A bicycle odometer (which measures d03u dy- 0(* cwzzlyxyxistance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on xzdy-(u30wc* lz y 0xya bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocin lymh(,f olk6b1a/d9ty. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases u m b(,fy/nl61ad9o klhniformly, 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 describa( p2wt3iqg* 9z5aq dgv4ufm)ed by a single value of the angular velocity $\omega$ Explain.

Can a small force everw;z*dxt*)a jd7 rm1q 8hwvmr 0 exert a 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 hands behind your head than w a/t6i,,mf5 vwwfhvno5b t; r)hen your arms are stretched out in fro5twvo n6ir 5vff/w,;a bt,mh)nt of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel acx . p7c br1q;v4 2d5acr/lkoknd three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a lab./ 4 l2oc5kkva7 x1dcrq;rp crge front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs wihhq(5oq+ hn g gb/t+doc7 x+r9th flesh and muscle concentratx9 gq(/rh+c hn +gdq thob75+oed high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35w+0s +kbp jvukfn9;a( f7g0 z8w5 d5tz8undl h) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net ttlhva ;5nt/to8,u t c lfz517ju+ eh7yor fuj5hla o7t1,t5n8vczhu el/ty;+7tque on a system is zero, is the net force zero?

Two inclines have the wkyjzr6mxq 6;ee7u rb*p q:* )dmj3 v6same height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be gre3 j; u 7j:vb6drqmxqk rmeewz6)6 yp**ater? Explain.

Two solid spheres simultaneously start rolling (from rest) dok3udkq 4j q2x(wn an incline. One sphere has twice the radius and twice the mass of the other. Which reacheq2uk kjdx(43qs the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same .8jtduc y 6e0bradius and the same mass. They start from rest at the te8jtb0y.6c du op of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angukb wjgd3 5ihsovv;48z/vgy /qd,47f k lar momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. ,4v5/ /vk4;3 jwkd7hovqd8 bzif ggsyExplain.

If there were a great mi-o,fzz vy)z-s*n6taagration of people toward the Earth’s equator, how would this affect the length of ttzz* nfvs -zay,6oa )-he day?

Can the diver of Fig. 8–3bw7+lr ,jyyre q20xdb)t fq+29 do a somersault without having any initial rotation when she leaves the board?2yerd70bt +bq3rj xwyq+,l )f

The moment of inertia orf0q14re94kzl e8qkxgz3 x l2f a rotating solid disk about an axis through its center 1 z9kqefl0rq4ek xr x384z2l gof mass 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 each 6 mr0xx0 vavh32gucd 5outstretched hand. If you suddenly drop the masses, will your angular velocity increase, mr6u dx02a5gvxcvh0 3decrease, or stay the same? Explain.

Two spheres look identical and have thzpv1bs9*lj.6 fvmtf .e same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is which.p.sz f9 tv*1v ljb.fm6

The angular velocity of a whe jc/6tpi* 8e k7q1qbweel 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 acceleration points east, dek1 q8e/t eq*ipw6jb7cscribe 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 ro4sz nt*h+ l0k3uh0h kfpeugqa+3:zn6tating turntable. What happens if you walka pfe:kl*4+nthgq u sh3z0ku6h30z+n toward the center?

A shortstop may leap into the air to cfa2 wz+m;qoqm8e 6+mq)g*rz batch a ball and throw it quickly. 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). E +ma g;qo 6)qwq+mzbz2m*8frexplain.

On the basis of the law of conservation of angular moment w lo1+,*3re:pwx /:j2spacif r2p xmhum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propellp2ajfi rc2hxr:3,p+e /sp : 1ox*l wwmer can operate to keep the helicopter stable.

  Express the followingtb+pbs :dk x 6ebp9+jek7 4vb; angles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence.k.5ycni( .tnz Calculate, using the information inside the Front Cover, the angular diz y5 .ktn.cn(iameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. g7x mh8 adgcwh1hx*mg ,khwho/q(71 ,The beam diverges at an angc*7h,gxh1mx wk7gqwahdm h/1 h o (,8gle $\theta$ (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 the motor is turne*v4)xggooz1qg1 k a, ad off during operation, the blades slow to rest in 3.0 s. What 4vzgok )*aoxa1q1 ,g gis the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the bal4bf4/ yx 3tijrgw +:wkl makes f+xt4i:y gwbr3jk4w /15.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How ma:l1qd kxb05)yizzv 8l ny revolutions do the wh1:zq k xdzbl5l0i)y8 veels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter r ot1ogbjq-o: 3:fhfc/otates at 2500 rpm. Calculate its angular velocity in hob3gqojf :: /f-c1o t$rad/s$ $\omega$ =    $rad/sec$
(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 make6xom;.;c1ncq 1r,o8 bf yjpho s one complete revolution in 4.0 s (Fig. 8–38). (a) What is the lineayor,;nqc 6m8.o;xb f1 ph1jocr 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 S(v4 qd;ufpfo/ un    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spei, s3i7hwb 1b1e)ps4blaml3 eed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rot,nf3xue1h+gx6 bn()pq0yim oate if a particle 7.0 cm from the axis of rotation is to experience an 0y qx ,fnon)b6uhg3e(xip+m1acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly aboi *xm5;p srx34q(mval.bjkl2ut its center from 130 rpm to 280 rpm in 4.0 s. m 2sjax m;3xpr. (4llvb 5kqi*Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiu fda50fl91 8wmwycp/ds $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollv51ustj2/y - k-n yhkmo spacecraft put themselves into a slow rotation to distribute the Sun’s s y2hjk -5-tu 1ykv/nmenergy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest tocpl 2d*q2qy(y82qe oz5 jo9mpb nee 6+ 15,000 rpm in 220 s. Through how many revolutions did i8j 2eo 5yqqq92by2c*zo6 pnm p+dl (eet turn in this time?    $rev$

  An automobile engine slows down from 4500(.ui jrgc ohjf1d2ht: kr/p1s -ip 68f 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 mm/3vlblq p29 8r0f-msy pwy3 for the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its fina-bp830wyfl yl vq3/msrp2 mm 9l speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly fro0zpy9 x q 0sh.lr4(qozm 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wh9x(lso z yz00rhq 4p.qeel have traveled in this time?    m

  A cooling fan is turned t qqd 2rj:(gn6a; g7izoff when it is running at 850rev/min It turns 1500 revolutions before it comesn 6iq; tdq g7j(zgar2: 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 65mbu2cy c9 wvlj53ub eis1(.x*t 4z (hf revolutions as the car reduces its speed uniformly from 95km/h to 4z 1(4lftyb9i h3 uwmvucc(xjes5 2 *b.5km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly f0zqflp i:y0asf5w7co 1 3k3zwrom 95km/h to 45km/h The tires have a diameter zysk:5 ff a017pcw3zw3 qio0lof 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 otu34v i2e9tfzn each pedal when climbing a hil9 t ezt3f4uiv2l. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force ofzmyj /s7w,p li/0wn .p:) cpleof8 /no 55 N on the end of a door 74 cm wide. What is the magnitude of the :/ynn)e. ,wpz / /8fpc7i0lpolwo sjm 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 ab+qkhrvi-hs 42 out the axle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.4k+qhv 2-i h4sr $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are a45k9 e3f d4f gfmq61vxm( fbrlttached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released6m4f1 gm3xrdfbffv4 ( 9kqel5 . Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine, llqd62 db ux5z:v6wj- (ee /iftmp9a require tightening to a torque of 38 bw(2t ze5/vqam9jdx lli: ud pf-,66e$m \cdot N$ 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 radvngk1k pm x8y b)-.k 4vdamk+1ius 0.648 m when the axis of rotatio18+xa1dk -4vv)pykmnkgbmk . n is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. Thd,e pq s.i7x1qe rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ign dixe 1q.pq,7sored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated inkxt l 4yr z)ej*ypr2*9(edm; w a horizontal circle of radius 1.2 m. Calcuw y2 ly *me)(drt9e4x*k; jzrplate
(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)h0ma9ns; edq potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction )9dmeq 0s hn;aforce 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 inern;d5kggq3. bh y;xr/hdi *s ,ttia of the array of point objects shown in Fig. 8–43t.bk3gh, yhdx q*5nsrg;/d;i 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 atoms whose total mass isj6gp4cn;(ppo +a s6is $5.3 \times10^{ -26}$ 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 satellwuyd:m6;il1 wite 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 id wwu:;16lymi n 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of wfpfom2i7 kvx ;n y,: 6ldosstp(oxy 61*z;.v8.50 cm and a mass of 0.580 2np7iy tx;l vko6pso6y:1fmx,z ow (;fd.vs*kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, afngk1 1n)u2n64.kfk6yxfs 9ygs t2o accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangent55myg58w:zi* .. 2uzduqx)a btvfzovially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 152b .voy5 8zu5mwvgd zu: )5iaxqzf*. t rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually brcj+)x7(fm a:wd -g)v5w zfxf xought uniformzjw )x-mx w:) c57adfffx(g+v ly 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;9o hlm55om-fq rxvlq6) uh te 5vx,j; ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of toe c:u u)3r /a37l rubhn:maf8he forearm, which rotates about the elbow joint under the action oabfm lr 7ru3:ohn8e:ua /3u )cf 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 c;wmzw )e,n5 9rgxvhj2an be considered a long thin rod, as shown in Fig. 8–4,g9vjh )e2; mn5rz wxw6.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two mayvo t0( 9vten y8h.h4 h 8 xoo8w7lgmyzc5--iesses, $m_1$ 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 (r8 ris-dh4 ro-wevolutions) -r8d4-rhsiwo and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a m-q1c m3*;6 znyrgtocb oment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 2imvb6 pkduqyr87ct1 ,;t4 2a g80 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping doezeb42z 1z:b k(: 8bvv(wxi cawn a lane at :zb 8b(i(avc 2e zv1ex4w:kbz3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the cimbf:,sti*ug9 axy + dj7(l( sum of two teia*tsx7u (b,+l d( fcjyi9g:m rms,
(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 ry.y/v.4d bfft8fg sr3adius of 7.50 m. How much net work 8y 3 dfbr 4svgf.ty./fis 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 y c+eh fgq0sk,n9*h)cand mass 1.80 kg starts from rest and rolls without sl0,cy*s+ fc 9 )gknqhehipping 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 bal,i6::ks nlhblvy q9if l* f:wck(mc 5;anced vertically on its tip. It starts to fall and its lower end does not slip:ly(: ;vim 6sfiw 95cqlkb k l,:hc*fn. 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 gr/.apjsfqw(dat:3 *z 0gm -pu/,kl x ball rotating on the end of a thin string in a circle of radius 1.10 m at an ax3 p/a0.j/-sudwgalqf*:(,zr kmg tpngular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grindijnjl x5f a5)ze(mm49 ong wheel of radius 18 cm when rotating at 1500 rpm? o n xjm(9ml54ajzfe5)    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a ra(x0id/e 0jnc9a*guzf te of 1.3revie(*9 0fudn/ gjz xca0/s If he 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 ok9fhbw / dc9:h xhplq) :.jig;f 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 s :cg:h)l ;hfq.9 dji xbkphw/9peed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of 1.e0pqem,- iy8 f0 rev every 2.0 s to a final rat qeyipfem80 ,-e 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 ric sfnxt( y7+h40x.qls w0d7rotating around a vertical axis through its center at a frequency of 1.5rev/s The wheel cqwhdc. xl +i sf4(x07tnsr0y7an 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 to it?    $rev/s$

  (a) What is the angular momentum of a figure s fuiuz+abeg +e)yd8-6 kater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the *gal6)6i*qqze m3uv dEarth
(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 isav9imzwbk6gpzfn)2z k6 h-ek+ mk8. ) dropped onto an identical disk roae.k9m+w-k z ifnz6)b )hk8 m2 6pzgvktating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at t uttlvpd41/mrc 1l-.s, i0v g2.4 $rev/s$ 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-gy5-fn (f;hepd o-round platform of radius 3.0 m an ;yhf5df -epn(d moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rmm,2r9)l 5i8 v0 hu oyvr+ixilotating freely with an angular velocity of 0.88x rr9vivl 2lmiho)0my5iu+, $rad/s$ 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 whitb a he)3gsx8-r2gd-do e dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what woulbe-ag- do 23r8) xsdhgd 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 windscyw75mg ;bx1t j8af- f 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 pqtpd 2,jq/ (jpux):d$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, z5gznhl 4/4h0bbmgt6that can rotate freely without friction. The moment of inertia ogg45/nhl4bzhz bt 6m 0f 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 edg /opl1 u+u3vtge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1gt+ul /u31ovp700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rovj- v1y 33r-q yj.iryc 4 nygq7y/1zsnpe lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rvc3 . gy/4 -irq7jny1jy3qs-ry1ny zvope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that +ev44cy;tee8x pu f7dthe same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) tocpf 4e ;4etx78ey+du v its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from:q68a8sfnkekmi xr 6. vvd3u52hfvc7 rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of k8)4u46 ,i wchovq eofa uniform cylinder of radius 0.20 m acquires a rota kuoc6h4ove 8 )qwi,f4tional rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass l rq :oghcm 6t6b3o5r+0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is 63m ho rqbcort: g+65lreleased from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular sl+zs .)vuxp ifm8-f.fpeed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass l70f )vus1yt mk9ok:2w 4iiej8.0 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 ye4mi127vk0t9:w ios) ufkl j 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 it t dw-:gx+ .b./sa wjczto use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass .+s dt :x/gwbj-.cwzaof 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustratefww1l/l v5ea(khxjf0 nrq) 1/ s 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) ik x5m ydm36ni q:am*)rs 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 pivot freely (i.2mfm 7; y) z6i4zyxk, 37 leginu vl;hife/f4re., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then l2n 463r;74 e iieuz,vkl;zhy f)gm/ yffi 7xmreleased. 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 vertica3/g5dqbvj 9p8jbfumc:fsv(,d vew +6lly on the floor, and we want to exert a horizontal force F af b3vvu,cfb:smdq 5v89/wde jg ( 6+pjt 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 jnlrvh flf2u4;bo.x 5: d.py9sr1 *rv a turn with a radius Thyx5b2jfv rs* ; 1: ulr4pfnv d..ol9hre 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 0.50-kg rock into a sling of length 1.5 m and b xl/51kofgyw/a h) qy;egins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achiqwofgyhy //ka 5l);x1 eve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid c, c*u4etqv +gn mou4/yylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skctgv*u oq mney/u4 ,+4ater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consispnw cpfh .+,nyn;9h :o;,jk mcts of two cylindrical plates, of pn+jhy ;ch.9w,k ,nnm f;ocp:mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 amcaqq( t51.j track of Fig. 8–58. What is the minimum value of the vertical height h thajctm1q5a. (q at 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 wcq,oig/3br 2assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 rev -nvfb4rqqmo; oq7,vr;ne9v ; olutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of ;ef;rrvqonm9;q4 nvb,o qv7- 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s