A bicycle odometer (which measures distance traveled) is attached n):rm;dd+tldp4 amm2x ear the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch whe m+tdad:d );m m2prl4xels?

Suppose a disk rotates at constant angular velocic oz7l ahcznx 18:k 899, i,mm;nmapmvty. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the9988 hk7azca n,om:v m1m nzcl,xmip; magnitude of either component of linear acceleration change?

Could a nonrigid body be d4d m.ewuve3;)u3glezq. s/zjescribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greaq05gu1umk3x5w ptl p/ 3b ced(af 6y7iter 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 t6b)7dkkrw/u7g8k yas1 g:ru:h q-lm2 erg ts9han when your arms are stretched out in7hs8-:9eua )tdlrg6 /mk1 b 7sykguwrrk 2:qg front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three;es+8rcvgpe4o7.uv7pa+ ef x (oxelce ));di at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprockoxep+(a8ur x4olegd;+feecs vc7)v ; p 7 .i)eet? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with fk1-ks m+g j3xjlesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is a jk-kxj31+gs mdvantageous.

Why do tightrope walkemuchje +ow+(li8.si, rs (Fig. 8–35) carry a long, narrow beam?

If the net force on a syste-o u l 6zl7p6d- (xnpy10)fpsog- 7ebzf uzv9em is zero, is the net torque also zero? If the net torque on a system is zero, y-zu-6f- 7p0 pgnzofxbduz()7v9 ee o1 sp6ll is the net force zero?

Two inclines have the same height but make different ang) aveik+ t* dm4t7 8ya4dnvh2zv7do; h1rgj2o les with the horizontal. The same steeln; 2mv o)zkiaoy va4g72edt 8 71*+h4t djrdhv ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously staf mz oke.0( r ml3knsxvhm17(7rt rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Wh3r(7 o7mm.es (0nkvhm1 xfk lzich 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 h ;4zv;o )recpmass. They start from rest at the top of an incline. Which reaches the bottom ;r ;hp4cve)ozfirst? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. 0qiif (-enro0a0w :98yo bnvqYet most moving or rotating objects eventually slow doiqrobnf9oq0w80vye( a i0 -n: wn and stop. Explain.

If there were a great migration of pmj v4emyl,mx et* /)7oeople toward the Earth’s equator, how would this emyoelvtmx7*,/j m4 ) affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any init, jp ymwglgq;q54;hf1ial rotation when ywg fq;5 h ;qm,jp4lg1she leaves the board?

The moment of inertia of k)1ffz, h y7kka rotating solid disk about an axis through its center of maskkzy,1f k)h 7fs 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 holdin+zbvwu -hofi5xc bjihw,.l 2(+k*3yu)zkp g9g a 2-kg mass in each outstretched h,2cl -opihif u 9*w)5gu(+ kw zj3bk. xbzhvy+and. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identicaleh;i9( wds ) m-by:pzl and have the same mass. However, one is hollow and the otp :hmy;sb ()lzi9 d-weher is solid. Describe an experiment to determine which is which.

The angular velocity ofng07t8/; jaljjvf e8 -x4hpz o 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 acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. I4/ eajnhlojj78tx v g-p f;08zs the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntaboh pzx-m9s1:-oj qt8o/9 uwlpn5 -osz le. What happens if you walk towardo5z owx tp z-lhq8p oou91 j9-:ssn-/m the center?

A shortstop may leap into the air to catch a ball and9ji25cjf8 o nl throw it quickly. As he throws the ball, the upper partjnlc5289 fj io of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a helicywko*6d.ia8fy:fa b b99s +0kbsm,wqopter must havei9fwb:.sb8* d fk+ q9oba ykaws,6m0y more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following anjh3,3fh k qxl7xd7q(i gles 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 becausl6a(uorepa 9 +e of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diamet9p+(le6 uaoar 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,*+jue2dls b7x8gs5abgo 5(a u 380,000 km from Earth. The beam diverges at an angl2el(bs sd5og8j baa+u5*gux7e $\theta$ (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 kr)8+ qs-woeqof 6500 rpm. When the motor is turned off during ope) -s+w8e qroqkration, the blades 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 level floor 3.5 m to )+pw+ sl xl9bmanother child. If the ball makes 15.0 revolutions, what is its diamet+ l+bws)plmx9er?    m

  A bicycle with tires 68 cm in diameter travev+ua 3d;hr11evu ;yq.sfzs ;els 8.0 km. How many revolutions do the wheels makhq.a;d v1e zu sufv;;e 1r3y+se?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its anxsijt93d 3i;i3mthqd9 ;0sc agular vel0ti;d;txqcsd33aji 9s 3 m9ihocity 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 rev6q g*kr fkva40olution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m faq *kfkrv0 4g6rom the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular veloce6jja yyb5i4lb 1xy- 6ity of the Earth (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 poabgww o n8+,u.int
(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 centr8ta1k5nigaos6*scy/ ifuge rotate if a particle 7.0 cm from the axis of rotation isga *scytk6oni a8/ s51 to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerate*k 5ap0xmt -fes uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determinfkea5p0 *txm- e
(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 radiuj +0 x*evunf,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 Apollo spacecraft p i9qoz4je0ib oq-myy,,-ma s 4ut themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their tripjboo q- q4yyi-s9i m0,zma,4e , 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 acceleratescp g6 bn,a0 zvqprddfh:o- p z/jp+*6: uniformly from rest to 15,000 rpm in 220 s. Through how va6g6nr j ob,:ph+0fd*czd pz-q p/p :many revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Cals7s45jw n6du eculate
(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 st2 udmmut 8g/2xresses of flying highspeed jets in a whirling “human centrifuge,” which tammu gx2td2/8ukes 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 acceleratej/1x r3z3rv:dpaw wv;zg q m),s uniformly from 240 rpm to 360 rpm in 6.5 s. How farmj1 dwrgv:3x r/; zazwp),vq3 will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off we3*w g(uzq+ vwhen it is running at 850rev/min It turns 1500 revolutions before i*wq(ze3+v guwt 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 speed unt ddt:6 gatt/6 s9-glcu7aih;iformly from 95km/h to 45km/h The tires have a diameter of cg/ dh6taatul;g:i -6s97t td 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 k,8ffi,sy w5y 65 revolutions as the car reduces its speed uniformly from 95km/k, s y,ify58fwh 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

  A 55-kg person riding a bike puts all her weight on sq:qakg(-r 2t each pedal when climbing a hill. The pedals rotate in a :ga tq2k (qs-rcircle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. Wh2, 5c45uyona3n uxk hn(my6bc at is the magnitude of the torque if the force is5 bnc3y5 4m (na 6uu2,ykxhnoc 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 axllo wf8utw9 u),,mfo. re of the wheel shown in Fig. 8–39. Assume that a friction torque of , 9tr)fl,8.mfowuwuo 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attacheemn5vfbm1ym hx ) 0,h5d to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod1x bfmmy0)m,5 5hhv ne is 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 a torque of 38rs4 1kn; vc0hrfgre- x nnl9:h;d3ht( ;h ln1r(f3n;h sr4 ekn9cgtvd: hx0-r$m \cdot N$ 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 10.8fh do 8 e6.w-6okpn9qc-kg sphere of radius 0.648 m when the aed9c w6 on.opqf68-hk xis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia oodor4;le5 7 w- 1swneyf a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of theyre7l 5-nsow ;od4w1e hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball 4ie oy ji:jn 9,zf0bm4b5po2 ion the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculai feb omj b5 ,9jz4:ip04o2inyte
(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’. q ;ja-bajs (evw7;bqs wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N totas-qeabj7;j (bvwq .;al.
(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 pointzn g-yruu qg:u)y1 -bw64jyr- objects shown in Fig. 8–43 aboutrybq:gz-r4uy- 6-1un) ugwjy
(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 consistem(z4rpi+ (wkj ex4c* s 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 cylindricvostw )s,t)8dal satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if tto vt) 8sdw)s,he satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.61rn , qkny rwpn l5ng9/oe35h50 cm and a mass of 0.580 kg. Cr5pn lo9nnwq g,y35nh 16/erk alculate
(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, accc5 jft rjg-a/0 j, bha: hykaj23g6yk(elerating 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 tangentially on a small hand-dr es fn 2g1t -db8brkec)2g-3i+r 6jrfsiven 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 raent2c61gfkd-j)g+rf8 ebb- 3s i r 2rsdius 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 rota1ln 4 ,mq lg,:y0c7en rv zmj:p;twg5vting at 10,300 rpm is shut off and is eventually brought uniformly to resmmvzge:l5cgp1n, jq wyt,4v7lr:0n ;t 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. 8–4xu+r-c kn;t3zi5 g:s f5 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 action of the forearm, whojnr:k0z bw: e+o,va; ich rotates about the elbow joint undrez:+jbw oo kna ,:;0ver the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered v-k mh67y/an9l- 0 u l4(vfitrak8onea long thin rod, as shown in Fig. 8–4 8yahevlv40 a7rkifn km-nul(t/-9 6o6.
(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 d 36kqxall)c-b7i vhn00k8yo masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within ;n69o4aamhk bfour full turns (revolutions) and releases it at a speed of 28 ;k6o a9 m4bnha$m/s$ 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 hap7b8d75wyb55 xk.cds0j zwnqz ;ynp1s a 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 develops a torque of 28y 0o*k :qrbl-h0 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 0r ka5e3a rup2kg and radius 9.0 cm rolls without slipping down a lanre3a5a2r0 kpu e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energn)if6 x7u,vuu15snpu y of the Earth with respect to the Sun as the sum of two teu, 7si) unxvu65f p1unrms,
(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 7.50 m. How mucirkhe+xjh3l9a wd x7jy en 0qa5h9 8 ju5-nq06h net work is required to accelerate it from rest to a rot6 jxh j - jruhdixy05+q79aen8 3kw5lehqn09aation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm a ,khnxdffv/:jn/t5 d. jzy3r:nd mass 1.80 kg starts from rest and rolls without slipping down a 30.x kjf3nnfzvyt 5:r ,.ddhj//: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 tny 9pi+kq0ois* / gm 13,tfcrfall and its lower end does not slip. What will be the speed of the upper end of the pole just befor9ptms1i3tgofr/ + nk qy, 0c*ie it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotatinclh+.0y4w0 hut q6yckxhjh 79g on the end of a thin string in a circle of radius 1.10 m at an angular sp tkq074h6xj+9hh y.u cwchy0l eed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum ofye 0m. (prql) 4,ladvf a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm whef 4r ame )ylq.(pv0l,dn 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 that is rotating at a g+dh3cn 9awu/ d5oo5vrate of 1.3rev/s If he raises h3doc9w5uvdn + hg/5ao is 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 reduqw6,vvm6z. y hce her moment of 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 6h6vyvm,zq.w the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase hergnd509m -b geh spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a finn5g dm-9 g0behal 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 aiiog 52 iwvem(u- h:7center 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 c: (i-7emhi2owgai 5uvlay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure sk+bd .crc68xosag) nv 2ater 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:84cqexdn aa 9o 8my,v 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 m; zu mg9ursv-,oment of inertia I is dropped onto an identical disk rotating at anguu-v9g z r;,umslar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2 1ul8.xs (gejho4z+qi.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-gocr w);aawz (n2-round platform of radius 3.0 m a2n c ar(;a)wzwnd 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 rotatin3z 0qb -b11g luggg+mgg freely with an angular velocity of 0. gg3gg+ -0l1bq zbmug18 $rad/s$ 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 collaw)c1x h)c5ruhl;e ,vn pses into a 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 away no angular momentum, what would the Sun’s new rotation rate be?(round tox)v5n)h 1wc,e ruch l; 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 *0 f-kiopffy0 winds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass jgn:53 +sh -zyz y;yrh (r6tbpetgu.;$ 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, tha(2c; xc/4s45arq fuzpmqdo/ g t can rotate freely without friction. The moment of ofz (/gm42 cru/q5scqdp;x 4ainertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merryfuo;p r1;;l kr-go-round turntable that is mounted on frictionless bearin; ur1kl;for;p gs 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 ground with )sg dh*fwbqua ekm63q ev2-89 the end of the rope lying on the top edge of them69suqq2*v- b8 kf geedw 3ha) 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 the same side always faces the Ezasj,- euu**g1jyx9 xarth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earygx* u e,jsz-*j9 xu1ath.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ra )4k0d3pq9caqx o i4rgte of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform )s 8ai3pnq 6ev)t3 t3zriuyc 9cylinder of radius 0.20 m acquires a rotational rate of 3epyt9zaq ) )vc3uri8i36ns t 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,xys b.a rl157)(v lfls each of mass 0.050 kg and diameter 0.075 m, joined by a (concentri lrb5sfyl ax1vs7 l().c) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular sp.bkrf /e0yvyjjk +huw /h )68d*h6dmseed 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 8.0 tt: ;q+aw5m xsximes 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 ps aq:+x 5mxt;wrocess, what would 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 uzn7nt 14jkjo+-v cv(low-pollution automobile is for it 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 beoz4 vvukjt+j nc(71 n- able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates a a3.i69lrjf fyn $H_2O$ 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 v=6k1 ly1xja)y,7bv dlh1 bu5rg3.3 $m/s$ 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.e., we ignore frictio oh n93h4mboh n)o2* jznpy4zt,l6m6yov 0ub2n) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear azl 22nn3,)yzh*bb9h6o0uvyno6pom h4 o tj4 mcceleration 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 vert3n j ;pkzp;fe7w *s.ngically on the floor, and we want to exert a horizontal force F at its axlnjgp73z p;;w.* e fskne 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=y4x s,gmp6.pf jo3xq qsmasr .4:r)x 84.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normalr3:4.f s 4., oxxmmqq )ys86gxprspj a 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 ankr:1sqwc c 6.jd begins whirling the rock in a nearly horizontal circle above his head, accelerating it from restjk 6.rqc w1s:c to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rodsk2/ wt4d0 avqp, making reasonable estimates for the dimensions. Then calcq4k/av pd0w2 tulate 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 twotqfn m;21aah7mk9)m euf 1v+j cylindrical plates, of mass 21e)k1 m qu;nhamt7 fv+j9af m$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rollf;2wqrm8-wra yy .a m1 kefc;.s along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the traqea; 2r-cwm afr..1mfky y8;wck? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, burl4 ctrr871bh t do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unn+*:l3upx92b tik /c mbjy;buiformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular accelerat3y+x2k ntuj u/cbi*9:bm;bl pion 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