A bicycle odometer (which measures distancew xo sy:u 00 2+ 3txsii8gart*w):opth traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24- a y :+:owogt t *spuxh3si0wxi2t8r0)inch wheels?

Suppose a disk rotates at constant angular velocity. Does a p(l vivf(ra1h .bz,: tkm7gn0 voint on the rim have radial and/or tangential acceleration? If the disk’s angular mnl(v:gha ,vf(v0z 71b.itrk velocity 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 dna1 yv-rgq, (5 6gnmleescribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Erhl4y32.tq q aoc f 8up*ds+amq9(ki: xplain.

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 w9b 1dh9u m ,0sje7+8bbzkjv zmt ez:5hands behind your head than when your arms are stretched out in front ofhdz, b1:59kz0z8 em97+e uj vwjb mstb you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear cqcy;ni ,.+ pnwheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or acn,pqy +ni c.; large rear sprocket? 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 sljgoeo / .pk,.yg+6j6b pb xl(kender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34)/o6j, glkkxbjp+p.gb y. o(6e . On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope waljh8q2 p il(cb;ppb op7y 4d9(fkers (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zulfb 4 pgal7 22sd7xe7ero? If the net torque on a system is zero, is the net force zerose 72 lf ga2lx477bpud?

Two inclines have the same height but make different angles alvq*j).z50 y 9nniu9s+ri pcwith the horizontal. The same steel ball is rolled down each incline. On which *z0 +u)vn5ii rl9yj 9.qapsncincline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously st p31t p.puk)ohart rolling (from rest) down an incline. One sphere has twice the radius and twu) 3.optp1khpice 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?

A sphere and a cylinder have the same radius and the samq py1hsaiv-opyfakcse 2*:x 5,m7 :5cv4n k .ie mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater spc5i1xkvoiams yvyqa7hk: p,p fecs-. n2 :* 45eed 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. Yet most moc dcexby8m6 79ving or rotating objects eventually slow docxdc7e69 mb8y wn and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wouldkhoo 1dasl-u(4t :3zb hl45mh this affect theh hm l1 o(5l-b htkdo4zsa4:3u length of the day?

Can the diver of Fig. 8–2pu03h4-t (fd sseth-w9 do a somersault without having any initial rotation when she lea-wset h 0f3 updst-(h4ves the board?

The moment of inertia of a rotating solid disk about an qk,4q6mnv-izq;m (g w axis through its center of mass i4 6mwm;(, qvg-zkiqq ns $\frac{1}{2}WR^2$ (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 sitt 4a8chsjnre;6um+(bvx h+;r ying on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, dec;;ce+8jauvsmn4rxhh by r +6(rease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow an ( 0e:cl+(anbyl*d,stv)drdwd the other is solid. Describe an experiment to determisd (tyce ,lvdn:ad*rw0b ()l+ne which is which.

The angular velocity oflat;a/4hb3gc cdl ;s6 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 as3bac;c6dltl /; h4ag ngular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing ip547lq3:exdpg .8*j wymiao vx)nj t..z .qbon the edge of a large freely rotating turntable. What hat)d xpg.57l.iqa.zmx4.bq 8ie: jvwy3jonp* ppens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw z,ehoej4bbc ( 0r :axrlu*. p-it quickly. As he throws thez* b4bua e.cl0,p j:x-erorh ( 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). Explain.

On the basis of the law of conservation of angular momentum, discx4eso+;kcw : 1o g(0rmg el9ohuss why a helicopter must have more than one rotoowr+h (ko:lg1;x9e0e cogs4m r (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles inf 5, wc/ruyhwjkt21+6ald p;t 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. v(1j ho1bqe joh-bv2o5js-y*d. z5hg Calculate, using the information inside the Front Cover, v1-z5*.boj h2v doqojj5y- sbh1 g(eh 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 Moon, 380,000 km from Earth. The beam di+a.* eszh /ryuverges athr.a +u/ sey*z an angle $\theta$ (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 6500yk5 j5hk 0(nps5)xyx ll; hkb4 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the nkl x 45jxhsb5kyky)p 5h(;l0angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level f *onb.b -e5jk, qrouf:loor 3.5 m to another child. If the ball makes 15.0 revolutions, whatkqfub,nbejo o. *5-r: is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions do-et 2aqc-7nm3boa d t6 theocda-ttm q2a7b6n -3 e wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calc o c 2vrk3muo kd4q8uxkl6)+f-ulate its angular vel kc4f l863u-o+k vq2mkrx)oudocity 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 completvc c/w+r1us3xku 6t5 se revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2w kuc1tu s5xc+ rv63s/ 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)9kt95 5wwssq lxz+2jt 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 p b.2bb6dun 5wwoint
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from thv:fa uo-8o ae.0aga**g r5gvw e axis of rotation is to experience an accelerationwoa*gaeav.rv: *g oaf08-5 u g of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its cent2,xf yon asd26er from 130 rpm to 280 rpm in 4.0 s. Determ2of yn ,a26dsxine
(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 pp-i6m27/)gg bo0dw fny/ (wmc tqfl;$R_1$ 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 put t8rn8uzi k2cv9 hemselves 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 time 8zn 9kci2urv8 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 l1;z .cwb w;uito 15,000 rpm in 220 s. Through how many revolutio ;wul;. cbw1zins did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s.b; a+cdka.+e t Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highsp u3*lv 7e3jqpjeed jets in a whirling “human centrifuge,” which tak3p*evujl 7q3jes 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 accelerate0wf .iei 2pta;/7hm ses uniformly from 240 rpm to 360 rpm in 6.5 s. How faamhe p2it0es7; / wfi.r will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runl3 +h w+cuobo lw3zi.-ning at 850rev/min It turns 1500 revolutions befor3owc ++lubwho 3zl -.ie it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 63cb-xo8y rtg+ 4epls1 5 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The t13yg-x+8 b pot4l rsceires 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 juvms r/5acp,*gx (-vits speed uniformly frxv/ uj 5pgvm(-*s, carom 95km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbing a h6e +.e1tmaesv tv +bu w/3rn3dill. The pedals rotateare +t1mv3t6n.e+dsbw ue3 v / in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74,49 l qs d//py ho9ht-87,fbsgxewdfd cm wide. What is the magnitude o9- pdob,s7hte/h qx4sy8f w lgdf9/,df the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the :h8 uoixn2ygam +7*z yaxle of the wheel shown in Fig. 8–39. Assume that a frictionm:y7 *ix+h2g anz8ouy 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 the en-9yp /t8** pl wmobm - rduv:s;pj6gftds of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal poslmp:*98 yj; opts/rd t-w6-gbfpv mu*ition 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 tii3hl/ j+jdcro; fwe, b+/v f9xg:9a joghtening to a torque of 38r3a cxbhw/fl ;j,9f i+9: +v/geojdjo $m \cdot N$ 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 oee/w;:-aiel,l2l m: t 0ix.wd)2yke6efdr ckf inertia of a 10.8-kg sphere of radius 0.648 m when the ax.c:mly2ixle; 0ie fw-w/ketr2 ed6de k,a )l:is of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheelrx7;wbakd5vu ff .)/ h 66.7 cm in diameter. The rim and tire have a combined mass of f)r a;bwf 57vxh/kdu. 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 a thin, light rod is rotated in 25qox)o ) apdrj+q2xm a horizontal circle of radius 1.2 m. Calcula25xmaq)dp oxoqj)r+ 2 te
(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 f+a osb7)+mdg ynsf+:h * mb.9crah9ca bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). Thers+y mmsh:d +9*f.c oc)ag+bn b9 7haf friction 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 of the array of point object5ot 94goxtuv +s shown in Fig. 8–43 abou+vox9guo4 t5tt
(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 tm3 xs d4j*z-;ihqg2ujotal mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, engr cw;4eeyc 1- :sd bil8e)tsu-ineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass cdi:y1see);8wescl b-tr u-4of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0.w2ht liff 5jqt 4au,niu0 ,8f*580 kh4wn 5iqt,fiu28tlf0 , af *jug. 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)5 uig08zs 9khyww22dsa:4erbe /da jbt*y4t , 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 tangentially on a small hand-driven merry-go-ro3c-du 0rog7l3 *gxi rmund and is able to accelerate it from rest to a frequenggri3*xm-u7c0 dlo r3cy 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 10,3 7wdeg/0/w ih1 bgsu+e00 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1g eu 1/be/+iwd swgh07.2 $m \cdot N$ 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 acce/cl16nx5qey 6 uhiv 1wlerates 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 ballu zcbw ny y;+l5i43ja5 is thrown solely by the action of the forearm, which rotates about the elbow joint under ta55 w njuic43l+yy b;zhe 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 cqqk ir *s:a, b;gfy.k*an be considered a long thin rod, as shown in Fig. 8–46 *rqgyqi bk fa*;,.s:k.
(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 consim;fb ifexudhf)wowt; s)03 ff+ o- l)-sts of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hung4 l( z8c1)kjxufo2 ammer from rest within four full turns (revolutions) and releases it at a speed of 28 xuco)ul8n 1 (fkzj42g $m/s$ 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 inert* u+x yvtkw8t5/pqs el8i/ c+qia 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 75tqg 2 jfity9of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without sd 874,inw 1c evrw2whqlipping down a lane at 3.q i2,c7h1 rwn 48wvwde3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kineticuf/bs 5m+yr+5zf7pv 2u r*cn6bq zvr , energy of the Earth with respect to the Sun as the sum of t b, n7 r+ucz2u/q+vrym5s6v f5f*rzbpwo terms,
(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 r81dor4pd *yk8)lz 1,tuopf h fadius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolu*p o, 11py84lzdkhfft8 odr)ution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg s0wcclmf+ol.(ae.8 ittarts from rest and rolls without sfameo. c.+ il0w8t c(llipping 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 balanced verticallys yky5mlu4t 8; on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper8t 4ky sm5y;lu end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the e+ljr n eik:phol.2m*o 0wp j92gg20 tond of a thin string in a circle of radius 1.10 m at an2gwk0ptnmh* .0 gjoi2elp +:9r2ojol angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform clg9 5 j(ucoo3cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpmo c3c9luog(j 5?    $kg \cdot m^2$
(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 )zr77y zaf0vnkp 3/f fplatform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed rz7vpf/z70 f )f ak3ynof 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 rv-*j w. 8nyytreduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she manyr j- t8.y*vwkes 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 ie7:non kgkiru3 2 y3x3ncrease her spin rotation rate from an initial rate of 1.0 rev every 2.0 n 2grkuyno:337e3ikx s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a verticalyna. i-twp;9i nzs5 --1 jrdww axis through its center 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 aftes.wr 1n-n;ai ww ijz95pt--dyr the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater qawp h 9x.)nf1spinning 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 m u3.pb1mped, of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk oxuiww2iki939 +xh;6 snp g4lef moment of inertia I is dropped onto an identical ini pke6xhl2 g3 ;x9wwi 9s+4udisk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 kf.k9 *jc;ebl ta1zud2eyo:3 $rev/s$ 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-go-r-rshx- )teig+jz 1+w+hn,suw 9f: o cwound platform of radius 3.0 fw+wotz+-,uinssj+1e c: 9w gh)h-x r 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 an anguo4e m; bpjh(k3lar velocity of 0;bpe( hm4k3o j.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 white dwarfr m.v4 lhc8vq*, 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 n8vc mhvlq4r.* o angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excessr 2ud/z 4ctn7m 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 n kn3 h :1n,m.yx*rfqs$ 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 oe3(kkt *fax2kq)a)4sg5 8u u 9vmdtqrest, that can rotate freely without frictm 39fe( x gqus*)q)2 ukovd4t aak58ktion. The moment of inertia 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 mrndhi30gtk)v:mq-a o5/ha4f x j li7* erry-go-round turntable that is mounted on frictionless bearings and has0 7 m ln5fd:3jh ah*i)rq-gxkvi /a4to 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 8.lxixztc 1ymwi13nap 4 /; yuground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolt nmw; iz3.4c1/1ya8y ixlp xuls 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 tdsg,a8 vfhsp+b08 cj ,9mkhq 0hat the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to ,8s cs8kgp 9hbhd+, v00fmq jaits orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at4a 7boczp2is mwp adc33 dh60joa(2 )p 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 shapek7ix.l*+x ozyl6d 7* imt vk8y of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculik z*7lt 68o xm7.yd vyikl*x+ate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, bhmt/qb0:2wme07 x*likc w(f 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-/*ib2k 0x:emtl w0 (hbfmw7cqlong string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheelb581i 6,bygwg q/zbf r ($\omega_R$) 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, f,:c)tcms 6z bjxd.i5 were rotating at a speed of 1.0 revolution every 12 days. If it were to undx.csmd,zti:5 bcfj)6ergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stored 2f2vuoguqub;6 nks5vj- q.y37 vk p 9oin a heavy r9u3;- g bvvuquqk2yvojfo ns6 .72p5kotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to 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 +ho 9;y3 8j :fj xtwp8lit+5gt9upt wu$H_2O$ 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) edo/n : 1;qzbkis 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.e., weto vs 6eu4uu)z3+3i zj ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravit3u6 s+3ut)iuvzj4o ezy acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically o vx,0mkiut 5l:pi2b+ tn the floor, and we want to exert a horizontal force F at its axle so th2,u kit+lb5pix0 tm :vat 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/r sf3g;knk1n(s on a flat road is making a turn with a radius Thenfks(nrg 3k1; 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 lennea2ow/ vptwso. s. 68t ny84v ;0ztotgth 1.5 m and begins whirling the rock in a nearly horizontal circle8/n4teaw 0tsttyp oo.w 8on v.2zv6;s 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, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder an / ya:gmj2)u atc0o3pld her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and wi:agcay ul p3t)o0m/ 2jth arms held tightly against her body.   

  You are designing a clutcttex64 m 3lkb+k iu:c0h assembly which consists of two cylindrical plates, of mass tkk6:l3 u+bexc 0 tmi4$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of:xpfek/k 3gr 2 Fig. 8–58. What is the minimum value of the vertical heix2krp :/ gf3ekght h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not a9,q fwqpd x8xd 64h.m rkwo56kssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly fnw(k*0o;zxc od4as t) rom 90km/h to 60km/h The tires have a diameter of 0.90 m. )ta zsdoknx;(o*cw4 0 (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