A bicycle odometer (which meas qbsl4i8 nz(/f- aysk:ures distance traveled) is attached near the wheel hub and isqk 8bzl :-fn( s4/aiys designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constantmcwp17 9 jm/+kiggz3z w/1om z angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point wm1371z+gz pjzok9// wim cg mhave 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 of thef gptqii,z* :jf4 wp/.lm3j/(raj ka 9 angular velocity $\omega$ Explain.

Can a small force ever exert 4:32xx k i wi,5b,zbxlhltd06:ajb tta greater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hai6p xw kxxmm77ez sn15-2 9nuunds behind your head than when your arms are stretched out in front of you? A 7z n5 e 26u-xwxmsn9i7pkmux 1diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and,buitjz8 ; .dsbl y*3 5hie hq(sp4aq+ three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In whyp .za4u,j3st*q(d b+ bsl;e8ih h5 iqich gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being ablebmy4scz7fhrw l2 +ed/vf*3n/t euh)2 to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Figns)drv2 h mcb 72*f4/3y h/+zetwf eul. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (uxept5 q4ixzy3w16 bkj9rl 4nrn7 x8(Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net tzdh/q 2f4yx1 onvc-3w orque also zero? If the net torque on a system is zero, is the net force zer4q 2ov1wdnx 3y c-hfz/o?

Two inclines have the same height but make different angles with the horizontal.h3gt / najy,m+ The same steel ball is rolle 3nyh m+a,g/jtd down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start -..miba p/mve 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/-ai ep.mbv.m 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 sekt)ehq6o 9d9j :gwznl9/ m(o0n8ha etart from rest at the top of an incline. Which reaches the bottom first? Which has thjwe9mkl( eodq:an)ztgh/nho89 e 690 e 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 an 4p q(jwou+cotuq uhd5z./-p- d angular momentum are conserved. Yet most moving or rotating objects eventually slow dow +-tuqzqpj p./ o4uw-5(do uhcn and stop. Explain.

If there were a great m 3pqbrdrc1 b pd7957 43:npf hspbeg:cigration of people toward the Earth’s equator, how would this affp17 pcdqpbs pge 47: f9h3brc53ndb:r ect the length of the day?

Can the diver of Fig. 8–29 do a somersault*rz( xr rrc)t016/ jqmtfr( fu without having any initial rotation w *cxtu6/qmf(r r rfzrt )j1r0(hen she leaves the board?

The moment of inertia of a rotating solid disk a2j( glo 6 y0fm4gvo3mabout an axis through its center of o2j6yla(gfg03 4 o vmmmass 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 sittinv ja 9j8/x-x9nnjha) e+npz73rlai *e g on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular veloci jj 3l/* nr 9iez+xvanah- px7)n8a9ejty increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howeveut-q or sb83n0 h32yw2v:fvg pr, one is hollow and the other is solid. Describe an experiment to determine which is whic3n0qt2f s-wo p: 3uybgh2rvv8h.

The angular velocity os8v(umw 0dvf ;f a wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular accelv 0;(wd8ums vferation 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 re2v d2r+xjfeyov/ /v(,.x sex otating turntable. What happens if you walk tovvy x.//(fee+oes xv2rj 2,xdward the center?

A shortstop may leap into the air to catch a bnir vp5legdla )wu2 z8dt 6p-v45i9r2all and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you wil5n 5pigt)4vzw8l6ddpav e 2-2 lr 9uirl 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, disc9cd0n*pb4ejajs n 3 5juss why a helicopter must have more than one rotor (or propeller). D*n93danep b0j 5 4jcjsiscuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in rad7s.v, rqzvr bv9;-zroj(.g wvians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coi6vkv.ggd; (y )u8vd)ja o0q isncidence. Calculate, using the information inside the Front Cover, the angular diamet)j o (;6qgyug8 av dkis.0vdv)ers (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 3.3(4dkc fq wl e)xmw/z80,000 km from Earth. The beam diverges at an angle4wkd)e3c/fxqzw .ml( $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender ro+x(pcv9w:ur u tate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration ascxw+9p vuru: ( the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the balls6 zalhsgf*ys-gr/, / makes 15.0 revolutions, what is its diametr, *6g- h/ysalssgf/z er?    m

  A bicycle with tires /z4-srf:-b;np a)q- :fz ,fwew zbcxn 68 cm in diameter travels 8.0 km. How many revolutions do the wheznxbcf4)-ew :w/ bpf,qz an-;-zs rf:els make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calvn tkk5y8g3o2culate its angular velocitov28 5tyn3 kgky 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 revolution in 4.0t( i/*7o jdfm l7xa9bx8kuoq0 s (Fig. 8–38). (am7lbk8t j9(/xqa* u oxof0id7) 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 aro : c)ax irs 9d6sknyjy i:jq.jiz/w2+;und the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speediujust0+e 8 r1 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) must2rjnm4c-q*ngx 1shjri 7,5m8hhen4 b a centrifuge rotate if a particle 7.0 cm from the axis of rotation *ncmrg4ji8m2n4 n 17,hb- qshexjrh5is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about itsbnj sd7uj ,ee2u/c77 y center from 130 rpm to 280 rpmyd7ue/ ,u7 csj27ejbn 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 radius rkdl7n-)8+qiu o p0t xv.5u jc$R_1$ 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, astronautb:luxa/* dg js/8;hdls aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their tlxslb: /; adg d8u*j/hrip, 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 accelerate*f5orrgs; (f/d8;vyqunk g(k s uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this timf/kq ;k gnurs vfyo8*rg;5((de?    $rev$

  An automobile engine slow8k:g.a1 qioyg y 5 er/z*zbuk1s down from 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 whirling “65orslzskx(10io :bm human centrifuge,” which tz(xiobsm l6 rsk0:5 o1akes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates unot:ulj2y+z + miformly from 240 rpm to 360 rpm in 6.5 s. How far will yzo+ :2 lumjt+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 It turns 1500 revod8nnvyz)zp8t36n28 m ytboa x t u1e+ d*,v0jelutionsaxyey2oz8nu pne z 1 m dvtb38)0n,jtd+*6 tv8 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 revolu.askm+yk/z ni,oy3 gjk(;y1e6s(vp q tions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80jskov+ kn (;(.kgi/yapqyezm,36 s1y 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 theio8-tdt; qj6a car reduces its speed uniformly from 95km/h to 45km/h The tires have a diametett-i8 6oaq; djr 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*ngf(7hrb-+rshq u 5q on each pedal when climbing a hill. The pedaurqhq n-5fr s+7 bg(h*ls 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 therx5clvp w2 dd-5m5 qruj+js +3 end of a door 74 cm wide. What is the magnitude of the vjr3q+5ujc x sm wld2+5 5r-pdtorque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel ag(p d,mrbl+,; x c/bmshown in Fig. 8–39. Assume that a friction torp+( b,a / md,r;lbcmgxque 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 rod eamt2almai.kud ,* 35emn6x 2which pivots as shown in Fig. 8–40. Initially the rod is held in the h 2t5k6aamie dex.3n 2,am *mluorizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder hyovxr. om28m/4q-z(bah, 3t )s um7b.ucd yfpead of an engine require tightening to a torque of 38 h2y xtu. 7r3 bu4 .z,bqm-psmd/) a oc(m8vyof$m \cdot N$ 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 momentbf 1dr+5*p mox5xj sa2 of inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotatiojm+axo *5f d52spbx1rn is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel78qa)xy p7xdkpa+oq-o z /f .krtfnly*/ 0o)c 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg )yp o p8t zofl.dxk-ry0x*fqq/an/k77aco+) . 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 ahix k*:nxk bk s8ee4s/ 98uij- horizontal circle of rk kiih js :9bu4xe-8sn*/kxe8adius 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 rotating at constant angular spe1aoe 4(so krggas(-(bnb /: yned (Fig. 8–42). The friction force between her hands ano ae/go4 as(g1b((r n-ny:sbkd 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 poiyfzxe9e3 d wd5n -+9fpnt objects shown in Fig. 8–439w 5+d3e denzx -py9ff about
(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 conrzw 40.d ub sbh h,p75hcgo)hkj e803usists of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, en5ev ydw od.6 i-ktu3zvc+3vr )gineers fire four tangential )5 d3-tv6ky+eic wzdru3v ov .rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unifort:zqi( io6 pc-.3 a +pw x)qstqijc (o(dda5q*m cylinder with a radius of 8.50 cm and a mass of 0.580 kgi:s(5jao 6 )t3 (t+od (aqdp-qc.qixcp zq*wi. 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: j)kdyk/dr: t 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.)7m ug7) nqav9)bn h d2sshca 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 chnshv)cdan q9 bs m72 h.)g7a)uildren (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotyr 0jip q*ky0-ating at 10,300 rpm is shut off and is eventually brought uniformly to restyp -0j0k*q yri 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. rwli t :cu+z78 l;al7h(g in+g8–45 accelerates 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 acq0;eo/bd (wedtion of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from reste eb dwq;od/(0 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, a ktnxyt02modwrt :7 5.s shown in Fig. 8–46xknwo0d .tr t:57t2my.
(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 vlhu86x./ e)p th4q5 u m 4nc.gf*fkijconsists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer fc0avf ah 7;arq5yq a7l d04iz;rom rest within four full turns (revolutions) and releases ital 0y;qr 5 0d ifzv7h7;4caaqa 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 mo14fcdhm 4+8xr,0 xwmmyp;l g xment 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 enginenprqe52aj)luqw5hc,q.; r8 wkh5y.b develops 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 massqpfd3rs(+ow ao k9u4u4 d5c)5sof, ms 7.3 kg and radius 9.0 cm rolls without slipping down a lane at ) 5s5kos fq49rd,cfswu m o4+(u3daop 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respeih 2qb ;j;+ligct to the Sun as the sum of two terib 2glh;+ ;qijms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius o* l )itbk;te;hwa4s(yf 7.50 m. How much net work(b )lsa 4whte i;k*y;t is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1p8v-3 .sftavk z si0;m.80 kg starts from rest and rolls without slipping down a m80vf3s-p ;tzi.vsa k30.0 $^{\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 on8)+dhd:a u rua its tip. It starts to fall and its lower end does not sliu:a)u a+ dhr8dp. 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 0.210-kg ball rotating t)kw9gqv;p-jon the end of a thin string in a circle of radius 1.10 m at an angj wgvp-9q )tk;ular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding h, 2u yd2g*wphwheel of radius 18 cwgdh2p2 hu,y*m 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 side, on a platform th z5a;f/s(+ )ixggmnynat is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal pos ;si /fy+ 5(mngz)angxition, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment ozm,kazqf)ynuvu0f)fe.2 *r.y 0 . zomf inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ( 0 ) zyz.n0)*eyk.q,zffa ou.vm2ufmr $rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of 3i;7ou sb3hkue, 4 hyz1.0 rev every 2.0 s b3 yzu ,7h4 e3sihuok;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 (sp5io0c.x)r kpmh j. 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 after the clay sticks topm 0pshr . jcx).(o5ik it?    $rev/s$

  (a) What is the angular momentum of a figure skater s-+v (q 6gmu8pso7uwc0owiv6y pinning 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 momen3wiwqoirt :w/ to*2h7 tum 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 droppe; i7y/2 txuk5(jo mp;c2w qyeod onto an identical 72 yup /i2m cew;ojo5( yqktx;disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4pm7axw5lbcx* *g;g crs0h4 +u $rev/s$ 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 y2)8 8bdij txu7uk5ha kg stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of ineruu28) tdi5a7xjy kb8h tia 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 angulaqe;-0r7b x rciwe.na (sht ,2or velocity of 0.8rq(xat72w ,r sce; .h0 n-eiob $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf,sin9o 5q5j5opov; wlw57y6wgkp5 r j0 losing about half its mass in the proces5;7p69inwk55gsyp55 wjvj rqol0ow o s, 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?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 1r4aia( r8 9hujy* zvc420 $km/h$ 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 dfg k m);uk;4ta 3fzn5da1 .91nocfxa $ 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, b,:;nzblc;:z y4o b/y 3xw bmuinitially at rest, that can rotate freely without friction. The moment of inertia ofbyy w,mb;:4bcu3n/;oxbzlz: 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 yc +-pgk4kt1le/jeb .merry-go-round turntable that is mounted on frictionless bearingt-y1 gpc e jb.4+l/kkes and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the *o p06d:d ike3by/va4tfo2 be ground with the end of the rope lying on the top edge v:o 4dte06*/bpoi e2yfkb 3da of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that 7sn-yx-vrm f+ 3omd;feg7ch2 the same side always faces the Earth. Determine the ratio of the Moon’s spin angular movmxg e-7on+2;df3mcs - fyrh 7mentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1rrpcs; i06.r xg(hzssi9f9 2q 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 mh.y9*g 3 2kcqo7fnem of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the 9ng*yhe .32 f7ocmq kmtorque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass os)w, ps 07bnjv2evr:z .bi9ewp g3y)0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of ,r) . gyibpevz bp07jes o2ww svn)93: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 angular speed of the rear6( blw8 nqq2j ya)nc6i 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 sik1kyrd -qa l80ze of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost aq1y rl8k0kd-mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it a / bbm5 (t2ut8bs.y:xvzyyc-o+ut8(p/ chs i to use energy stored in a heavy 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 trav( z /(yty.:5txt-obhmsa2 /vu+p ycib sb8uc8el 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 an1fa9vi*61hpd v bo- 1zv 6zvpu $H_2O$ 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 (h7njdsezw x /*6v ..ltuoq5y+roop) 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 L can pi5nwn7cbtjp -2vot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod i7npt 2w- bjn5cs 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, 94kaxtfyc6h zu n-9j;and we want to exert a horizontal force F at its axle so that it will climb a step against which it6k 4- ;cz9ynh uj9tfxa rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a pa.: w9z5 ryjwybrd:o1e5 )pu flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal force z)ow15 pud yae:.9 prb:jyrw5$\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.s8an qm9 abrhln-n8;3 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. na9hra8b 3;nnm -s8q lWhat 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 mb i 2d+p*wq,ssolid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds fpq, bd+w im*2sor a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists ou8e ;k aqf/(k d8d1hij)fejs/f two cylindrical plates, of 1/8kfjeu;q8h)s kjdd( /ei afmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track rbglh0w/,wue9f *lktq375l z of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it be/llkh0z3 u5,r* 9fwt g7lwqis 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 not assu698je xwrg (i jef)8hkme $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its sn,*:gxlvljx 9peed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tirexjvl*,nlg : x9? $\approx$    $rad/s^2$(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