An automobile engine slows down from mo* +yw*.kxnm h87 ttb4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeejeqzub-9cco t6e/yd 3;l 3 ;hod jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching iy c9lhoze ;d-qc/eu33jobt 6 ;ts 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 rpm to 360 rpm in 6.5 ,jrq;;x xf9( .yl.k x:j cjradsjqj ,9xdlar.k rj:;f(y.c;x x. 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 850rev/min yf;(eo4:)4bld vkwajiu;9 yyIt turns 1500 revolutions before it co494ujfio ayd :;vyw (ebyl) ;kmes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speevrf ms4 ,sqy 4+ja,o;ygg -z3ed uniformly from 95km/h agv yf3y msj-s,; z oeg+q4r4,to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unis.gej)(w6g z: x x+bogformly from 95km/h towbegs.xg+o :zx g)6j( 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 y9 oa u,cfvth edg7t87 to(-63h kqf;ieach pedal when climbing a hill. The pedals ro-y;c 9fe 68uotiq(h7gtv ,7 oka fhd3ttate 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 74 cm widev5boy*-(* fd j5amuk f. What is the magni(5ydfofk5a-* *j ubmv tude 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 o**nv(pmf (1fjj 7ltb9kn./supg hh+g f the wheel shown in Fig. 8–39. Assume that a frictionm 9f tfn g.lh*pk7h*sb vn+(j1p( gj/u torque 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 the enw 5f;sk5;x igyds 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 net torqueks5 xg ;wyf5;i on this system.

  The bolts on the cylinder head of an engine require tn7df) mar4d8 tightening to a torque of 38 )7 am4 t8fddnr$m \cdot N$ 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 ofg ifr+pax4d8 j7/lje9 a 10.8-kg sphere of radius 0.648 m when the axis of rot+e pjf9/4 jdrig7la8 xation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 9ubeagrk6nqlyk3y157 - /rno cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (w 7ne nok5gry-byq /31a6u9rlk hy?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in p 21n/hy*lox eyp: a.wa horizontal caoxp*h2wey:/.n1 y pl ircle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rot3ghn 3xoez8j h j9cs72ating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 g3sj98c n7j3 oz2heh xN 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 shown in Figj-ray2a78ma 09oumke . 8–43 aboutmj ro209a aaey-k8mu 7
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whos6,ha*/ :b l8hmbrtc*t eekq 9xe 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 tid(qrhd2 +(di he correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a masd(+ii r2(hddq s 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 mass of 0.( ,vc-z.czzsfj )m;gf4n22o qgyh v7 b580 )-c fvqs.g27n bj (h,vm4cg2;fzyz zokg. 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 from rest to 3nfcd9+ bn9z/wsh*3a 67oc qzo c )z(my $rev/s$ 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+ov 8ea55 zw jc0gh4ddd is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictionawzod c+ vjd5 5h8g4ae0l torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating awv4n-q ,rnn 4rc r+u1ut 10,300 rpm is shut off and is eventually brought uniformvw4-nurcn+ n1 rq ,ru4ly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 4k;t2/susa vf k 6zxf4accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action +je1eu;o te9jv/qak( of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated unifor/jo tk ;aj91vee (que+mly 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 kfn6yagvy 962h 1ynp 0in Fig. 8–4 f2ag1nyy6h9kvny60p6.
(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 k(awn-l l 9t(bof 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 hammih ,jkfw ayh 9om0,h;*er from rest within four full turns (revolutions) and ra0iw*y mo;9hf,,hh kjeleases 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 y +q7b-ts;so+ct 7s yqdp7a q2of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine developsbk u v,pmpx/;8 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 slirsz2xvwb(mtmedd2 p4(wx( a4m a ww ,+q- );fapping down a lane at (mt(wvda ewqabm)4ad4 zrx xw,;2f2+ sw-pm(3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth wi y-qup1gm .hu0--zp5gj ykz (wth respect to the Sun as the sum of two terms1y 0z g5jpp- hkqum.yg(w-uz -,
(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 x7za-b(ypg. sof 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a ro 7-g(sx yzapb.tation 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 sap.hdhzr in1 /0qp( d4l;l*p rolls without slippingz(*ahp ld1.sp qnhpdr; 4/i0l 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 f(uo-3isv b2g to fall and its lower end doe(3s f -2ougbivs not slip. What will 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 0.2sc*mh2 ,eydqv85ad,z10-kg ball rotating on the end of a thin string in a circle of radius 1.10 m a8,m dq25sec dz,y*av ht an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momea rfcqg2zth-(8rj6 j-.fg1hantum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when r-ah8. fq-g2cjah( fzgr6tr1 jotating 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 cjnk-9eqz,wp0koh7h7 lpe,cb: y b4( at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the :-yhnehel0bkpw oz j bcq,,cp ( 477k9speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can r s 4z*xppvlb yl1*x0h+:ya;-ltcqmh4 educe her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuc0*hxtcsl*4m - va+qp:p41 h bxlyz;ylk 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 /)ar.dk( ymm/n,txn af ) jk1mher spin rotation rate from an initial rate of 1.0 rev every 2.0 a m,fm. mtxdn()nk1)/j /krays 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 at a fre9xfumr f11km0x :ho/*n)jfw dquency 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 w fn m0/uxd)9ojr:f1 fwh xkm*1heel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure n;+g zs6ybu8u;;z himskater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Earth.p9xk:ar vf4i6g r 7mb
(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 o6mhq:*3ja me9qnff1x.ub k68rqj5 u tx2+ipanto an identical disk rotatinrj8:. 26x6j 5qq fb+ i*mfa9xq31pun khmetua g at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsin88b-pmg7ur 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 resmy2avp /a eslr3cz7 7f8x 9g3q-0fthe center of a rotating merry-go-round platform of radius 3.0 m /as7cafrfsq03e 89pm32y7 gerzlvx - 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 pv n/:tr/db4l +qc.ad angular velocity of 0.d4bt qdr l./p van+:/c8 $rad/s$ 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 collapsessdz*p,gruh b gfz (+*wx -l,/k 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 momentumu/sk+flrz, hpxg(,z*-d b* gw, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in0hz, 7 rjh5p4ro6*wbmm kj5yvmp 9z-k 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 8u ktp0pse v)6i isct w(76/kn$ 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 p fy xk: tq3ue;8 -tni9/tc5paalatform, initially at rest, that can rotate freely without friction. The mo - ;nq:pxcyif uekt9t83/5atament of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-round tk.j;)j hcscs q+( .g1r 1vduururntable that is mounted on frictionless bearings a (uk1q;. rcj+.s)guchrsd1 jvnd 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 o -zgst s2;mkzi/nf *d7f 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 - k7zn 2d gtizsm;s/*fdoes the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. Detee s )/6 mklke4chr) gyerbnan+3e2 y6if;5k d(rmine the ratio of the Moon’s spin angular momentum (about its own axis) to its o+/bekg2kd5 )ecylmr e6)(rn fs ;ne4iy3h ak6rbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from restfj .+qe)cl 9hu;6/ wijwwf 2ju at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m a jljr-i:mcerfc,ak;o s- ;-(r cquires a rotational ratofcj;r,( e-k rr-c s-j la:im;e 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 cyyziyqdw: 7 9t2lindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylin:w9q d7y2i ztydrical 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 is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angulak 6k y,qxsj9q5r 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 with mass 8.0 times as great, were rota pid, g01su5p8kx k/outing at a speed of 1.0 revolution every 12 days. If it were to undergo gravitatio,uk1pp8g/sxkui o 0d 5nal 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 all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobilgl e9jz:j gg ke80*f3le is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kgjg jez9g0e8l3*lfg :k, 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 buuo6.idc x)zm n+c/2$H_2O$ 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 (hoo0pq )l74o rpazttik3- p) is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length- n1zl0 -skhft L can pivot freely (i.e., we ignore friction) ah-kn-1zs tlf 0bout 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 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, and u5xys fwfspt/qcl+ .(h5n (-w 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 sten(5t(. sf ys5+wuf-wpqxchl/ p has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is ip(ty/+ qxhzf2rqk5: making a turn with a radius The forces acting on the cyclist and cycle are the norma /ytx2p(:k r+hqqz5fil 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 lena ex6b ::qq5 zill0w5ggth 1.5 m and begins whirling the rock in a nearly horizontal 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 doe 5q:i6q:0ae lz gw5xbls the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin r.iinhn4.5f f;/h hvns 5w6kxf ods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and wns.5fhk x ih fv/hfn;45.6niwith arms held tightly against her body.   

  You are designing a clutch assembly which consists of uvr/(bp d **9,vxg/omt-f tgt two cylindrical plates, of ma9t*v,g (d/bv pt x ufg/*tmo-rss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radx5.8 yso)qizjmb.(6 qa65ibz u0fl puius 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 reach the highest point of the loop without leaving t.impx buy6(z)z5lqbi oa6s 8u.0qfj5he track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, bhg.st21hd-8xa b: f wwut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 rev+cmqmkc 7pb9m23ma+eolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a di2m79eam+ q3kmbm pc+ cameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s