A bicycle odometer (which measures distance traveled) is attached near thez3p28 k8mwkuwf kef3 aigi83,2rpj5r wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicyclf8p 3kj8keu8 z33mrgwp ikr2 ia52w,fe with 24-inch wheels?

Suppose a disk rotates g mt,epfu,yi9w;65zm at constant angular velocity. Does a point on the rim have radial and/or tap mzu6m,59etg;fi,yw ngential 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 acceleration change?

Could a nonrigid body be described by a single va nczkstacx/w8b// -25ppe w1 plue of the angular velocity $\omega$ Explain.

Can a small force ever exert a gret8x6tr3:*ur*iz r f jwater 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 to4oc byxh9/lg2k*:-ur c /j kak do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer : 9 y2korc k*b4jgucal/ k/hx-this.

A 21-speed bicycle ha 9z;92, o(lvnihwv8. spfenxj s seven sprockets at the rear wheel 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 pedalf2 ei 9;wn8oh .xzp,9( snjvvl, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slenymm/ ccyzpe ;xd29,/a4cx vg(der 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 advantageous/; vyzdcexxa,cm294 m(gyc /p.

Why do tightrope walkers (Fig. 8–35) carrfk n(yq i3,.+sbyn ax6n.bm :hy a long, narrow beam?

If the net force on a system is zero, is the net ttmtbu8c6eq 0w) jl36 ;xsp6fporque also zero? If the net torque on 3u6 ;p6)tp8 cw me6qlfj0bst xa system is zero, is the net force zero?

Two inclines have the same heighyas9j: w0 7cdbt but make different angles with the horizontal. The same steel ball is rolled down each incline. On which inyj:d9s7b0 a wccline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simuydbom xr+;08 wx 4 -c;tq9dgt dw+w.qsltaneously start rolling (from rest) down an incline. 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? Whichqro;+bd0cm.sgwdw w;+8 x t9q-x4tyd has the greater total kinetic energy at the bottom?

A sphere and a cylinder48cx9l sd, mmu qlt:ywucqwu t) -7h98 have the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom yd c9uw8s-ctmuxqtw 4 7q,luh8)m:l9first? 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. Yet most movinbc2,o /is c*:y8gp;-m btp 8 rfkid5eug or rotating oby:sec2 *m,5gfuitkob rpdbicp;8 - 8/ jects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equatoup gy ul+vi/8tlz+6:n 5sipf/r, how would this aff/6zpf5+v8ln ugt /ipsiy+: lu ect the length of the day?

Can the diver of Fig. 8–29 do a sojyodox46 m y q-m*o(stbv;r/. mersault without having any initial rotation when she6*o v xrst-oj 4q;(bo/ yy.mmd leaves the board?

The moment of inertia of a rotating solid disk about an axis through its cente i8 h;/jgfm6eksk zq2(r of 2mj(f8 k ;zkih/ es6qgmass 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 stohz39m pd0eabr8l.+4y7 wgj a uol holding a 2-kg mass in each outstretched hand. If you suddenly drop the 09d3eju 4.b 8ayr+w7mzg p halmasses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look idemsyop33r5 5el3 n jfgswe) 0ihk ,w0z5ntical and have the same mass. However, one is hollow and the other is solid. Describe an experiment t53hy 55n ,k3 o wgp)0lsez0es rj3mwifo determine which is which.

The angular velocity of a wheel rotating on a horizontal axle pointygmg/ky2v : c r91vg.is west. In what direction is the linear velocity of a point on the top of the wheykr iv1mgcy2 9/g: .gvel? 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 tjf sw:2ze 6k5uurntable. What happens if you walk toward the center?fkuz 5w s2e6j:

A shortstop may leap into the air to catch a ball and throw it quickly. uw 9ir .w )0bq.gsfx).*z9qhe5m8t ln 3 lpofoAs he throws the ball, the upper part of his body rotates. If9.ue loq093n s) fo*8mwp g)ibh.tw rqz.x5lf you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the la a0y2o79/sh3cssp ptmw of conservation of angular momentum, discuss why a helicopter mustsy7 ppc0hms ost 239/a have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in ,3pfr6/uu ifu 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 becaucyd6f i4z/d hz0/to5a se of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on ty4f0d/ h5a d6i czo/zEarth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is dires : y2( xjcr2kct3nj6bcted at the Moon, 380,000 km from Earth. The beam diverges at an3:cj x2 (jbrcn6ks2ty 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 65 aaw;/kw plw./00 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the ana ;/pw wwal/.kgular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 39z1rq4/ c /j evoaj:tm.5 m to another child. If the ball makes 15.0 ret94j m1r:/jo/aq ezcvvolutions, what is its diameter?    m

  A bicycle with tires 27gsb rbk(* 8zpsms-p68 cm in diameter travels 8.0 km. How many revolutions do the wheelsbrm s7 k(zp2*bpsgs8 - make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calczd a-j7p8(h7v 5wn muyulate its angular velvn ma(h578w zp7 d-juyocity 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 rxk c(mop 4jg;b.fc5dl7yj )c( evolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from th75c k jc yp.;(jgf col4)xd(bme center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit aroujak0 xh6b3o.e iris6/j2nm y 1nd the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ofg1 * evx:-b11g :fnp;veflgzh 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 particle 7.e35ya qlcnp *-0 cm from the axis of rotation is to experience an accele-l5a *3yqpn ceration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acce9/ v tvw1a9z)7op vm2qnni-i iak2 u0elerates uniformly about its center from 130 rpm to 28v12 auvptm2-nin/vz9q0w iak 9o e)i70 rpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiu 5zb4t*i)b cmxs $R_1$ 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 Apollo spacecraft put themselve nq hf;isy44x(s5 jdi4s into a slow rot4( ;s fyq4d 54hxjnisiation to distribute the Sun’s energy 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 uni1wxh7a un p*5gformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it tun5 1*xg hup7awrn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200ql3b+pncgri,zh; 4 v ;qe*:ge 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 highspeed jets in a s8*+on afam9s mh5u) iwhirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachingm*aa s5 9m )uno8is+hf its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 36/f 2v) gfcx9bz0 rpm in 6.5 s. How far will a point on the edge of thv9f2 /f) cxbgze wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns c3w(hg ;1 fkwy1500 revolutioy1 kch3w;(gw fns before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduc xlgv i4.dkqgdx: ,04hes its speed uniformly from 95km/h to 45km/h The tires ha4h ,xdldkvqi g :x04g.ve a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly f7ig*krn2e nn.2y qh6 nrom 95km/h to 45km/h The tires have a diameter of 0.80i6.eng kyn7 nn2q2*hr 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 he.(pb w vpt(/mxr weight on each pedal when climbing a hill.v.b(pxp m(tw / 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 55 N on the end of a door 74 0-8wm2hde 3kbfxh ph1cm wide. What is the magnitude bd2 13mkf0 -hh8hexwp 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 ther)fpv:dzx(z -fq-i e- wheel shown in Fig. 8–39. Assume that a fprz-:d- i)vq- x fefz(riction 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 ends of a massless roc;y w8 yktjz/6+oec (kd which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released.t; 6 (oj z/ck+yewc8ky Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requiaeg1xll mbv)+yjr +2/re tightening to a torque of 38 ga mbyx/rjvl2+1e + l)$m \cdot N$ 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 inertia9 ojv:t,.c zph of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through ic.h9jtop :, zvts center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 c7y:q *oy ui );c*jcjggm in diameter. The rim and tiru 7yc;o jcq:gji* gy)*e have a combined mass 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 a thin, light rod is rotated il*oyztb1 t7y cxrya )5 (z;.clc3nw u2n a horizontal circle of radius 1.2 m. Cal3c nl)ywc 5tz*cza( yu.21xy lbrto;7culate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant anenhg*q b6ha.0m qnm1 :gular speed (Fig. 8–42). The friction force between her hands and the clay is 0bg*hm n1eqqm 6.an:h1.5 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 iw qx)vie.k2-dnertia of the array of point objects shown in Fig. 8–43 a-.dw x2kiev)qbout
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose *a mup+xd /;hmtotal 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 cylindricalxq- 8 0n f p7cu -.kk1rujjvu,nwk.x;l 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 0pvjx8 1-f,- ; rkk.lxcn juwuu.kn7q 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 massb 6x:jdd :a1eu of 0.5da:jebxd1 6u :80 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 swingu., aqs he/inyi2wp -2s a bat, 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 tangensb6 18a 7nb nuqbel30stially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting 8un bqbab e7s1s60 3lnfrictional 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 eu q5rw fadxe,0mg; j8 )1hnz54hqi h2xventually brought unifor8rq52zd5mjx g when1fh; h x04 qu)a,imly 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 accelerates a 3.k7-ji z3z,inwi ;ymzt81xv7xj7jyt) 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 soleurc/ktsd * ,a+:p v -q.j.dlzkly by the action of the forearm, which rotates about the el . l+d- c:pz*,/vsdktj.uqr akbow joint 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 aomw7 qyuwe fpbcocnj+, .6jm-(v+06o long thin rod, as shown in Fig. 8–46 0-n+7e.6bpoqm6 j(cyf,+ ouwmowvcj .
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two massekuj e cxt);rp4giyja.3 p;v 1a4f2nj 9s, $m_1$ 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 acceq3z zkcv;;4 up4ngkr+lerates the hammer from rest within four full turns (revolutions) zz4+pq;u3r cvk 4k ng;and 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 pirt8 k4lv*;q;b j4np8run-x of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque2 l2,tesky- wp 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 d8vs)l)yi2j wgzt tb)8own a lane at 3.3 b)wi lsv2j8gz)8)yt t $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the yvdx f8z g/*b)Earth with respect to the Sun as the sum of two *fdg vb 8)yx/zterms,
(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 massp ,l:2-dwgzmcc +bl8g of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotationm:g+b,lz2-ldp cg cw8 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 1.8g fc8b v s;5wt6 5yg 3iypc8railz*;j50 kg starts from rest and rolls without slippg65 czws;*ig f icpj3 58va5rylt8b ;ying 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 stalz(vllr; dnv()ke/3k2 qbby) rts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before ilk)bykd;n ql( v ebl/3rvz2 ()t hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotatin9j 9u2c9mvzy mg on the end of a thin string in a circle of radius 1.10 m atc9 mmvzu j29y9 an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.81-1 w7j1,quqnjtw. cyhlc*bpj/* otv2s p ox0-kg uniform cylindrical grinding wheel of radius 18 cm when rotatint v7uc/w1j*j1p bs2nchpqo yoxl. 1*qj,wt- 0 g at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a rate on)v/g5e;y.ab71l7 hlc dr-9yyj o v azf 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the spee 5-r e;ly7 b7dhv9cv.jay)/ gaylnz1od 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. * r)sat jl0u,mugu0g–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck positgl)r* am gu00jus,u.tion. 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 ra oqg)x/i+o5cpsyd x/au:9 / lel kdk;;te from an initial rate of 1.0 rgdcs/ + :l)kp5;9xqixku;/ oyealo/d ev every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through il 1m5v-yh.hs c5ta3 ssts center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel a .tysvh -s5sc31hm la5fter the clay sticks to it?    $rev/s$

  (a) What is the anguhp/y; 3vl bnvk:i6n43h2 cm 4mqo i+wzlar momentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular m.sc skve /yly-( jam7,omentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an iden/m lcv6x48 t)dan owq dko3mz/01agj f*d20uk tical disk rwc/kf*dx z mt3gd41j n6duolvq0 om0 )a2k8a/otating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4pvm,c,t 66x(izedh l2 $rev/s$ 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 merry-go-ro+4zt d2n tv2lfp/oe: yund platform of radius 3.0:2p4f dty lno2z/ve +t 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 n*9s ) 5axkdpzw4nix0velocity of 0.8 nxs*904zk pnax5diw ) $rad/s$ 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 whitya1* bu/te)j 6 zmvyr6e 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, *e)ar 6utm1y jz6/bvy 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 invol+3z1ao9a ej. ha4n*yq-xwika 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 )bd1hs- d z0+ork hc0k$ 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 s9fdz kkp*-w*at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform dpzf9*skw-k* 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 als-w0b 8avl* v 6.5-m diameter merry-go-round turntable that is mounted on frv*l0avwl -b8sictionless 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 thei eoah 58nvju8:x1eu- ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, F1 aij-e5evh8x u8 un:oig. 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 Eartauiw isx+ ; +n/-y0pnj9co,tlh such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angulpwxl-oy+ i9; +taic ,ju0snn/ ar momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ,qpr fwiy0x-(xlv9k r( 0twb- 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.5e * bo;kpfib.nu8ic of radius 0.20 m acquires a rota *8n.i5kbe oup.fcib;tional rate 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 sdlpl s3j2( lh:olid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reach2ldsh :3p(l ljes 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 wheet-i :skzj6.m6 hnnd z//qp/rol ($\omega_R$) 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 yrs1- bg - .6ymcm)imytimes 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 all times, ans - m1)y.-y6bgmcmiyrd that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is fows*8:l o a81nn9ntsf vr it to use energy stored in a henn9af l:1no wsst* 8v8avy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to 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 c9st8vp ;1 hhpddp)8mps sc3- b8ao6kan $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speed v9vecxz 3 ez2wt2q4xx 7=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,3y awua -i. qh0pk)ob pivot freely (i.e., we ignore friction) 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 rod, and (b) the lineaowyq0u,b)-ik h3.aapr 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 standi3iufg 7zze 52:d e,qoeng vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a stq, 23u5oeef :gdizze7ep against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2oma(q+ 37o*mmysni)9yx t.z/mo7 l zx m/s on a flat road is making a turn with a radius The fol7m m) z9o/o(yo3qnymi zxm x. sta7+*rces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.-si:w9ie bq+dm4pb d+b fly 6w ym8n8wt,1+pv50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his b:yesd8-+ndl mi tv4y ,b ww+iwfq91+8mbpp 6head, 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 cylinder and her arms y)z /gjk4a09d q wc,mx6:aeq,6hsunx as thin rods, makia4q ) kh c/ezjqd xnw,x:,gmas9606uyng reasonable estimates 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 assembly which consists of tw:+im ek(vpy:w o cylindrical plates, of mwv :k+(: myiepass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 and9kbx v(ouf xnp1 (k ja,6:yg8i radius r rolls along the looped rough track of Fig. 8–58. What is the minimum vagx ub1xnv( 9jkaf:k,yo86ip(lue of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not7ut-n.1+ln o zf jc(up assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions ac uy,c8g-2npstb7 0u xs the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was thec2n0ycb7tu- u8xgsp, 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