A bicycle odometer (which measures distance traveled) is attached near the wheel gxh,d-ligq x,lgi:38xf7 j7h hub and is designed for 27-inch whg h:, d lxgg,3lxfqi8x77jih -eels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angul m5eps.( jsi/a3l 3y(g)rlblv ar velocity. Does a point on the rim have radial and/or tangential acceleraa(y (3 sgm5l.i e ls/rlbj3)vption? 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 value,s rku r4k,pd6 of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater tor;s2p ,2/zq,)na;o*oujqpc 33c5g qw v mj vimaque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your handsb;slfgbnq6/3 d p;ie :z6 v7si behind your head than when:bfg7v6qel;ss;6 /i iz bdp3 n your arms 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 t+pr be/b,xafl bv6cx 9:y5)edhree 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 id,9)la/fc:be 6 px x5+bbey vrt harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to r 9kow8bir6c wiwtjl92k 3w8i+un fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. b892o +t836kkwl9jiiw w rcwi8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–si/p5x 2 dl(bx5bwg8c 35) carry a long, narrow beam?

If the net force on a system is zero, is the wjy(f (ls(zmko )6jo3 ;o;vp g*x.eohnet torque also zero? If the net torque on a system is zero, is thej(3;kopohxy.) gm 6o *(owzes(l ;j fv net force zero?

Two inclines have the same height but make different angles with 3)8j2y6vty2 cxh lwhothe horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greate82 j)3cxvyol6hyth 2 wr? Explain.

Two solid spheres simultaneously start rolling (from resr dsl -8-wih4yt) 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? Which has the greater 8-rdy s4il-w htotal kinetic energy at the bottom?

A sphere and a cylinder have the sam. qoutw bmz-f1 :jery3u az)8)e radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater sptu81e- oqjzbzuw) ay3rmf).:eed 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 momentumd4q idh(h2f8xi g-)n2q0 kbfc are conserved. Yet most moving or rotating objects eventually slow dow2 dfq(h0kn-dihbf2qxi4 8 cg)n and stop. Explain.

If there were a great migration of people toward the Ear7ub 5y7hvf txej1s ..n9 a lgl:fw4cl(th’s equator, how would this affect the length of thhvyesn. lu9wj lb5agf74:17ftc .x( le day?

Can the diver of Fig. 8–29 do a o txw-+*cl; dc:id yx9somersault without having any initial rotation when she9; -d:cty*w clixo+dx leaves the board?

The moment of inertia of a rotating solid disk about an axis through its centj1,7b rla5h dger o agh rd,jl75b1f mass is $\frac{1}{2}W{R}^2$ (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 rotat2j74c( 5fg qx *snmqxjing stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Expl gqxjq (*s4n27mf cx5jain.

Two spheres look identical and have the same mass. However, one is hollow and th: rzmt/.th 3foe other is solid. Describe an experiment to determine which is whio.htf: zr 3t/mch.

The angular velocity of a wheel rotating on a h.hzt/anp2hy vknm05zq:jazjn/y zz .d ) 3s/;orizontal 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 naz2y;5mhz/ yq .j 0zk a./n t3p jzs)nd/:zhvtangential 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 f-*bu yi0q5g/ire)8vm 3er jka reely rotating turntable. What happens if you walk 3i*)evgy 5 r/-m beku8ajqri 0toward the center?

A shortstop may leap into the air to catch a ball and throw it c5cbqk )eg3fm dg+);;p nv 9oa k)tp8tquickly. 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 (Fig. 8–36). Expla 3;o;mt9vpad85cgb )ek f g)c) ptq+knin.

On the basis of the law of conservation of angi,b(tfg1p7roencc )2ular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operati,rpf27bcc(t) 1e on ge to keep the helicopter stable.

  Express the following angles in radians: (a) 30te l2b l0 imk/kifb+6+ ${}^{\circ }$, (b) 57 ${}^{\circ }$, (c) 90 ${}^{\circ }$, (d) 360 ${}^{\circ }$, and (e) 420 ${}^{\circ }$. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculatez8+qr :yegkd-:ac k5afg 2 b)d, using the information inside the Front Cover, the angular diameters (in radians) of the Sun a)agr8aq-2b: kedc:fz5g ky +dnd the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divergej fgcz xj24n2+s atc2g+n jz2fj 4x an angle $\theta$ (Fig. 8–37) of $1.4\times {10}^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor e2y;5w y a.t het6(nzqis turned off during operation, the blades slow to restey(wtz6qte. hy2na ; 5 in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a levxxb hxsqo)3j b/6pylq3qcc: . 30l j;zel floor 3.5 m to another child. If the ball makes 15.0 revolution 3jq/ 30zlc3c syx; 6xojp.x:qbq)bhls, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How2 ;ltq t psh2,eofrt 6;u3o1vo many revolutions do t;t 3souf ,2vlhq2;r1 eoottp6he wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter r g o)rle+ef .l0rs0pb(otates at 2500 rpm. Calculate its angular veloci0rp() lgos+.ef0elr bty 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 b nt)*l txu9/:u bpq3rone complete revolution in 4.0 s (Fig. 8–38). (a*bl3p qn/:)bru 9 txut) What is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around the Sun l3z71 4qt 5l8dqdv1 u3fbbxvf    $\times {10}^{-7}$ $rad/s$
(b) about its axis.    $\times {10}^{-5}$ $rad/s$

  What is the linear speed of a pi.j8d.w -o egdkc4zr +w9ozuck-m2j( oint
(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 k ln0wbi /l:v3tb-z50j:osl)kyfdccz6 / y, c from the axis of rotation is to experience an acceleratf:j00, 6vw 3)c5znczb- ktc/s:llyyolkd/ ib ion of 100,000 $g^{\prime }s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its c1rfcyx )f/u4 z5z ic;smh--tq enter from 130 rpm to 280 rpm in 4.0 1zrf/iyhmc5 sq zxt)-c;uf4 - 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 radiu3chw hmopg2t4r /.):wsi nq 2hs $R_1$ 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, astronautu 14d. k3aytkks aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they ta3 k.yud kk14accelerated 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. $a_{tan}$ =    $\times {10}^{-4}$ $m/s^2$ $a_{rad}$ =    $\times {10}^{-3}$ $m/s^2$

  A centrifuge accelerates uniform5lpszo( g0 .ybly from rest to 15,000 rpm in 220 s. Through how many r0gb .pyzos(5levolutions did it turn in this time?    $rev$

  An automobile engine slows down foglwo2 :mjuoeq4wj6) z ,o33krom 4500 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 highspeed jets in a ;y a6omeu1av)kna8*n whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its fiuykn)6an1 av 8*eam;onal speed.
(a) What was its angular acceleration (assumed constant),    $rev/mi{n}^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 cy.kr:i. i /u 8spmx3mrpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time? c . p:yir3uxm 8i/.smk   m

  A cooling fan is turned off when it is running rqpr 0(qze3q9at 850rev/min It turns 1500 revolutions before it comes r0(qq3 zq9epr 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 speed uao.:wb; 4tsbrniformly from 95km/h to 45km/h The tires have a diw; s4 r.a:tbobameter 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 tp f0*2j8u0auy5*rw i i2is lyche car reduces its speed uniformly from 95km/h to 45km/h The tires have cij2yli0r25i0* f*y8a s wpuu 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 e)x0a v-xwmdam5) sj36ypm( xvach pedal when climbing a hill. The pedals rotate in a circle of radius6yvv) pd( sxjm wmxa am5x0-3) 17 cm.
(a) What is the maximum torque she exerts?    $m\cdot N$
(b) How could she exert more torque?

  A person exerts a forg.twqyy.u6(lvt o* ,fce of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exertet.t luy ,fg.( qw6y*ovd
(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. As pd;k x3sdbsm* s0y.,nsume that a frict0ksd. s;*y3 p n,mxsbdion 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 masslese bcqv ;l:ledf ho)t c2-c/1-hs rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position ande-t)eco2;vhl-hb cl: f1/q cd then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of*ifyxwgt7o,mc6s (b3n c+ )c h an engine require tightening to a torque of 38(,)+hom*yb wt n3c7c6is fgcx $m\cdot N$ 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 when the e+u rffeth;3,axis of rotation is through its centetfh3 e ruf,+;er.    $kg\cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. )c 6qw uh93vhcThe rim and tire have a )3h c wh69qvcucombined 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 in a horizonamhvp7q;7g))d e n *-sy ay:py vu1c1ztal circle of radius 1.a:)m1a*hcnpv;d7s - pvqy yz y1ug)e 72 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 rotating at co82tm/mht/eg, ab rs-snstant angular speed (Fig. 8–42). The, hgs2m-t m/8a/r sbet friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m\cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg\cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in 7tq oe.:b/ fpaFig. 8–43 aap e.q of/b:t7bout
(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 total mass 3q dzg,ig40o5tnbtu( is $5.3\times {10}^{-26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $1.9\times {10}^{-46}$ $kg\cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times {10}^{-10}$ m

  To get a flat, uniform cylindrica7xm )3bqydk*v 8jm q/al satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5 x 3ma 8dqvmb)j7*kqy/.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a .df9rj c4e x-qradius of 8.50 cm and a mass of 0.580 9 jc- .f4edrxqkg. 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 t*-x xo-,lxif do 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 t ;e.xm10;-ncb f-yuger*cu mmerry-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 acceleratiyem ;c0ntfmbu; r. g-u-c*xe1on, neglecting frictional torque. $\approx$   $m\cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shutzo2 ndx0m5gg8si))td off and is eventually brought 5ix2)0 )do ndg8t gsmzuniformly 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 3.6-kg ball 4jw w2dzj).* gxb0rkkat 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 of the forearziq.u, / bdr0w)of l9duqx,n1m, which rotates about the elbow joint under the acti.z ),,rdw/1idfqx 0u qlnu9bo on of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as cgwietkvtgz 9 p(()*cy8, iz ;shown in Fig. 8–46. ) *izckct9ggptwv8,e y ;zi( (
(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 ps+c+rr 3 i)gnof two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (r 1 wcr6h1kmzcac,3l w)evolutions) and z,kc6a1h1cwcwlm) 3r 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 dc-(luo) 3 yfva moment of inertia of $3.75\times {10}^{-2}$ $kg\cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque9x.z6t 3caezf 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 /0.7ycevb gty/:fjkr7+yv khrolls without slipping down a lane at 3.. +kvy7//v b0cjyfty h7k reg:3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to th kz.(f6srd2ldwk6 d*fe Sun as the sum of two terld 6 fzf*(62.kd kwsdrms,
(a) that due to its daily rotation about its axis,$K{E}_{daily}$=    $\times {10}^{29}$ J
(b) that due to its yearly revolution about the Sun. $K{E}_{yearly}$+    $\times {10}^{33}$ J [Assume the Earth is a uniform sphere with $6\times {10}^{24}$ kg and $6.4\times {10}^6$ m and is $1.5\times {10}^8$ km from the Sun.]$K{E}_{daily}$ + $K{E}_{yearly}$ =    $\times {10}^{33}$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much net worl ;4-kjjn erisc;+q ,pk is required to accelerate it from rest to a rotation jnjkeqsc4r+;i, lp ;-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 er39clvapy)mc-2 a5f)/ fqs2c0mcg k without s a l apmrmg 5v-c2) y0e3sc29k)/cfcqflipping 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 :2prv atx-78y2, opm*i gqk fgfall and its lower end does not slip. What will be the spe7mtg a:kr,2g o-v* 8p2xyiqf ped of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg bqt,4,v- vvr/ vf: vymlall rotating on the end of a thin string in a circle of radius 1.10 m at an angular speevv-f y:v,/v4vrl, tm qd of 10.4 $rad/s$?    $kg\cdot m^2$

  (a) What is the angulpayb 5n/2g7wyj.+yja ar momentum of a 2.8-kg uniform cylindrical grinding wheel o2/a + nypajyybw.7j5 gf radius 18 cm when rotating at 1500 rpm?    $kg\cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m\cdot N$

A person stands, hands at his sjia72e k1,-ruyw /nb(qcbsn :4wqss ;ide, 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 speed of rotation decreases tosu2sice 4nkn s;aww:/,1b( q- r7 qjyb 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) c 3pw rmi)bzy* 3e;a12y7nxbuhan reduce her moment of inertia by a factor of about 3.5 when changing from the str;3127b b)*ih zyr xw npmaey3uaight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can incxbn*tte 6p)e(m0bwm 3rease her spin rotation rate from an initial rate of 1.0 ptb0b) (xwm3*eetn6mrev 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 an,6xy- eb ua30,9ontpfvn. eppff8:sxis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What isb-.:0su3e ,fnonne9, pt axyv pff8 6p the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinningjax 3kp s-judl,ujg)u4m5l:4 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 mometpqqt+kmvs, d 2+bvba. ,-hxk2 +0ng jntum 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.    $\times {10}^{40}kg\cdot m^2$

A nonrotating cylindrical disk of mo8wdwm. 8;ilx xoc* kp5ment of inertia I is dropped onto an identical disk rotating at an wcodmlx8 .w*i8pk x5;gular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsxu-i hy k8vnk1edl041 at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round plamsmu7fva) / u-tform of radius 3.0 uf 7/sa)vmu-m 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.$K{E}_i$ =    J $K{E}_f$ =    J

  A 4.2-m-diameter merry:gkz-(o 9h 2qz*dcwyc-go-round is rotating freely with an angular velocity of 0.8 hz2gq do:y w9c(czk*-$rad/s$ 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 dwarff+0k17px z sfe, losing about half its mass infe kf7z 0xs1+p 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?(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?$K{E}_f$=    $K{E}_i$

  Hurricanes can involve winds in*frdc v m6,-t0unw,vm excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $\times {10}^{16}$ 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.    $\times {10}^{20}$ $kg\cdot m^2$

  An asteroid of mass jw55hv:m4xi72 .n jyfqlifu1 $1.0\times {10}^5$ 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.    $\times {10}^{-16}$ %

A person stands on a pl/4kn.2fv7)mdlxe,wl hwwg a j1; zar 8atform, initially at rest, that can rotate freely without friction. The moment of inertil7 zh24w f arjekmvgl.;d,8ww/)nxa1a 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 a(yuy ( c6vc t*jrs6rn0t the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment r6 tjvys6*(crn0(cy uof 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 iev9 x7p*9hojl u3vkwe1 i(e.rolls on the 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, holdklji u eew9e*vxipho3.v 7 9(1ing onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always facdkk)fd(4)e5 q.. rh 6lmx9koy lfz haam8) 0rhes the Earth. Determine the ratio of the Moon’s spin angular8 xm 0oa9ef)5kml)6hh ) qh. z.fyrkr4ld(dak momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times {10}^{-6}$

  A cyclist accelerates from rest at a rate of. w(a*49tsiqv)foq tx9d6hxe 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 ifqiejxs6t tmx4wn spo :u3yqq6 9.j 2fd5o3)3 n 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 constant angular acceleration. Calculate jp ty326dw 6nm.3ujqqtsfio:q5 e 4s) of9x x3the torque delivered by the motor.    $m\cdot N$

  (a) A yo-yo is made of t4;um4 9w(cpq xadudr;wo solid cylindrical disks, each of mass 0.050 kg and diameter au49mdwcu;rq (x ;4dp 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angul sxq:x 6ew3wrbfbu *6.k28khvar 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 aw: 3hx9)z( ssho;qgd+ l:7winlj yv4Sun, 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 all times, and that the lostisg;n3)qjls 9(hzwa +7v 4 w:xl:odyh mass carries off no angular momentum.    $\times {10}^9$ $rev/day$

  One possibility for a low-pollution automobile is for it to use 9fh) j pwhr2.zp1(f4mfrq yy0energy stored in a heavy rotat prf9)hryzq02 y h1f.pwf 4jm(ing 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 $1.7\times {10}^8$J.    $\times {10}^8$ 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