A bicycle odometer (which measures distance traiv crs.j fbx7q 4.ne.6veled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if ybev7r 4fc6.i n qsj..xou use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Doe 1alwegzd q672r)ih*j s a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial6w2jz* qe17h)dr gai l and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be describeekv 5lv-1v t 0gs(vwh/d by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torqutm1zs0i3h s64 pb v.zae 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 hands behind youq(t q *or7 k*r.bn;vfxr head than when your arms are stretched out in fron*b nvft.r7(*rx;k qq ot of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at /dj4ufxu 1np) 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 pedal, a small front sprocket or a large front sprockefxn) up/d u41jt? Why?

Mammals that depend on being able to run fast have slender lower legs with flee;;kwz/dep 6 ge3 e06 t.sndrnsh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distributioe ne .6;wesd ktn;z0 36gdpre/n of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow b 08nzfn dmzy*./x*dv 4vl5 ubmeam?

If the net force on a sy ;pw8ao6ti d7:1toxsyy msa 2*stem is zero, is the net torque also zero? If the net torquet dxa6*twp8:7;1aoy ssmyoi2 on a system is zero, is the net force zero?

Two inclines have the same height but mab k60xc -dno),t1bdmoke different angles with the horizontal. The same steel ball iso)1,modb- 6ckdbt0nx rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down *aka wjr,0 -n0(zvca:y rtcf7 an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of thef7- rca:tzv*(ajn yak0w0cr, incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder ha-zyon)y5wd8 s9 dv +ueve the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the-)5yo n8dwzuyevd s9+ greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or h( .n-ojs . yp5dve:vhrot. h jyehn 5s(ovvp:d-.ating objects eventually slow down and stop. Explain.

If there were a great migration of p3 p5rt(lz t17l+6mbten4ud 0jw94u1 f r wqnxseople toward the Earth’s equator, how would this affect the length of td4tr6 l7j(z4u9qf+e0txs t31 nlbwnpu w5mr 1he day?

Can the diver of Fig. 8–29 do a somersault without having any initial rot7g xti5 fa0c -n6mr/ um8zr/6anb5 ctjation when she leaves the b t gt/racunmz6-bc5xf8jn i/a 0m567r oard?

The moment of inertia of a rotating solid disk about tv9hzd*5 e1zran axis through its center of mve*9 zdz trh15ass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in ea1k0qafm,m) i l-fm1 4x* hlgqsch outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decreas0x4mmsil1 q*-q lagf kf1)hm,e, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow aa9g4 o2m2s9ioam)i fzndx p,9 nd the other is solid. Describe an experiment to determine whf29ias2 ,na9 gzop m)imx9do4 ich is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In w;ga-lzbfc1x2. ytej1 hat direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangentbjg2z.;1- aflex1c ytial linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. What fx2(sf: en +gmhappens if you walk toward the cente +s ffgne2x:m(r?

A shortstop may leap into the air to catch a ball and throw it quickly. A0pwjmq2 )pgnx,n)z1cs he throws the ball, the upper part of his body rotates. If you look quickly you will noq2n)pw 10 zcgpj x),mntice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conserctekx/ui47i ;k-2j.x/be ib l vation of angular momentum, discuss why a helic bb;li/e k4.x-e2iut7/xk icjopter must 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 radifr5 kfg35j pc.ans: (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 coincidence. Calc3sg;sf rzzbp/9komiv5m) +;u rm7u/uv .vbq 0ulate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and thu)gm/5sr k 9sbzfz0/3brvp7mmiq;;vu + vo . ue Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is direck xmkvnvm /);47y(uup ted at the Moon, 380,000 km from Earth. The beam diverges at an p;u4 kvm( mu7 x/k)nyvangle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When thr/xhlq 0s wgx9 n3 5n*rabgj.(k;uiv/fvr8j 8e motor is turned off during operation, the blai/n8fvgjv5 0kwr s/l 3 ;(xgjr8nab.h 9ru*xqdes slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a lec0uei wt60n6pnv2 f k6vel floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is it pnwec ktn 2066fvi06us diameter?    m

  A bicycle with tires 68 cm in diameter tnsc .a .9eb6msravels 8.0 km. How many revolutions do the wheelsn9c ebam .6.ss make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates atseaseu5; nv 63 2500 rpm. Calculate its angular velocv 36us a;nes5eity 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 4.0 s (,ozkj s-, r-ww5n hs;qFig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the cent,zqns kh5srw; w-,jo -er?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth ()xue9 5b62vxhrl4yml a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a 4;it 7nwqycu;suttoe.sn :.0 point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from 6 d;u,fk- hsrlthe axis of rotation is to experience an accel6lh r, d;kfu-seration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelu/smv9y7 e l (mrx+f lt3z67wferates uniformly about its center from 130 rpm to 280 rpm in 4.0 sv7 rmw7m ls fyx/le3f9+(utz6. 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 xjze,.cu 4q+hq-/- :j ikqil9 sr3ele $R_1$ 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, aspmt zs+;g sj3pv2-h,wtronauts aboard the Apollo spacecraft put themselves into a slow rotation 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+vst- g;sw mp2hj3p, z a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 2rw9 b -tnt79 9dri5xiz20 s. Through how many revolutio 9drx99twbr-nt5 7 iizns did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcul*w,1xekv ; u5xb5jg wmate
(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 s.n , ah /zq*4b 3oiwtbny;uhxl)c(e(r tresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachingx ; , a ) hz(o(c/yeq.ntb*bhl3urwn4i 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 uniformly8gn- pw1:zzjht2 5skt from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of nwzk1zt h5gs-:pj28tthe wheel have traveled in this time?    m

  A cooling fan is turned off when itzw 9wd5b (r)uj is running at 850rev/min It turns 1500 revolutions ber 5w) b(9dwzujfore 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 reduces its spe5mxb -1tldty7-g ma d)ed uniformly fromgdt7t51y )-lm dxba-m 95km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions z 8f m(jay;rme)-*tvv as the car reduces its speed uniformly from 95km/h to 45km/h The tires v)jmt; -v( emrf8zya* have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her wl2s(uk-av)1nk7uffu; a5xd l eight on each pedal when climbing a hill. The pedals rotate in a circle of radius5 lfxuv;)l2fk(su aa nu7d1-k 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 +mdg.eg,;3na: e;o ba/d iwk oend of a door 74 cm wide. What is the magnitud ;omi,:eaebow n/dd3 ga;kg.+e of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle o.lko( +t ontz; e*z/kjf the wheel shown in Fig. 8–39. Assume thk*k.o zt/nt +;ojezl (at a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are atl3tetf:z)lp y 4031hof- ( prthvd;xktached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is0(t o3k1 h y4 phl)pde;vlxtt-:f3z rf held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to l()zvmivkm 00a torque of 38 i0z(0mv)mv k 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 inertia of a 10.8-kg sphere of radius 0.64l sgw ;k,k;iw+8 m when the axis of rotation is through it;k;kw,igls +w s center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diacz4l:h:m cy i-p3*v xmmeter. The rim and tire have a combined mass of 1.25 kg. The mass of they-:mcc p*:im4v h zxl3 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 ho6 /fbq)l+p/djr,z uq(l+ph r vrizontal cilu6rq,vqj(/fl b+ph)/ zp+rdrcle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on sq( dc4 /x)kfn8dy5mha potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clad mdcn/ 4sf5xh(8q)yky 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 sho(y(52 sjojru 8. bxnqpwn in Fig. 8–438 y srpu5bo(qxjj2n.( 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 consists of two oxygen at2wdsm loi25e 5-k-e fioms 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 spigye8l*/ -mf /fu.n5zrn b5l- ueg8qwvnning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. b/f elwg5n ez-uu*vg5n / 8m-l8fq.yrIf 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 uniform cylinderjs7:1d ,9i6*iswm-zmlpc ho v with a radius of 8.50 cm and a mass of 0.580 kg. Calculatsi*o jsipl7w:,c1mhvm 9-z d6e
(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 fronvrlsj975 x3 z* gkh:xm rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round a7. *(ipw: zf*.q bgec )uhzvknnd 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 c.(u7z hfgk:*b e qvp).nizw* 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 frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotatia,tl k1z (bl:) zsublft1v(3w ng at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.l3 1)ts(t(awb, z1vzblfk :lu 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 ba:g3e (yrg 5shgc p-bda u*0vr-tr kc31ll 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 byo(v(*nz ;lom9vai y 3z the action 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 restyoziv 9a(n*lm(3;v o z to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig. 9ak;-h3j43k6 ;2efhbbpi ,xj sm rssq8–46mjh9 4sqsx;ak 633j-2k;, bsibphefr .
(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 co-r ba+s lcsql4v:/cc d,7i+nx7ltts (nsists 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 from restlu9 :c8m0rfrx;q+dx o within four full turns (revolutior x flc ;+dorm0xq:u98ns) 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 an(f6+5 e r:dh mdq*o)+ptrpmk moment 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 developh2d. df3oonrj1.l 5mok/ *xya s a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls withij reb*xriv 0c(m*s:3i/d*obout slipping down a lane at 3.3 s r 0*mbi/iivro*db :3ce(xj*$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic ener wj0w+g;v2lm kgy of the Earth with respect to the Sun as the sum of two termsg0wkvl 2j+ w;m,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7. 0/pwq38eq r:xaxwbh- 50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylin :abxr0pq-w8whexq3 /der.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and roliwb9jlqrupu9t8 3:gax+kkd ,f 0-5f pls without slipping downitra3 g+09u: x pu9,qk5-8kpf fdbw jl 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 far:xd jag rs+7. e2nfr19hiq sw km8/f.ll and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hef+d1 hsrm/i a7w:. xrnf8jks9 g2q.rint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg gqvg 79s 9mp.8d;s()dt,y 6navh hchlball rotating on the end of a thin string in a circle of radius 1.10 m at an angula ;9qg g)y7hhdcs l9d, ns .p(8athv6mvr speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical g) d2;)tgy usbvrinding wheel of radius 18 cm when rotatit))v2 dg;ysbu ng 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 rotat 6 /mu7km9k6jwdzn2qxing at a rate of 1.3rev/s If mjd 6k/zmwu269nx7kqhe raises his arms to a horizontal position, 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 of ine; 8y3lzhr-gciox 5:uk rtia 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 posit l8i;ykurg: o5 z3xc-hion, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of 1.0ratx4*wu9moi 7lw/g9 rev every 2.0 s to a final rate of 3r7/ w9wo*tla9ui mg4x $rev/s$ 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 b8,srveo+s * blew5(jat a frequency of 1.5rev/s The wheel can be considere8le5,+(j wvs *obrbes d a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skaa)ta1jy;wsdxae +6ta 2.c8 c mjlb 3*cter 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 angulars2unbv3ejg 6 7 0ep4zq momentum 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 04fgugu k(zt 1is dropped onto an identica( f041utgkzgul 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 2.4 r -yu99nf2 lb/(orsfmm5 ux;x $rev/s$ 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 merjl(sev5wfr 1bt to6/fvc ,3l /ry-go-round platform of radius 3.0 m and momeff(e 1jtlwvc6r,/sv bt5o /3lnt 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 veloci ck n 32+lrsc*lud(xn .ju3si8ty of 0.u 2c . ukxn rdl(83l*j3n+cssi8 $rad/s$ 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 h lqny187;d 5ff9 q+ou0;hgdt g3ejrf white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries awa3oh1jl r+fu0ftq;f5d 98 y g;n7 qegdhy 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*)hs o0 3;7a feo w0m*gqgxqv9glz)qm 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 . pqp;fo hc6r+$ 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, /zlbsna-90q4oie:l9. k lco linitially at rest, that can rotate freely without friction. The moment of inertia of a lzq9nlo/49kllbe0o- .sic: 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 dct v,r7z+.ax tiameter merry-go-round turntable that is mounted on friczrct . +,7tavxtionless 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 onhz96g wrujx) -pcom1((vap q - 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, holding onto it, Fig. 8–50. The spool rolls behind the person with-9(vzaopmhj cqwp1) 6rg u- (xout 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 faces the Ea6 +) i2zhp;3gm wvvbgyrth. Determine the ratio of the Moon’s spin+ 32zp y mihgg;b6v)wv angular momentum (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 o j(w (it;ze7fy;n l5ba(uprfs6h hv,/ f 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 1b,t m3xm0lwjr /en.,)stmobthe 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. Calo/wbel 1tm)ms xb3jn,m.0 tr, culate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 k.agl2tu fsdx66 -h ax4g 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 reaches the2lgs6d xa a.f6t4x-hu 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 theb s+h:vnqon *2+z-ucx 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 g8(tmk)9q nsiu(5 pmv 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 wgmu5ti sv)k((n m pq98ould its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for ijx571j1ixlc9ene a o4 t 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 trav1e jl1ej5aox ic7n 4x9el 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 illustratey z/p be6mq34ps an $H_2O$ 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 7r/8w b 5 gnqrl.lpi/bv=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 lenk.e zrutx/a44q.f9z+c4.zma 7yq jnwgth L can 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) j.czz+.xrw .umyn4qaa4 tk 4ze7/f 9qthe 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 flob0gqh3ol,: mtd3 x ;wqor, and we want;b 0gt,dxmq:qo lw33h to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn with an , )ej9sba/ykunc0n4 radius abe0nj c),n/ 9uyk4 sn The forces 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 0r)gs)o7 iain.50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it 07i)giso)nr a 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 armsrp6vyu p3/7o -v0wi qpg4u-je as thin rods, making reasonable estimates for jq6p-u30 y 4 -p/ugv poiev7wrthe 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 two cylindrical plates, qgps/ 59c; zulof ma5u 9l pc;/qgzsss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 of Fig. 8–588lwn; ro5oe26h ,rbsjsk ( b5r. What is the minimum value of th srhewonj2(56; r,8bblor5ks e 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 not assnees jd+(zi:0 ume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revp/opo 9 ,erj- *qwodm5olutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of eachjopo, p/o*mr 9 de5-wq 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