A bicycle odometer (which measures d lgu x/xi*u40tistance traveled) is attached near the wheel hub and is designed for 27-lu 4uxi 0g/xt*inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular ve7qv,:db(0p d ol pw7kylocity. Does a point on the rim have radial and/or tangential accelerati0bq (dwyplk 7 :vp7o,don? If the disk’s angular 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 de30 xox3h mh7dwscribed by a single value of the angular velocity $\omega$ Explain.

Can a small force eve -ej9) bnfq/o8+f tx:n )hubaxr exert a greater torque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do f jq(gbjc h3+/b7v)xm a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagr 7j cb(b/x3mgvhqjf+ )am may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at th;mdzkk3n;8 gtu 8uc ,iyze w2+e pedal cranks. In which gear is it harder to pedal3 mk2tw8yeu; n,i c; 8zgzduk+, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs witll olsp4)g,7m.xgbt28 dg9z vh flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dtop 8 x lzmb2)s4 .vd7glgg9,lynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 83llg/rrijt2xub36 l 4–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? -c (k8 kximr)9)gblx cIf the net torque on a system is zkmr (gb9cxx c ik)l)-8ero, is the net force zero?

Two inclines have the saang s5 sd9:p+2 yfo; yxfze61nme height but make different angles with the horizontal. The same steel ball is rolled dow:n+ 561p;xfszdfs y9ao n y2egn each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneolex pyfa9l806 vx9nt) ,jnn -rusly start rolling (from rest) down an incline. One sp0-xy) 8pr jlen,n xvl6n99 tafhere 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?

A sphere and a cylinder have the same radius and the s ey,kh0( sk (qn9r.kmcn ,pm.kame mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic r(,,.hmk cnsq(n9.0pkyekk menergy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. /u p;l*w*-)- pm-yblzmd7oeg fw dj2w)l2xup Yet most moving or rotating objects eventually slow down m u dulllm7g2p;-fp)yo*-j)w-zdbwe/ p *w2xand stop. Explain.

If there were a great migration of people toward the Earth’s equatufx f65.imn jy9-ci .x szv-;yor, how would thisxmj5icy-nfx- fz. si96u;y .v affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without havina (o4wy/.dz ylg any initial rotation whw(odly./ 4 azyen she leaves the board?

The moment of inertia of a rotating solid disk about an axis through its centepclsi(9b-sr +r of mass l -sribcs+(p 9is $\frac{1}{2}WR^2$ (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 hod t wfyv8.(q7qx0w5 yplding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, tv ypfxydwq.( 5 0q7w8decrease, or stay the same? Explain.

Two spheres look identical and have the same mas:a c2jj ,xylg ukv8i);bo4-s zs. However, one is hollow and the other is solid. Describ kbasvy;4 joi)clgx: uj8-, z2e an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. Ijxotx(;ow1 /f dmlgu)s, 5o(zn what u 5(l/;o xojdf,stxzg )1(m owdirection 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. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating tus5w5xbu e7 desbt-x1 :rntable. What happewed7s 1 -5xb5tx:use bns if you walk toward the center?

A shortstop may leap int l/9v ap5luh2uveb91 yo the air to catch a ball and throw it quickly. As he throws the bala/9bp9yv l5lh2 1v uuel, 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 ofi0wn0 1i s3xf.zf;sm u conservation of angular momentum, discuss why a helicopter must have moreif;m1.x su w zf3s00ni than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (h2 vlh1w ljaara3o /s054e:v ma) 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 e5 4 2)nggk+xhbtz0wx because of an amazing coincidence. Calculate, using the information inside the Front Cover, thxhtkb+g x2enz50 )g4we 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. Thebmt,m1nl tuqi / os ;w1;za;5/(p mw0w *txglg beam diverges at an 5t*; m1t,w1qb0zw(xsltw ol/ima;gm u;n g/pangle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpmzfj7b)z+zqeq p 6d)cn4iwj h. 13zm2u. When the motor is turned off during oper) 2hp+im1qcd j.3nefjw6 u) qb4 z7zzzation, 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 another child. If the ball 6 cc6g2if hwr3makes 15wh2 c6rcg3if6 .0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0m (4pst h2ht-ol73kx2 keaq u0 km. How many revolutions do the wheels makep3 k27(x4s2he ml0 ttqhu-aok?    $rev$

  (a) A grinding wheel 0.35 m in diameter roxcz; 9e0c(yg) -i csvbtates at 2500 rpm. Calculate its angular velocity sb;iy v9c 0c)(xgzec-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 d)t5(w ,smav:9rmc vd complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m c95: t),d(wadvmsm rvfrom 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 Ear loaa elakf; tb 8 nd*h(8kv3;e(0-msoth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed 6vz:op ps5h5 veta9mqtj866job k: 1aof 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 ceghnejq2ar14/tl h 83f52om w 8(tccnsntrifuge rotate if a particle 7.0 cm from the axis of rotation is t81no cqf gn2thj(8 rc4t2m sh/ l5w3eao experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter whee892 yffc-sor rl accelerates uniformly about its center from 130 rpm to 280 rpm in 49 fr-yf8sc o2r.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 radiuo*b *xu+wovv7(gol6q--bc 03au anegs $R_1$ 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 aboar-7tzq9 lc03thmwm . tjd the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft ca jct -0mtzqlm.thw973n be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 u wbf 0r*.vu+ nwcm0/ds. Through how many revolutions did it turn in this tiuuw0.nbd0+ /cf *wrvmme?    $rev$

  An automobile engine slows down from 4500 rpm to pjcoh4lb)j0kqhq5rzg4b7 z6 414 uou 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 st)a4u + kkeyl3m; +;:jste sjyeresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions ba4us kekltj3);++j:ys m yee; efore 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 240 rpm to 360 rpm in 6.*joxpl nbfo0j5 3h.0 g5 s. How far 3o x l*jjh.0pb05fongwill a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turn h sug24)6 m)oa3urhtned off when it is running at 850rev/min It turns 1500 revolutions before it comes to a4agh)u 3hst26un)o rm 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 unifovrc(e0k+p a9 crmly from 95km/h to 45km/h The tires have a 0+ckpe(rvac9 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 zvrp 4yz u-ao1rg e6/2the car reduces its speed uniformly from 95km/h to 45km/h The tires have a dru/ ory-z 6pv124ezga iameter 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 h;-uwpb:y 7b r6cxl2je4b ;pbnamx8 q 9ill. The pedals rotate in a circle 4 wnpbe9:l cx rx8q2u6p7a; bbj-ymb;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 o,n-jwq nd5zht5ych +ln8r4; 8z (zpiqf 55 N on the end of a door 74 cm wide. What is the magnitude of the torqz rz n8n,+ q(c5li ;h5 d4qyntwj-hzp8ue 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 dl b2s57vjns- axle of the wheel shown in Fig. 8–39. Assume that a friction torque d-jssl7vnb2 5of 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 ends of a maz6;.e(y0eeo bc k8jas ssless rod which pivots as shown in Fig. 8–40. Inbc es 8y0zeoke.;aj6( itially the rod 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 requ9 8 .rj.wawqkc; 7abucire tightening to a torque of 38 kj .ca qr97uwb .;wac8$m \cdot N$ 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 ino a,6a g8ksx v pjxuq2c v/7w1*ztu0/jertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotationu j/za gk2*8tq/cxjv 6ua ,v1xsw07po is through its center.    $kg \cdot m^2$

  Calculate the moment o*xwi*8jq udyj(+ fvu( )mxur) f inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored ( r (j8*wyud+q*))mjfu( xiuvxwhy?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotat 1iq /sp6*30vgh kyjpued in a horizontal circle of radius 1.2 m. Calculateph*yg sv6jk/u pqi01 3
(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 whee3g )f /q+sdvhzl rotating at constant angular speed (Fig. 8–42). The friction force betweenfghvq dzs3 )+/ 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 cpom urf)2)x 5inertia of the array of point objects shown in Fig. 8–43 abou 5)ox)rmcpuf2t
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total mass isk/-, 52 gwbfdzd tno6v $5.3 \times10^{ -26}$ 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 thom1qe+6qgfr: sasci -wk6 42ae 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 forcekqa-i m sr cwsa+gfq6:214oe 6 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 r5-vpfuk ,o:e-op 2adjrm6,g radius of 8.50 cm and a mass of 0.580 kg. Calculate 5dgmo,,ru-6kp p o-2evja:rf
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest/v 1a lr*q,cak 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 merryx nsa, knt-n/aj8n02 uco*( oylt;x q7-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 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 to s /n-tac(at *ky,nu o7 lxxnn8jqo2;0rque 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 st -u-hk :w-g- jr z0xhdwo/hq+hut off and is eventually brought uniformly to regwodqt:jw z /-h+-0k -h r-hxust by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball at :qzt -cry8*mf1m.bq fw+6vbu7 $m/s^2$ 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 solely9qm me5tjvf /grc n-.* by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest tr mgn*fqm /je-9t 5.cvo 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 boagro4( i(olol rw,h :mh()7klade can be considered a long thin rod, as shown in Fig. 8–46h(m 4oolr,l(7 (ig )akwoohr:.
(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 consistsdu486 q5qc74+ slsubga kb9pp of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer z6t-97yhjnmn from rest within four full turns (revolutions) and releases it a- ny nh9m76jtzt 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 inertiv yd:qieq+ z35a 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 )ub6e2kiv(ifhm i; v;w bk-g/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 kgefxkn )w*7q*c and radius 9.0 cm rolls without slipping down a lane at 3.3*7fwx *qc )nek $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetickdh* o(h b)p-b energy of the Earth with respect to the Sun as the sum of two tep*k)dbb-h h(o rms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius ,auvt p8qu,x z3cugw4 ray+ 18of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per8z gxut4auav w1 +ur3y8q,p ,c 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolqh htgl;p2cw,f)+7 p uls without slipping down 7h)q;fhpt gc2lp ,w u+a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall and it0 f nz,6lz;pfoum+vdkw6fn.;s lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint:;mz ld06uzf,n k.wfo vpn;+6f Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end o p4delb56u,dvf a thin string in a circle of radius 1.10 m at an angul vbl6d5u4 pd,ear speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentunhw zlpn5 r8yn4q 8nlbb,.+, qm of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm whennb8h.z,pyqllnbnnrq w458,+ 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 sw0kc j3v sxts hem(:rj-zl 2/4ide, on a platform that is rotating at a rate of 1.3rev/sezk0m-s:wh( r/clx4 ts2jv j3 If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of inertia bys:v mx7f 6( 7utg4qq.f alke5w a factor of about 3.5 when changing from the straight position to the tv6x.ult f75eq4 fgqs mk(aw7:uck 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 increase her spzhq9l5nc- vw. j /mk0ain rotation rate from an initial rate of 1.0 rev every/a0cjnm9.h z wl5vqk- 2.0 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 vertical axis throughtitntc0 /qa 06 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 3.1t 06/0aqtintc -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 spinning at :h07q) hlrocu 6dp.uj 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 Earth9:j1ux22z 3pi9nd9gafr q lap
(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 cylindridw-iegcv4h v3+*c ec-cal disk of moment of inertia I is dropped onto an identical disk rotating at aic-cc3eh vv4w gd-*e +ngular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.aks /lll1t9 - j-(kzm;i3lppu4 $rev/s$ 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 stansch:2emcohc5 ( vt4(vyf xp8 *,w( pgsds at the center of a rotating merry-go-round platform of radius 3.0 2yw(5vc:(sv sgmexco*p c(hh, tf4p 8m 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 angulara,x 4p5 t6x tspcj2ft+ velocity of 0.8s4+xtxpp6t5cj f2a t, $rad/s$ 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 dwarf, lol 2of fbb n)q9;(bin5ising about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost fbi ;b b(2oln9)5qn fimass 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 winds in excess ofxr kcdlw*of ;s 3(0x:dq:naf8 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 h vwqmgz)omt8 xfja g ;(p7va9.29ne*$ 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 j9*p qwao+kfin 7ts-jm (6:+ek wwm, hat rest, that can rotate freely without friction. The moment ,9 j*6wfh pnqa+ :+wmem(ks-jit7 o wkof 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 persno s +6a9)g u0qzh7spoon stands at the edge of a 6.5-m diameter merry-go-round turntable that is apo zsq06u )osn97+hg mounted on frictionless 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 ovh*3m- wssi:sk2r2 gyd i-n x9fe m:+tf the rope lying on the top edge of the s:9f+iss 2it mg-w*dhyvx 23nmr:e-kspool. 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 suq;bx iv3k38m; y oy ie2qzt3,fch that the same side always faces the Earth. Determine the ratio of thez;fi;oxt3 q 8 y bmq33ykiv,e2 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 Earth.)    $\times10^{ -6}$

  A cyclist accelerates from reszur 7zc;;vsk: t 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 unifjm0bb7( q sie5orm cylinder of radius 0.20 m acquires a rotational ra m7s0j( 5qibbete of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical dis+btf:wfv2z zkxm8,te p9-q 9qks, 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-lfv2qe :+9mx8 twz tbp9qk,z f-ong 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+l xz f n0+pjsu9f-;pe 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, w khclck8 l:2: l/(525p79mwwzkntvae mkr 1j but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere atk7ew2:nmrk/ c 5t9lpv5(lkw8l: 1c2jz wmh ka all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobio 0 hz;9lvz f2).ogjywqp33s sle 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 be able to travel 350 km without needing a flywheel hp9 sjwz ;f.g3o0lyo3)qsz2 v“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 abb*ompglw,1n:qd7 tde1 :c(ll2pb. tn $H_2O$ 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) s.m;hr (.tpf:v0 wunxis 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 freelyl-,fh:ca8 dzz zlg/ 2qmzm48 f (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held lmaz4,z f8-d2g z8hfq/m: c zlhorizontally 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 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 stl08(h yci 8xvnjbc *(janding vertically 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 resi0(c 8 hvc njyx(jl*8bts (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn with nnngk :im*rjd,yb uy;3c.54ua radius The forces acu5n:u3 id j*nmn rbg; kc.4,yyting 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 39fq /x6elhmqhql68jsling of length 1.5 m and begins whirling the rock in a nearly horizqjm /3 6eh8qlhf6ql x9ontal 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, 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 r9bgm- .i*mu cu8m7 ;yqed;p wtods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning7*bu.c pywm; uiedm8mg;- q 9t skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, c0jnh*z91fpw of j90hcz*wpn f1mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 Fi4o-nu +5ksfhpj90ur l3e c) rpg. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest pop0 lr 9sfor4-53ephn+u kucj)int of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do notyrgjmb ) hi:k9rn(a)/ assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed qgbt*lqtb v74)w ;g(euniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular accelerb )vqwe(b;* t gqt7lg4ation 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