A bicycle odometer (which measures distance traveled) is attacr3k1 .k w3 jk7)ky ky/)qliffkhed near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle witjkqrkk f .fk/l)k3i k7y1 )wy3h 24-inch wheels?

Suppose a disk rotates at constant angular vk w/n 4yi5hrq0elocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitw4hqry5 ni 0/kude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular 33bzq; f03 x 9q zbibtrmssx40velocity $\omega$ Explain.

Can a small force ever exert a greater torque )78c cnwcjd s;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 4-rrc n*0n wi/txg k*cj0(gd aa sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer-cnc rn *wa*rij(dxk40ggt0 / this.

A 21-speed bicycle has seven sprockets at the rear wheel and y(3nzm 07zs3joqh vfp5*bms * three at the pedal cranks. In w q0z 3hs7y(so fnjbzv*mp35*mhich gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with flesb+dwvlv;t,v-7wee v8*s 1m)qew fhv (h and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rm; v w7e8+ -,e w(tvev s)lqv1*fvhwdbotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers -ex7zsk gipp,c ks;jzmn 95(2 (Fig. 8–35) carry a long, narrow beam?

If the net force on a str/+l q:3s w6jln+j --efa arqystem is zero, is the net torque also zero? If the net torque on a sfj:-6 la+j-rsw r3+atlqq en/ystem is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontal,r6 0c5hb jqpg1e(( hkug6fw a. The same steel ball is rolled dohbggfu6hjcq6a ep(1 k,w50 r(wn each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneor :/ (z)sf ,e 1bmlpo/qd.9wqyztrny +usly start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic en.qe)ypfb o,z z+1y(wr9t :d ns/l rqm/ergy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They c+jud1ctuo*o i*gy6j q9 n u86start 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 energy at the bottom? Which has the greater rotation *jjc6doy1t+ noc i q*g68uuu9al KE?

We claim that momentum and angula u+syrs7a7l -raint,9r momentum are conserved. Yet most moving or rotating objects eventually slo7uss7-anry,i9tr +law down and stop. Explain.

If there were a great migration of people toward the Earth’s xe) y2co)6y2w fxjjz2equator, how would this aff2)2xceyj yjo) f6 w2zxect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any ino bjzk;j n3eyb 8s)t*bt( 4nj-itial rotation when she leavetjn8 ;4e -osb* jkybb (t3zj)ns the board?

The moment of inertia of a rj2+idjrn,;g f )uv q/nbr6fs6otating solid disk about an axis through its center of masnd2qj rf6rb iv ,;+sf)6gj un/s is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each o)ro 9 ov 3w7 2keou9z8jxifpj;utstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, orzvrwi ep9j o of;9x27k3j8o) u stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollowlqf(+ kln 8 8hfsxr,5fsw3bn+ and the other is solid. Describe an experiment to determin(8q+nflrw +5sxlh ,8 ksffb3ne which is which.

The angular velocity of a wheel rotating on a horizontal axle p98ge3bp8tp pze0ok giq/n 6 ;evpj::points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe thev0p6 jg3pe p z:/ e:nibpg ;pk898qtoe 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 lar78cx l +kfdfkt*3-s yyge freely rotating turntable. What happens if y-+ c8ds7y3fkkxlfy *tou walk toward the center?

A shortstop may leap into the air to catch a ball and throw y l ;5o*62salucbx9mbkt/x5rit quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the oppom kl*5at6cry/ bx9 2ou5s x;lbsite direction (Fig. 8–36). Explain.

On the basis of the law of conservatis/j6l +6an wwezf)fy :on of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller cazy6 a ww)nse :l/6fjf+n operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30 wmt/0a 1ozqp7$^{\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. Calculate, x /ihhq*lg6eb1o qv * 9,zc3ikusing the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moo9q6h3c1 qezoh/* bi *v, gxlikn, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed atq8x3)3gi/ 6 nrnf,g urgqpr3z the Moon, 380,000 km from Earth. The beam diverges at 8niqrx, f3)6g gr qug3 n/3rzpan 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 rziqquk7 yg 4- ue4*zn.ate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angnu .4zkg 74qiezu*q-yular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball f22aki /uz zrsy()v5o on a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what izzy 2/ r2)av5fiuo (sks its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. Hdr7 q j5(bk:knheztl3+ ea)9aow many revolutions do the wheels make?ha:bzrjd79+tk ek5aq(e)3l n    $rev$

  (a) A grinding wheel 0.35 m in podgt i ;120didiameter rotates at 2500 rpm. Calculate its angular velocitd2pi;o1i0dg ty 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 in 4.0 s (Fig. 8–38)jlg0bb h6 7fh;. (a) What is the linear speeb7lhg0bh; 6fjd 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 o,ucw v4 nsk(u:rbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a +gy08uo(qw w9i/fk p/:pfzapo+ mz* apoint
(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 ro (,lq92pja6tpfp-iz m tate if a particle 7.0 cm from the axis of rj-piza6, 9lpf2tp m(qotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its centzll9krq*rezq+ertoq .1n* bu 8l8a j4h;1p3 aer from 130 rpm to 280 rpm in 4.0 s. Dezu1 .j*8q4ao3*;n+ r8qzqe hrlba kt 9lrle1ptermine
(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/py 9rli1lgyz-z1t69 k)xhe h $R_1$ 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, astrona- v :dr:x.brsjuts aboard 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. :s rbvrjd:-x time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates unifenw:1ftfs7 t3ormly from rest to 15,000 rpm in 220 s. Through how many revolutions did i:nwf7tt1f3 se t turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. C3rr- ytvfp3n4alculate
(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 ofr 8z2/c1ew a4 ddn.rwy flying highspeed jets in a whirling “human centrif8nrwdrz 2 a1/c4y e.wduge,” which takes 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 accelerates uniformly from 240 rpm to 360 rpm in 6.,a3,fhq(p ihs, fq+r-wv nco95 s. How far will a point on the edq,(-,+anwi9shq ,fov3 fp rchge of the wheel have traveled in this time?    m

  A cooling fan is turned off tn7;)o:v2v+p d xx et/dh6yjwqn u4z8when it is running at 850rev/min It turns 1500 revolutions before it comes to a stop.7xjt6nt 4/uh8zw: yx+; nve 2)pqvodd
(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 uniformo/r49zeo4k tzr9 l :ugly from 95km/h to 45km/h The til:erz4gu 4 koot9z9 /rres have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed un --dwvkzr,mznkd;2x ) iformly from 95km/h d-xzw,rdzn2vk -;km) 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 climl;(w*n8, cfy 9 wgvribdb+0 labing a hill g8 0b9 +c,rlbyd (vn;a*lwfwi. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force326(2hythpsyy toblyq g7 j9* of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the fopjsh*h22 q(bg yt9ytlo67 3yyrce 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 axle of th df oqgw-tsvts/19su -/ks52me wheel shown in Fig. 8–39. Assume that a friction torque of 0-mt g1t k/d-ufovs9/qss2sw5.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are aa*iru*d i zb ,5ty3iq;ttached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held;ud5** iiat, yq rz3ib in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require k,uic .o z2jd5tightening to a torque of 38ui 2z.okj5,cd $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when t; czu r5ed)rtj jfc1khyq; ;0;he axis of rotation isf;5 );yj jd1r;h; c0krqz utec through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7ng+ 0q q3iwxu: cm in diameter. The rim and tire have a combined ma+wng:xq0 iq 3uss of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the vr fl.6r *kd:6zwxh1yend of a thin, light rod is rotated in a horizontal circle of radius 1.2 m.lf.r r*v:y 16xh6dzw k 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 /sv(hvo -9lrlat constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N vhso/-lvr 9(l 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 objects dzy , g mq4k:c,i;/qxqshown in Fig. 8–43 about g:i 4y kq/cxzm,q,qd;
(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 conh a.j)no(j-7x5-jskr zaa + lusists of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning attfmztn81zg2oh 5 s:w( the correct rate, engineers fire four tangentz28wg(:s1nmt5h t ofz ial rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius0/rm. 6 se-hofh ugli+.9udoy of 8.50 cm and a mass of 0.580 kg. Calculatr-+guu.9h6l mhfo/ d.se0oyie
(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 to 3hzthlsv2 wg 1-264kjr $rev/s$ 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 tan ch9wi1a8, wcz8ny wwsv)rn() gentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, an)8w rcnwa n()1cihyw,vw9 8szd 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.cj zbj50hw1 p uniformly to rest by a frictional torque o5.cjb j zh1pw0f 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. 8–45pl3g y5hpel4eocf 6ct -62p43mvumi 3 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 th, y61;cchz. l;ylbeyjih- i5ue action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniforml ; y-ly6h;.h,ebj z5i ilcu1cyy 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 a long thin 4shvh :25betarod, as shown in Fig. 8–46. ahe4tvhb: 5s2
(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 consisn3o,ljd;ac5(- t/0qzs fjfvz ts 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 ha+:e j+xeb*;59g ;;,is ajgkizz5wf at lbyho:mmer from rest within four full turns (revolutions) and releases it at :b tyzo:i+5jel*;;a fgg ;awi+x5ezkhj,bs 9a 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 i ry* 3,jz3ryh 1xro;nfnertia 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.e:is(rpt z2cz am:) o torque of 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 withos e tocusz;4kc6*1gt -ut slipping down a la *se c u-ok4t;szgtc16ne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to t51)b; 8khjx8g) 0gti y :zfymkoek5 lzhe Sun as the sum of two ter o )5e1f8:yz 0kj8)mk5b ;tglxkghi zyms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much ndy p8tf7 c )(/ud54qbd lo7 kguk))fgjet work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a sol)fq )gfj47d8/ dulg( 5ydtc )kpkb 7ouid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg start3x*vrvp: u.i0s/r wmx5cs,iqs from rest and rolls without sl cx,/ ri53.uvqvpsx: mrw*0 siipping 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 balancedos3 8k -ikb7 zx. ,wzvj lp,f(hk:a3tz vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the poles.patwk7 ji-zv:b k xhf oz3,l 3z,8k( just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of r.dfco9wzx ;aems * 63a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular spee*cxr6d9a f3zw ms.oe;d of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cyltz*-k s/y7j5tm ixjjo)b 9t4 pindrical grinding wheel of radius 18 cm whenp79tits om54jj byjx)*kz-t / 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 sid/8q .sbqe6tfqttabue/3pzi x gm+*9 7e, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a ho+p zt /6./etmg8 b7qb3u9q q fitsxae*rizontal 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-zzmvukt ; -i +4fmw zjo7hqk+5/h +dl) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, zlu-;mq 4mzo kkhh-+ij tf7+z+w5 vd/ what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate fp -q)nhy zoz 8y0pme 0c5(ua:of 1.0 rev every 2.0 s to a fq8(znzp05a0m) - p hyeoy:cufinal 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 vertp8pp w+7evt6pkw(/ djical 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 radiuspp w dkp8+tep/7wj6v ( 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 spinys-8u+ gx 7tqining 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 Eart8;a0dafhne+c7 j; oz)iszy4vh
(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 ofg(htjpfiw- r :; 48xne moment of inertia I is dropped onto an identical tf:jwn 8gh-4;(x irep disk 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 epr u m*lw7mtii+ )3nnh(mz 512.4 $rev/s$ 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 stf9qkgt sq/;.db 15o imands at the center of a rotating merry-go-round platform of radiumb f d1q.gotk9/;si5 qs 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 ru(g fp5xta 975mt w(lhotating freely with an angular velocity of 0.a x 5p7tgt5wfm ulh(9(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 dwarf, losing uzrvaq 84a m*(,k p0mcabout half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming ra,mzpck m q(*8 au04vthe 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 winds/pa f;fl(hktq 6pw2w)e6dcd 8 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 o6px+-jyt(n yqlh*4 v4m sa0dpy )2 yg$ 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, that can rogps9nkyhnc* ,av+ * +ytate freely without f,9*p csa yyng+*v+ nhkriction. 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 merry-go.0:sezdcdnm h -xo.*td/svzc2o e 80o -round turntable that is mounted on frictionlemet0s.2o8v:z hz d/nd* .d occxeo0s-ss 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 rol*fgd2c9 gd)bao c3i l0ls on the ground with the end of the rope lying on the top cg3d2c*bi f9olg0 )daedge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces th y t24dvn5- ;jedln/uce 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 the Moon as a particle orbiting thec tdn;u2n d-j4v e5ly/ Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rtka3azh m- 40a/y1 mljest 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 acq)- -4;xlu/jm tjsgmp cuires a rotational rate of from rest over a 6.0-s interval at constant apl t/4;m xju j--)sgmcngular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of *w3(qvz, j+.siwzh bwtwo solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (conceh (3s w,qbv.wi+zzjw *ntric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rehs+c6(stbz hm2s 7. iwar wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but withl-jm7h ;keucis8 8hsriyq-/ 1 mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational cokhi-lr1m8 7-jyqe hsi; s/ 8ucllapse 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 ss;*cem v1iqrv5gn7(c e m;g2 qtored 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 tmcnqi v1ems;2e g*5vcr7 q(;gravel 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 as, bmi3qi yd08n $H_2O$ 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 horizon;- unh :+bd- yx5w/u1emrcwwetal 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 freelybjex 9g*a . dq0.fyko :mh,qd6 (i.e., we 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 gravity acts at the center of mass.kojby : qdfe,m*.9d0h ga6xq of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically ont : 474rzfxo 2rp7jnh*fxie/ i 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 has height heofh2 i7:xt44 nf*ipzr jx7r/ , where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn wis* tix/ :i*eut+mtwsn)k ox 48th a radius The forces acting on /*ie4 stxim us :xkwt)8+not*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 ro 3vco707t9 kgrossxs*ck into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm 3g9ko7c s* 0srtox7sv 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 armhwns1 +r0 spa3b 5c;bps 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 with arms held tightly againstphnb;s0 ab c1wr+s53 p her body.   

  You are designing a clutch assembly which consists of two cylindrical pla( kx. 7q mlohj-kc7mskcvhot )-1t:)stes, of mas1oct c7so))vh7 kh :(j.qxm-k -m tskls $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 zp;3ad,l zd )ar rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical dp)dl za; z3a,height 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 assume eije// ;f1xy)ry;vyi $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces p r: m2n pj-xcrzgjr3n52.1ui3ix qh 3its speed uniformly from 90km/h to 60km/h The tires have a diameter of 01-xpi2 hr 2m.:3zqrn 5x3gujp rjcn3i.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s