A bicycle odometer (which measures distance traveled) is ac:pq/fy5 8/ gnshnc i7ibo/*u ttached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a n u /58: y/hfbq7psic /nog*cibicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocim.v o8 kpgs+c33x-p asty. 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/3.gx s3po -c8ks +mpvaor tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value;w1nepi g0 .:clqgrtqpi8+k :m w(4 eg of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a la1w,no*bnj0nxv k3*h n rger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your headcg0r:otu4ek l ug) tmb*0j -6o than when your armgu:4k*m g) r0ttbco0oeju- 6ls are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets a :,1ore 7e6 6,rd heb5v(tk,bq joexwjt the rear wheel and three at the pedal cranks. In which gear is it harder to p odb6exhk,eb(5r ,vt6or17q :we,jejedal, 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 witrje:c)e. wl uhd n2w0nos1;i:h flesheins0ewhdr2w::l ) n.1u co;j and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long,r 0dz i;2.k* pk/sxywb narrow beam?

If the net force on a system is zero, is the net tokd,1-p**x+2bi tlifejaf6 * 3 ogwfh hrque also zero? If the net torque on a system is zero, ita ibf+2 wj ix g*6*p,l1of*-ehkhf3ds the net force zero?

Two inclines have the same height but make diffz yx,qh/urg +6.yoqh4erent angles with the horizontal. The.u hq,zyry/ ho+q x6g4 same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from restkh +s7+ :9zyiypgl ulsf d,m*fn8,t:o) 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 energy at theto*,i7ld nzy+ 9khfp+8:m, f s:y sulg bottom?

A sphere and a cylinder have the same radius aq9 y(dl7g*ibe /ufhefohp5 ; 2nd the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the ; i*ede7 uoyb/2 hqgh (9pflf5greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or 4w) y v.x-cal xcoik-+rotating objects eventually slow down andx+wlk oy.-c4 a-i vc)x stop. Explain.

If there were a great migration of people toward the Earth’s equator, ho7lsg 0h52gwrk*nub e 3t(-jy hw would this affect the lengthh t52hul*kn 07bwg3( gryse-j of the day?

Can the diver of Fig. 8–29 do a somersault without having any inititgj(im+.udh z75nh7f isgl. /al rotation when she leaves the board?hmifhg.7n7/ug( +d 5z itjls.

The moment of inertia of a rotating solid dis- zplx+ 9xnp1ak about an axis through its center -x+9azlp1n xpof mass 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 iof+574f) xan wz3g fa0v y+pfzn each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or w+zf70og 3v+ynff) x54 a pfzastay the same? Explain.

Two spheres look identical and have the same mass. However, one is3h*tgh9 lf0sa hollow and the other is solid. Describe an experiment to determ9* at3hsl fh0gine which is which.

The angular velocity of a wheel rotating on a hou/0-jnu br-zxrgy.q.v, w,hj vj0 yd;rizontal axle points west. In what direction is the linear velocityj,ur-zw.yg.0 -0rbh ;/qyvuj xnv,dj 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 qox ymp i757:f nja+*n 3catk1a large freely rotating turntable. What hat17njn+7pc o ax akqym:5i*3fppens if you walk toward the center?

A shortstop may leap into the air to catch a ball and thro/gd:+ k1xcgeaf t1um *w it 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 opposite +t1x a/1kfgec udg*m :direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss y*jlr*:avc z0why a helicopter must have more than one rotor (or propeller). Discuss one or more way** l0v za:yrjcs the second propeller can operate to keep the helicopter stable.

  Express the following angle*d.fw g1rgv u3s in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth becaus9r6b) +. uilo315 pzmh:s wp-lh3lonxfy 7lype of an amazing coincidence. Calculate, using the information inside the Front Cover, the 3+) smu x7ln rolp3obpl9p5yz h6wlh:if.y 1-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 Mooks7 4jx yi3i)/ 5in sc29yxzken, 380,000 km from Earth. The beam diverges at an aj23en xii)k7 sk ciy45zy9sx/ngle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rot bzh*y :k.0pgf sjb ap98,6o+b:uyrijate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as thh k: s.6 p0b,+f9gjb8ripub*yo :ya jze blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. Ipckw,1+ unz 1w2d v bqn0vo::gf the ball makes 15.0 revolutions, what is its diaudvq vkg2,n w+p0 :wo:cbzn11 meter?    m

  A bicycle with tires 68 cm in diameter travelsus. )yqfmo;itn7.y+m 8.0 km. How many revolutions do the wheels m7fu+ ;tmisyn ..)yqomake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcu4s v hu;4ap4a)nrkxv 7q758yjbx 4szilate its angul8bj4 z4vys7x 7n s4xi) aa5;rk4vuqh par velocity 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 make*k)jp sv6t:zzsg**u ts one complete revolution in 4.0 s (Fig. 8–38). (atv )u*z pj**tzsks:g6) What is the linear speed 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 ybq,ae/j./ucmsill ().bq qab u-.,h (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed o/yq- j6iskdi0s 8tq8uf 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 centrifuge rotn,ieye h mph/qbj8s.ys47.4 x ate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,qyi .4 sh sn ex/4bemyp7,.jh8000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center qsn3:kvc)3y z from 130 rpm to 280 rpm in 4.0 s. Determineyvk nz q3:)cs3
(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 ;o9buq tokc l.kz5.b5 $R_1$ 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 yfx6l1iw( tf2tv7p 2 mput themselves into a slow rotation to distribute the Sun’s 21xvp6 ltifmt7( fyw2energy 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 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 to 15,000.bkxjrk7j+;yxvt7eg/ lig gur d115+ h*zvw6 rpm in 220 s. Through how many revolejx d+./h7g jk t7z115vlgb+y6gkur *irx; vwutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to f ;p)*:bh/ *0cr,xtsqn jikd rf8ua v)1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling “hu: p8/8ndllfatman centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speedfp8 /adtln l:8.
(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 rw .w0n-xvrn 6xpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this tn6-xxvw.w r0n ime?    m

  A cooling fan is turned off when it is e;qo0q83 ( 4damngdojw:a c kmr5m 1e:running at 850rev/min It turns 1500 revolma(dqc 0o3eer5mo8a4 gdkjm wq;1::nutions before 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 65 revolutions as the car reduces its speed unifojvj+ +cet )k(kg/ *,dutaxl1p rmly from 95km/h to 45km/h The tires hacjxdj+t (+,/*et ulkvp) gk a1ve 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 cjg2gns k.a;l4 m;z mc;ar reduces its speed uniformly from 95km/h to 45km/h The tires have a diam4k;.gn;a;j l2cgmsm zeter 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 weighwo4g9h5m rx 6 /)0qg2lqimbi ct on each pedal when climbing a hill. The pedals rotate in a circle of rao)mhq5b ix/qgml 40w26crgi9dius 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 o1 sp:sqj82qpwa6m kr3n the end of a door 74 cm wide. What is the magnitude of the torque if the force is exerte6pp1 8aj2wmk :s rsqq3d
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. *neq/hd)o(wlg(-n:.ouu*w y ch(sjwAssume that a friction tor (leq*hw su)/.- d(jw:yc*woo nug (nhque 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 ends ofd9v22ntg r1by+zw,7epz3l x d a massless rod which pivots as shown in Fig. 8–40. Initially the rod iwt bgl,22z3+ev zyn x 97dpd1rs held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tight nn53vtt(9u lmn*gs/f:spe a ;ening to a torque of 38 5 nl fpa (vn9*3ue n;g/m:stst$m \cdot N$ 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 p/fmx.diun0cx ic) wj 9l r1l.;7up m-sphere of radius 0.648 m when the axis of rotation is uc )lu/0xwi1dx7 r;lpp-ji m..9n mcfthrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diamq+f;9gh; xf:aj2 to- we y2vnqeter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub canf; qjaqw- vn2+ 9fot; hg2yex: be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on tp61ae9 hooa y6he end of a thin, light rod is rotated in a horizontal circle of radius 6y po6 ah9eoa11.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a ;ci )6fx/ey k*m nmj uasfq.7qi-y-5m.zu.wj potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between f6 j sex./5zi. qy*cujmy;u.fqw )i7n- a mm-kher 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 9f xu5dmi,wfo 65eb9gof inertia of the array of point objects shown in Fig. 8–43 aboutog5 5,me9fbd9fxi 6uw
(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 at2h*rdrr (c -ip+2fzp goms 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 at the correct rat+;0zox2 hjt: +:zk.r5nmyvguj1 hef4dh t 7 zee, engineers fire four tangevf 1.n 0z :oztjy :k+ 425hhhdje;x+uem7zgrtntial 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 radius of 8.5 )n9n4p 2aydfcec9kd7r+ u(o,gs/ se t0 cm and a mass of 0.580 kg. Cgs2t9nkn4re9 d)as ( c u/o,y7dfpe+ 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, acceleratzzpbpnr7259o ing 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-2mq7r zpgldiw(ap -1r*uc;,ydriven 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;*pr w uzrg1l(- cqipda27m y, 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/+ q5dmhnkv ctp, 4ld7jij-*i at 10,300 rpm is shut off and is eventually brought unifornd *lmp7-i / t5,qkd4+ivchj jmly to rest 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 acceleratqa9rg j; 0t1k,tsni s x50ev3nes a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the acti uhixc o79 x ib0.sgb-v:wa5g0on of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45 og a-gxvwhi9s5u:xi00 c b7b.. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a hx04g:c em.5ivx k:j xlong thin rod, as shown in Fig. 8–46mg x:cexji. 0kv4h 5:x.
(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 pzj, c9,foep- (zd:dmconsists 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 from rest within four full(n-obrlpbca+uhm 5* 3t e31p p turns (revolutions) and releases it at albr1( pp e c+5h3npbu-3atm*o 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 mome8h0 lq 8+fcvfdn:tcwc ,e6 p+xnt of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine dedyqq:3gr h (5sej o/6mn:cs9yvelops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0s/84 h- r lq n,gjmuqj9hdb4l3 cm rolls without slipping down a lane am8/jd r3qjqlsb944,g-u hnl ht 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun a ut6b47wdagwz; 5zf7es the sum of twt6b7fwdza4ze5 ug 7 ;wo 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 radius of 7.50iqjw8 ,p c0k4l m. How much net work is required to accelerate it from rest to a rotaickqp0jl ,48w tion rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 k v0xs u7ct6-b/e:mde0uru6 uig starts from rest and rolls without slipping down a ti m70eeucu 0s 6 x6:uvbu-rd/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 balancedhxu d3.yq8ham c gw:*: vertically on its tip. It starts to fall and its lower end does not slmg q.3x cdu:: y8*awhhip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum9(4 m14dvwj etmm)6y q1 eczqe of a 0.210-kg ball rotating on the end of a thin string in z4 j 1dm(t 9cewy6m1v 4qmq)eea circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg unifozf qmlv z596( zlip(3vrm cylindrical grinding wheel of radius 18 cm when rotating at 15 zv i9vzlqmzp6 5l((f300 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platfor -cv jt2by5fxrv:t n g)9to/1d qs7uu;m that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases tfxv7)s /nj;yttdo 5 brug-vc:1 q2t9uo 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 ozhtk91:+wxo)*a(wyw m pbp 8mf 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, what is her angular spemmw) 8wtb9hx + (*1oyp:pw azked ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an88oodq: n2lcrcz+/+ew 1 fzqm initial rate of 1.0 rev every 2.0 s to a final +mn+1l zeod rcw c/f2q8z8:oq 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 verticuy;r l z4(bju9blunryu21 *-i: 9yopp al axis through its center at a frequenop*yp9u(yur;z 2n49lu -j1 bylir:ubcy of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a htuspgc9(g1ec3 e+8gfigure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentumcfe-ybh u6b6- 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 ;z sxu-z q4z:94kstwvdisk of moment of inertia I is dropped onto an identical disk rotating atv4 4-ksz:x 9wqst;z uz 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 0/w 2e5qyb7m1qirkrr $rev/s$ 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+a8qdym,c m*z merry-go-round platform of radius 3.0 m and mo*q ya+m,mz8d cment 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 an0 /ba8hnf1xy5 pc4z7xtc gh7 lgular velocity of 0.8 lg15xy 0z/cx nbht77fh8a 4pc$rad/s$ 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, n w-rd/y:nb.ht-v dk9 losing about half its mass in the process, and winding up with a radius 1.0% -t./ kry -:nbv dnwh9dof its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in exg3 vv5 5 pr 3pl0hpme,oc;7nmzcess 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 gviz+oqg vydvp )v;:40c5f+s$ 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,g u7q1k7 h btz(k1vgj9 initially at rest, that can rotate freely without friktg17jz kqhb(vg19u7ction. 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 edgcb*r53)nx rnle of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and hasr3 )lnbrx5c* n a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope l s-dh 5hohuxe+*6;nn sying on the top edge of the spool. A person grabs the end of the rope uheno 5+6x hs;h-nsd* 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 etrzd(4x8hus r *iqzd0a) )m.wq +mc5 Earth such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle h 4eazqs drqcu)mtw(*+5. 8zr)mi x0 dorbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a c y-jkc;f*oqe4/e4 c* n4hvsmrate 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 o( v)ug+k t5f.xzy huy5f radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at .v y yz5u (kxtg)5uh+fconstant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kfem0;oh)wjk5 u3 -qblg 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 ;5qum hwko)f3j 0bel-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, howcmbe 6ym j*z7y rcz7+ e82rmd3 is the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were sueqhy4k,+d 7 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 tuq4 7dkshy +e,hat 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 lowr egh cwz 1 mhjb*2kg-)*o6dc2o)9gew -pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km witho2rgb6zwo-d*w e)c2k ojh9cg g e) 1*hmut 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 peirdf58 q k5l+zqz(.h-bxu9 an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surf9umq-y 6l2 myod.f1ca ace 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., we ignore friction mz4bg3:sqee -) about a hinge atq gz4b:-3eesmtached 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 of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, f+ lj da) 5q1ihaos+vv17 s0ecand 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 s+7)a1a5lic jossf0e h d+ qv1vtep has height h, where h

  A bicyclist traveling with speed v2 lpu qjt4(igxlp+q5-=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal force -q5 p tupgl4q(+2jxli $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1jzb e73:n l:dm.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torqub7: je3:mzlnde 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 tqv;poa -i6 2a3y-,jfqpkycuful ), z *hin 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 against her bly3z*;2j -pvi a-,uyf6 uafocqqk)p,ody.   

  You are designing a clutch :wv ,c gc/cnlh:1wbw(8ijy8y assembly which consists of two cylindrical plates, of: w1blvcygcy/ni:wh 8cw(8, j mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rf: ak8gn5q: rk)l)zy uolls along the looped rough track of Fig. 8–58. What is the minimum value ofqkurfgk)8n 5::z l)ya the vertical 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 assum ip. gk;qpmu4u )m6vk9 3 5g+asgh.wvxe $r\ll R$ h =    (R-r)

  The tires of a car make 85 rex6heoqb53h ji 30as- cvolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) Whahs 6hc 3-b 5eajio3q0xt 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