A bicycle odometer (which measures distance traveled) is attached near i+j g e3m5 7/bx9um +rh;vfggmthe wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle witeg9+ 5m;v/gbr jhum+fx7gi m3 h 24-inch wheels?

Suppose a disk rotates at constant angularlku/:p1)i.md qd pg6l velocity. 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 magnitude of either component of linear accel ) d1pmld6u.k plg:/qieration change?

Could a nonrigid body be described by a single value of the ang7 y:egt-al 4qsular velocity $\omega$ Explain.

Can a small force ever exert a greater tory3qc-d oo:)qgf z4t./ *momu eque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head thaptrz5 l2k bu(3futp85n whl5ft kpr35ub8tz ( u2pen your arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprock kq5by*5 ie*dcets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?yq*5*dk ice5 b

Mammals that depend on being able to rtm7;e 5e6pvt 5p9coq hpyc6y.un fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of r;65y7p.th5c6cem py otv q9pe otational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) cart2 aynxa36cv v5 ra-j.ry a long, narrow beam?

If the net force on a systemfxn z0:+rzq6g z(8d xu is zero, is the net torque also zero? If the net torque on a system is zero, is the net + 06z u:xqngdfrx8 zz(force zero?

Two inclines have the same height but make different angles with the horizos 0h,oyml)p4ts 3ttv.ntal. Thev t.s ,tpsh3o 0lm)4ty 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 rest) down an incline. On.euxiqjp:+nv khm2 :7e sphere has twice the radius and twice the mass of the other. Which reaches the bottom oq v:e7+ k.2hnm xjpiu:f the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder h72 ;gm(tsyayf ave the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater fm(;g2ty s7y aspeed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum anm;jd) ;huhs((wuh: c0a u3nyay)* zddd angular momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Explaia)c(yy0u a)mh z uh*j;snwduhd ;:(3dn.

If there were a great migration,j3x; k7p/su nznh73cc set-t of people toward the Earth’s equator, how would this affect the lengtp-en;ncsc ux7/h3,js zt 3k7th of the day?

Can the diver of Fig. 8–29 do a somersault without havin( jqh+*xg,xk:oida *gtn j )*bg any initial rotation whentq* i x*+oaj(x :gnjbhk*dg ), she leaves the board?

The moment of inertia of a rotating solid diylny9/cd1-lu /7qsmvox qi 0 0sk about an axis through its center of mass i/y/c lqn07do9xv-0m 1uq silys $\frac{1}{2}WR^2$ (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 yex,mxs4+ f9 qeach outstretched hand. If you suddenly drop the masses, will your an9+f my,xse4qxgular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same r5a0d /g ltcbmn 9 pe;6lc/1f.q0mcbfmass. However, one is hollow and the other is solid. Desclf/mbcrlg/ndqc9 65cam.tp ;bf1e0 0 ribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle pointsefr8l0spd .)is uv y3( west. In what direction 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 decv. ld)ue(y 3fisrp8 s0reasing?

Suppose you are standing on the edge of a large freely rotating turntable. What (de1n o4 1x8gxxgir;yhappens if you walkxr(1xy4i en xd18g;og toward the center?

A shortstop may leap into the air to catch a ball and throw ih 0 *1dtg4zer9pyp6glt quickly. As he throt1 e6g*p yr49gdp0hlz ws 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 direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a heli bc)8vt*0a oqci.an9hcopter must have more than one rotor (or p.08)9o bhinctv qaa*c ropeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following a gufa 2r6 +e3 1 oz-s+p/euq3;vwdntgkngles 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 because of an amazing coi wmbfslzjf)3;jz jt 6p(ps6 /tk2ay02ncidence. Calculate, using the inforz/saypf(k6 f3 tbz6jp 2 2tmj)swl0j ;mation inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges w5bwe7zv a4h: 3bc+lv at an angle:z 7lhw 54+veabcwb3 v $\theta$ (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 rpm. When tcrtg)c/ s7 j :w5p.qache motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angula)rq w p:g/cc7st j5c.ar acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball oaxk 0x0ql l6b4n a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is l 6 0x0xbk4laqits diameter?    m

  A bicycle with tires 68 cm in l h4em1db,pa w6+/:tyc 4sjjgdiameter travels 8.0 km. How many revolutions do the wheelec w agp1 :6dl+hsy4t/ b4jmj,s make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 250d ogsn 0/mtm-.0 rpm. Calculate its angular veloc 0m-/mgsn .tdoity 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 4k*-f(; oidkkbz)5dyhwye-8xd* p5 wvp/+ v om.0 s (Fig. 8–38). (a) What is the line-;-hykwz dfiv*(+vmwo p*d ke5/yoxd 85) pbkar 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 (a) in its orbit around thf-( p2 m0y*q fuhp38xfepnzt/mij7 x,e Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed7b wm6 k-1l3lpaymkp/ of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a cen8m0i.yvvzl;ihx7 pr ix bxv5i4(/-gmtrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an accelera7iglrv bvi 0y5m8 i/ivzhxx- pm;x.(4tion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about i rc5d zl, (ctmz3c hz0emr +ibb16s(+vts center from 130 rpm to 280 rpm in 4.0 s. Dihz mr,c v+5s e1cb6lc(dz br 0m+t(z3etermine
(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 radiuwt()d9artcwn1 a d k0 op6)*zus $R_1$ 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, a0pn4 xo+cat5z fcs / -;km)txwstronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute theozx0t tmk)-5csw n4ca;/px+f 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 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 y gmddd5 iof3nmxp4) v.gd+at c/ //x,uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this ti4 dc,dfmx3 a/pd /v im+5xy.g n/)otdgme?    $rev$

  An automobile engine slows down from 4500 rpm to 120a qe(.,k cqvj:0 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 h-fjc;m4pl q)-l yq w 5q2yjx.in a whirling “human c -qlyw4 f.52)ypmcx-;qhqlj jentrifuge,” 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 accelerate ekkc-;kig;i y3lpjz3 c v*l77qpbv ;4s uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the p qz*ei7p;lj-kvkc;g4 y7 b ;k 3livc3wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 ld* /5)u0 m h(2 tcpmjp-bavr9i :waacrevolutions before it comes to a spda:w v(aa-bu5lm t cjhp*im2r/ )0c9top.
(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 tpjlwf4j7mdck, fdj: 0n;s.*fhe car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of;.cfljpjm j 0 df:n4dk7w* s,f 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 reducy dzr63 :miy/des its speed uniformly from 95km/h to 43y6:r dymz/ id5km/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 climbin0t*9rkhqwk8 q p: w0ong a hill. The po9*: r0k qtp8 nhqwkw0edals 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 force of 55 N on the end of a door 74 cm wide. k;r*,/a iuubnWhat is the magnitude of the torque if the force is exe,kiu ;rn/*u barted
(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 4;4ur ei.xsx2bfy(vj -o oq;xshown in Fig. 8–39. Assume that a friction torqyb;r(.jo e xx4;-ixus 2fovq4ue 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 of a massless rod which jpz.b r:c **ugpivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this .g c*:bruzjp* system.

  The bolts on the cylinder head of an engine require tightg r5a5ckz8a- wening to a torque of 385 c wa58rg-zak $m \cdot N$ 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 the aei4wql /hx 6q4x0g w,fxis of rotation is through its cente,/0 wfexix4gw64hq q lr.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. Thzw4)tfnzm 21s e rim and tire have a combined mamz2nz14stf) wss of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, lightfzv ///ew21jyp bs 6, s6dfmwe rod is rotated in a horizontal 6zepjb2s// mvd/1wffs6 ,eyw circle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a po -;tr 8khmw7i ydfg:ti9 6,odbtter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hanodyi;: b -6g8,r9idthkw 7fmtds and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objeozi0r* pwnrm) lf)d.+ cts shown in Fig. 8–43 aboutmrrpn*zw o+l ))0.df i
(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 twaw:5o h )i 6lxv1brv;do 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 at the correct rate, enginqzz*uji98hg c (.q i;/hj8yth eers fire four tangential rockets as shown in Fig. 8–44. If the8zzj8 ct*;u j(hhy9i g/iqqh. 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 with8 8xppoas0qs/ zv8p 4f-v1yc*l:ajpo a radius of 8.50 cm and a mass of 0.580 kg. Calcu8xoac8 pp/4*aj-v sfls08p q : y1pvzolate
(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 dpg)1nf414uq vkcf -/hpmwk-bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentx +/,qlg-j/d ims/qo eially 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. Assumoe mgq i/ljd,/q+/ -xse the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm w-vl 2xtl3jok 69 8 ,dcg/ccflis shut off and is eventually brought uniformly to rest by fc9w ct 2 ljlk x68o,l/-gc3dva 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 r kg+.f 9 51)scnb:vcna pvqv93.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action od:0 p;kxlvd o:f the forearm, which rotates a:l; dx:0vkdpo bout the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shg00v wf; ah si,/m8ykwown in Fig. 8–460gy ,sw8w hfk mai;v0/.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists omvk22r lh5*v0qjmi d8jdes ) 1f 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 x4,wepwhgk d5 ojp 04)four full turns (revolutions) and relk0hx o4dpj5wwpe4g ),eases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment 5z51 kah v2ott:t2tqmof 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 develfgg212z i 2* 1mm:spfu/h vrlmops 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 9.0 cm rolls without slippingx (;6r2*rp8l gn5bi h kw:wqqw down a lane ak5r:2 *x6wwn8rl(gwqpq i hb;t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to , 0+hgzccyxc7 the Sun as the sum of tw7 yhxg,c0c c+zo 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 wzmp. x+ fi3n-of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rxi+zp-mf. w n3otation 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 1.8 1qhlk) 9)itj 0-kydpw0 kg starts from rest and rolls without slipping down qp1l)tky) dk9hj-w0i 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 9a,hcm9z35+p8w p y uc3c(y svho,cdcand its lower end does not slip. Whaayzw +hu83d v,c3cc(9 c9 c5symph op,t 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 momentum of a 0.210-kg ball rotating rz,g*jy7y75j ilty ayd8 ee2 1on the end of a thin string iey*j7ely78gyzt 1,y25j i a rdn a 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 uniform cylindrical grix 6so3e9d0brqz 5*zpknding wheel of rq r56pk0o3bsez z *x9dadius 18 cm when 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, hand:ao: q:ezh)st1a .i vcs at his side, on a platform that is rotating at a rate of 1.3rtza: . oqha)s:cevi: 1ev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fiq 2/ zqcv p)4y , 8sosnk:c2.m4xwcnpeg. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from theq4e4mp) cov.wpsq2,2 ynx:nsk c/8z c straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate frt ,w-qq l;68e ,krdyi :uwt03fsf6a fzom an initial rate of 1.0 rev lw 8f,fauqd3ertki6t0 fz w-,6ysq:;every 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+6 q5qz-vqj j qml(dp p3d,qt4 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 shape5pzp d(3qjlj 4mdt qq-qq,v +6d 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 spinni(i9 ekyk, vrl7ng 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 oi- nud 2i*k-qj((jmlcp- v j5zf the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I ii78rhhq0 zd2jg : eb l9(+waofs dropped onto an identical disk rotating at a2i8: 7o+fdb(hhejrzg0 q9wl a ngular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at3w;mm to q29. 4o poiur3xn hem*hb*3c 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotooailbb mu./orqe; w1e1 )c;0ud 7hp 4ating merry-go-round platform of radius 3.0 m and moment ofh 10rel.wc b)bopoeiq4uu 1o 7a d;m/; 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 6wj r +wu*xqt4tv*a.w freely with an angular velocity of 0.8 *w 4r*.v twtj qxw+u6a$rad/s$ 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, loseb 48nw )- pu -6s. bm+hsmgaj.xduj.fing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(bu84jsa n.p me)s.bjfwhmdgx-.+- u6 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 of 12;q bi9yjgx0l (e7 mk7kup4mc)0 $km/h$ 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 vj2wlxj m*a62pm q s4vfzsx-;dj., eqt6j6v+$ 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 a5g9de yda7 .ttt rest, that can rotate freely without friction. The moment of inertia of the person plus the platform9ayget7 5t.d d 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-pg-0 g/hgxb *dgo-round turntable that is mounted on frictiog /gx*dbp h-0gnless 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 groy): eg9hyp 3 bnue5v3,v) 4tdmrw rpk,und with the end of the rope lying on the top edge of the spool. A personv5,dre3e:yt)w9p)4m3 nyu,hvbkpr g 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 the x,5 -2xle c fv,af,wscEarth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angcex,,5- ,lsxfcavf2 wular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from resta86zytmwxqu ,s t:5,b9*dcl f 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 cylind64vab t ew))w*rc7 leoer of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the to7)*)l 4wvc6 we abeotrrque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two:y :hxeh-,xnea pj7 a1 solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concenp hn :xehax-y71e aj:,tric) 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 speeov1q/uw ) lzl8d 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 wit(-7*fcij whx/gz.h2ch ii( i jh mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo grafii z*(- jgw j/hi hi(7cc2hx.vitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-poll9k5x -f0)eaw 7ehedgqution 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 thg)ad f5-ek e7w 0eq9xravel 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 illustratesm19khmy 7m 7jeq+-r cf 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 hore 6fift-kp8 :q/m iwceti4 ,vpc0da ;*izontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (imje ekgh46 j+ 0nb6pze7g3.pu.e., we ignore friction) about a hinge attached to a waen3eg.g4j + kbu hpz6 7emj0p6ll, 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 on2k+q 3nc rz +7tmtvs0wisp *ypj63 ln: the floor, and we want to exert a horizontal force F * vjtl7s z+n0swp+mtq3i:p36y2 n rkcat its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flxgt+s * d.zoc;at road is making a turn with a radius The forces acting on the cyclist and cycle+g.tz s*do ;cx 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 /w*9e3c(rmjl9d.pzw c1ah pqrtr , x;.50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above h*c1.rda;wcpm/ lt(prqr9x3zj e,h w9 is 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 a 9be 5uz7gci0pnahj0p gtf6,f +cnw15s a solid cylinder and her arms as thin rods, making reu5pieh+fwc ,a nn0g c70fzgjt615p9b asonable 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 body.   

  You are designing a clt:lk29bg 8 ju+: oxfjqutch assembly which consists of two cylindrical plates, of masstlj2fkbu 9x qj+::o8g $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ts 1jf)xron/b4ahos :n4 w*lkm6z53kvhe looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach tv nzbjk)4sl a rnk1:s/h x3o56mw*4f ohe highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but dz(fi263bk h,)mi tbz5 skz/p lo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as3 afwsj mezyw )te.;mw 9+(.jm the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleratio jaz9me3;et wm+.msw j.fwy) (n 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