A bicycle odometer (which measures distance traveled) is attached near the whek /c27gp9jfboel hub and is designed for 27-inch wheels. What happens if you use it on a bicb9 c72g fkp/ojycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim + q0r*utq01:qt u bbpkxeb* r nk ekvr5.x8)5ghave radial and/or tangential acceleration? If the disk’s angular vel.qxrqu q:5tg *+e50r p* x8b)b tkvnk0rkb ue1ocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of thjya7ez+9ef e of3zq puev79)6dz9c6de angular velocity $\omega$ Explain.

Can a small force ever exert :-af f mxeypav+t+.e;cnlo;( 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 you+ag g 0z+9*usoe2y eqrba.s6c r hands behind your head than when your arms are stretched out in front of you? A diagram may help you to aa gs0u6zs e+o*cgbq.+ r aye92nswer this.

A 21-speed bicycle has seven sprockets at the rear wheel an kn1jb9x./n gzd 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 1 zb9/x. nknjgto pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to runabgqo9as i:k+;brd)( 6k/k 5kd a r1wn fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why thig/ 1aq:)6a ikd o5kkrbs;dn +9ba(wkrs distribution of mass is advantageous.

Why do tightrope walkers (Fi)pt4m qv5 ;odpg. 8–35) carry a long, narrow beam?

If the net force on a system is zerost0 8j- szc5 h3hv0bit 4aeme9, is the net torque also zero? If the net torque on a system is zero, is the net force zero?8e t- 90h0z4b e3h svstji5mac

Two inclines have the same height but make different angles with the horiz 2j crbj:9w2y*p7q jsdontal. The same steel ball is rolled wp*j sdrjqy:7c 9b2j 2down 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 an incline. On7jhh zzgs;m4u q1o6p 5y ar7d+e sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?us5zyz7a14 +j6 ;dhm pg7rhq o

A sphere and a cylinder hdyxgimbw g5 np6-z+k*1t4s m0ave 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 bottobg+1mtxd si -* kz5n6mwp 0y4gm? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum an:1)kuco56 t7rwgldizt;6ejj d angular momentum are conserved. Yet most moving or rotating o;ir:dekjgt )ctj616 5u lw z7objects eventually slow down and stop. Explain.

If there were a great migratib)vuqij 70xpi+ z (,,hgt6yo xon of people toward the Earth’s equator, how would this affect the length of 0,o 6) 7gyhqj +xb i(ipxuz,tvthe day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotation 6uk4 x5:puoapveg - b *g x/kz6v.im*iwhe /ixpz:op b6k .-u6xvgva4* uk*5egmin she leaves the board?

The moment of inertia of a 2mys 8ygxn-k:rotating solid disk about an axis through its center of massn y28-xkgsmy: 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 holding2vg 9uxulk3tb7 *x:dvi ,(pbz a 2-kg mass in each outstretched hand. If you suddenl9i b2vv( *tgb,ldx p3zxu7:uky drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have thehcy-gris jf/;r k41 o9 same mass. However, one is hollow and the other is solid. Describe an experiment to determine 9 rf c/okiyr ;hs1-4jgwhich is which.

The angular velocity of a wheel rotating on a ho;nwq2jt v vylpgs (r).*:o tn3rizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points eaq*:ywstglnj v3) r;nvo p.(2tst, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on / kxk(e: 6m/zzs ecse0the edge of a large freely rotating turntable. What happ/(e6xse0kckzz/ m se :ens if you walk toward the center?

A shortstop may leap in.pixdl boa4+. 9j4wlnto the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his4wl.+l9an 4p.b od jxi 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 momenta. 8yotko/;t yj0p.k kum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the s/oot kayp8k;..ytj 0k econd propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a)8g(bp4qxx3v7q3 b h dg 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. Calculagapr dq5sh (m+o)q4z5 te, using the infor55hmp(s az ) 4gor+qdqmation inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon8ejh :6zwqg inuc 0o(5, 380,000 km from Earth. The beam diverges at an ango jh u(qc8n05we:igz6 le $\theta$ (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 s; -yuumaum4)vn c*+z rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What ismv+auzun 4u y-c;sm*) 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 ball make nz 4rpm fq-;1k 0w21:cixlbzbs 15xpcl1 fb; bw4q-kr:mnzi1z02 .0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. gyusc )reit*m1w++16 j4yk jmHow many revolutions do thei+gmt6kc 4js * y1u emr)1wyj+ wheels make?    $rev$

  (a) A grinding wheel 0.35 m in do* a s:jf6pxroq r9+vpsq7z0 -iameter rotates at 2500 rpm. Calculate its angular veloo sp0rvo z6-9 jps:qfx7rq*a+ city 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 i v n3lld:u/xg2n 4.0 s (Fig. 8–38). (a) What is the linear spevxd:n3 gll2u/ ed 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 arouu7ki vd+yi; doegqz*0u5f;h+ nd the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speeda h4 frd-c;7zf 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 centriqw fkd1ver( 4,fuge rotate if a particle 7.0 cm from the axis of rotation is to experience an ack1fer(4vq ,wd celeration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130dg6*pl kqp-if1b p; w7 rpm to 280qlwkd*16bp ppgf7 ;i- rpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius +vbn aywouxbxjcg0l g6+8;u-9g80pb$R_1$ 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 spacece:kv2r c0i1 oa kugm3l2g+n :fraft 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 a 12-min timea en32:1+mlr f :0uikv2gcokg 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 acceleratesv-u* -piyp(md uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn i p*-yup-vimd( n this time?    $rev$

  An automobile engine slowms iy16zygpngs, 0k 2o7q/. xcs down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses o35csl d97 7c.: gmavq(x epanhf flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min ton 7ca.mh:p 5(7d9ecx3lavs qg turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240nv zymr39d b26e- tr/dt -zce. rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in tnby/erdt.- tcv9 rdz 2-3me6zhis time?    m

  A cooling fan is turned off when it is running at 850rev/mibc6am/, rndm) yp,nh4n It turns 1500 revolutions before it comes t,4 yp/m ndmhrc6n,)bao 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 speedmsx5rt5 kft ruue9+ sb1h9a+9 uniformly from 95km/h to 45km/h The tires havetu5k5+ rrhf9au m19s bt 9+xes 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 revoluj zhs/ 5qe)*ugm88ah ptions as the car reduces its speed uniformly from 95km/h to 45km/h The tires hagh/ 8e )uq*jp8ma5zh sve 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 mx o,pt3u 8e uuwfs0,,vd/fqap( 3vu7her weight on each pedal when climbing a hill. The pedals rotate in fpx dqft8,up,7/ wu( u,s3va3v moeu0a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wuxm a75 v5.jwvide. What is the magnitude of the torque if the force is exertuwm .5vj75xav ed
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig.g z-nj9qwy kph3s9;5xp4 due.l*jjg .4m zq9h 8–39. Assume that5y 4hm q *shp kzegdu.qwx.l n9pzj 34gj;j9-9 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 attached to.7li fgrw,raz ei)e;2knb u06 vvw2o3 the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal posb6 f0iw v2ia u3 z.ok re)w;2,lgrnv7eition 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 tit e8n46akfc, wghtening to a torque of 38 fc6ea4,w k8nt $m \cdot N$ 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 sphnw7)ra5v wug x:0-gz dere of radius 0.648 m when the axis of rotation is throuawdvw 0z) -5xgn 7r:uggh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheiyw0n*wj s(f i/18ga e4 dxsjm.b 7f9sel 66.7 cm in diameter. The rim and ti/ d.wjn(71jx i8aim9wy s 0b4s*gsfef re have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of alq jnmml0(+bvc/8md5po4/ nn r5cz1 s thin, light rod is rotated in a horizontal circle o(qo1dclv nmc4/l5nn zs0r+ /85mjbmpf 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 a potter’s wheel rotating at 6qmhk.:9 lrk, ae1 pgwbota2 6constant angular speed (Fig. 8–42). The fr1b gka6 p9k. , a2:mhlewro6qtiction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia ofwh ifbhhidk;(g2+, 1 /2fhfp x the array of point objects shown in Fig. 8–43 abouhhf1,kf x2( g b;fiph/2ih+ dwt
(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 totab .8 lxijpkj0/l 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 spinningq ut8jrjviiho4ko:2;9 /9iad 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 ir 2ajt;ivoo 9 /uj8:hk i49qdto reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is aeb+xe e8n 8vww+u/wq5 uniform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calculaw+ eu+bew8wxve8 /qn 5te
(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, acceleratingk1eezze)z,9, kfdx k; 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-driven merry-go-round and i2kox p-uw +5xe9go2lwz6 5cshs able to accelerate it from29 k5u wx geozc+2p 6olx-h5sw rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the 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 brought r72 cb(q (6a*a/ sguom slg.mguniformly to rest by a frictional6srmlg7gos(.(gq *m/b au2ca 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. 8–45w 2nyw*ag;,6 rn3 guzr6ngtv. 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 ft v/ 8cx d*sreco;82ekorearm, which rota82dkc tc*8;e/rxve os tes about the elbow joint under 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 au, s ,cjly/tw ;i)f5ee long thin rod, as shown in Fig. 8–465ft ,i);e js/cuwey, l.
(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 9rryo4j zxy(t5s;4ib 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 thn4m 5fnkg/or gkx/vg.1e:x y* e hammer from rest within four full turns (revolutiyg .kgnxov14r 5enxk*/m:/g fons) 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 moment of inertia z/ci tc*h3vka8:7xd1nii40xi l0w rhof $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine deve+ocd*6d a/ac4vaq ho 4lops 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 mas*lri :c5f e.bkge/7 zo(vgw*ws 7.3 kg and radius 9.0 cm rolls without slipping down a lane aeol 5 v/wgg: zrki* e.(c*bwf7t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic eneby ,:jwqhx6 gcx l/g.7rgy of the Earth with respect to the Sun as the sum of two term6/b.gj xg ,cxywq:7hls,
(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 radivme2 at1 9gs2sus of 7.50 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 cyl9asev21 2gstminder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg mow sjhuk03i0v (h.* ystarts from rest and rolls without slipping yuiow 3(mj.0s*0k hhvdown 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 ve9)tn)ai sb/),pyjmogkokb5 - rtically on its tip. It starts to fall and its lower end does not slip. What w )) bikn km9g5b)ojpoyt/as-, ill 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-q tzy *a)m(a;t1k.k q,o3g daskg ball rotating on the end of a thin string in a circle of radiu)*.qt(oy az1kaa,qg d; skmt3s 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindri.7i cu2yggv +bcal grinding wheel of radius 18 cm when 2gy bgu+ vc.i7rotating 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 +j-reb2,qcs g a platform that is rotating at a rate of 1rseb -,gcj +2q.3rev/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 - dg4nr3 8mhy0lsfq bbi+zw l;x7( s4gshown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changnf7+ygb8;4g x(3rdwmli 0bz-l hq 4ss ing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can 2 w,s3zqi *auqincrease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate* aqw3q su2,iz 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 rotatd*au +yngm3o +ing around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be consigya+on* um3+ddered 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 skater spiyp2yvo* q- rk5nning 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)qaj r56k*a 3o b5hvxz Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped ,-ysev ku*mh )onto an identical disk rotating at angue) h,ksv-u* ymlar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at p*ha /q -c+adn2.4 $rev/s$ 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 rotatgpv/hxtikl*)+(js8 jc k mw7 9ing merry-go-round platforvs7xhklj)mc w t8*j9( /+ pigkm of radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with jl94/qq efce8an angular velocity of 0c l /e9f4jeqq8.8 $rad/s$ 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 w*q t7:*n0zm;dxnmqbfd jy si f,6-q7s hite dwarf, losing about half its mass in the process, and windiq;x7 dnm,-qfbmt:z*7isdf 0*nsqj y6 ng up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve wind2acd mqab;;;g s 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 p0mk(h 3wu e)pbb i*j le 6jhecs(+-r2$ 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,:z4w xbe9 ov)oyf c8p qml/15r that can rotate freely without friction. The moment of inertia of the person plus the platfoo/o1v58x: bqymec z) lf49wprrm 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 diamr7- dm5 ke+bhreter merry-go-round turntable that is mounted on fricti-r5mb 7+rehdk onless 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 on the ground with the end of the qy8lgf 2ex.h4 +mml2vrope 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 lengtx 2q 4mevf.8+hmyl 2lgh of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that t atb/ za1t:p- ,9bomoe1 dorar e9u(t)he same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat th(o rbb,autz1omt1)taa:99eod/ -rpee Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from resw8vf+)p /io,r po4orvzcrj 2 rio q-f80xj 8z5t 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 a uniform cylinder of radius 0.20 m acquq1 7e khqae*x)lnx: 5hjqa3v3ires a rotati): xk* lhq33a7vq hjeanq5ex1onal 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 cylindricaagiujvmp4,01 e 3h fo33d znj3l disks, each of mass 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,pa0343 z3e vn1d3ghmojj fiu released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear whepm :)4nmwhzk5el ($\omega_R$) 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 times as great, q*+5iklr o ewe br821ewere rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutroe5b*1r2lkw8r+ee iqo n star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use zlx :2o 2u7fhqje3- *j(plwcienergy 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 iwzj7 *flo:(l h23c2up- jeqxmass 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 illustrates an 3nk)m 3/ru jwd$H_2O$ 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 spf3m1 spv1icf ,8ftga:eed 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.e., we ignore f)jy+(lz1oqmnyfa l +mldx:1-riction) 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 acceleration of the tip of the rod. Assume that the force of gravity acts atmjmz(oy f 1:a+l -lx1ydnl)+ q 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 verticr a 0pq+x 5+ qvsqgbqkvt93 ;)*aka8uyally on the floor, and we want 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 ha*qv u+xr5y+8 s)3b0qvqtgka;q kaap9 s height h, where h

  A bicyclist traveling with spees2l tw l6,rib+d v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normaltiwr 2, 6b+sll 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 18rjz(sa z *3w7;d rdfa.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, an3z(d7 8w;rj afr* dzasd where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and herlg2 yyt.lg 9p. arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratit9 l2ylpgg. y.o 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 cylinlgx;2h utuvj k --w*gymd n-9;drical plates, of ma xh; d-v-t 2k9w;njugl*-gyum ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ro4)2n hm t)yvybdf qc/8s9:gl llls 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 withou /v9 2yy4) ):mq8n dscgfltblht leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but d 4qrbj ri,g.y53bf8 (ny v.yebo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unif8bw pb:/ embnhz931oe ormly from 90km/h to 60km/h The tires have a diameter of 0.90 m/1e8w9b bez:bnpomh 3 . (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