A bicycle odometer (whick0di r* q9v;2eep 2n( uqur/ ti:tbxk3h measures distance traveled) is attached near the wheel hub and is designed for 27-i:ri;v32 bn0/qkp2t( ee 9iud*kru xqtnch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on t9pp4 /s o;ewmy55dqhx he rim have radial and/or tangential s ;o dp4q5m 9wy/hepx5acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angul3 6wk.jrh) y6ctzww n/ar velocity $\omega$ Explain.

Can a small force ever exe*b13ss2vpx gj rt a greater torque than a larger force? Explain.

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

Why is it more difficult to do2 mno88i2i jhrhylckvau;1fgwya/ ;s6 l6 z2) a sit-up with your hands behind your head than when your aral82zs2i1w/ hr8;;6 naviu2j6yycgh kfm)o lms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at clwnz 4c+; afw uc r:b20ua7:zthe 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 ucwn2 b7lfzc; a cu+zw:40 :rato pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend +qzy sz, x17tkon being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantas7zq zyt k+x,1geous.

Why do tightrope walkers (Fig. 8–35) car8xqygix0/-gc u j .;zvy1ea r/ g;qfx2ry a long, narrow beam?

If the net force on a system is zere0,)u uxs q))8*l0clx.ip hkt odekv4o, is the net torque also zero? If the net torque on a system is zer,hxcxei )uuoqs04 ).80d kkv*)l lt epo, is the net force zero?

Two inclines have the same height but make differe2g(6 f+uuh(edh qjgh 6nt angles with the horizontal. The same steel ball is rolled h(d6h(eg6 + 2uf ghjuqdown 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 ie*gb .0 zb 9eiyz5j0wancline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of thee w ijg.*0b0zby9ea5z incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylindec 8 +tpsrly0-znr* c*cr have the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottomcrcynzct+-l* r* 8 sp0 first? Which has the greater 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 anguo 4m n;;xt-) u 6albe6abe(axvlar momentum are conserved. Yet most moving or rotating objects eventually 6;ea(;teavx6xlm4n) -buoa b slow down and stop. Explain.

If there were a great migration of people toward hg)c5/grr3vlgrt 6set5luvi;ns 4+ /the Earth’s equator, how would thit gucsnt/ hl 6ige3vr s) v4+g;rl55r/s affect the length of the day?

Can the diver of Fig. 8–29 tvk5;sr6dm5fm l q.x, do a somersault without having any initial rotation when she leaves m5fl. xqr ; kt,s56dmvthe board?

The moment of inertia of a rotating solid disk about; fz275fblk iy an axis through its center of mab ki;75l2 ffyzss 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-- 0rwq,n0hs ew.0f bezkg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay.-f wq00newsrhb 0,ze the same? Explain.

Two spheres look identical and have the same mass. Howeverw4 1pcbkcru65 ; ,jyoo, one is hollow and the other is solid. Describe an experiment to determine which is wyco k5j6,4bou1wp;rc hich.

The angular velocity of a wheel rotating on a horizontal axle points west. In w9:pvp/f u8 1yu9ilqms hat direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, duqmpf9i /:y8v9 sup1l escribe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a l/qtrp;nd)e8 a .lq9luarge freely rotating turntable. What happen d8 t.;/) qellarn9qups if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw na+no9 t ,in2wit quickly. As he throws the ball, the upper part of his body rotates. If you n,2n otwi +9nalook 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, disc+rjiohe. xs2n t.o/..d pov .zuss why a helicopter must have more than o+n.2izex.d/t.. o.s rjoho v pne rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the followinbc+3zan3 yen)l d. a1gg angles 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 coincidence. Calculate, usfk:dr ; m:4oircn(hznnlp48*sup 33ying the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Mocz;dpornsyufmp(3:3 n r nl8i*:4k4h on, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is direyv8 k2ibs5q4 + .bmwcected at the Moon, 380,000 km from Earth. The beam diverges at an av ybwbq2 ik4+mc.58s engle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blen3/20an fy psndu ll:s;der rotate 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 tfdsn 3;0l :n2/uspaylhe blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3. jbrz,m ;+bhm6eev 4q25 m to another child. If the ball makes 15.0+;2mq ,jbehmrbzv64e revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions do tw8jsv.rb 1 z1(5gikw ohe wheezkswgo5rvw( 1 .i1j8bls make?    $rev$

  (a) A grinding wheel 0.35 m in diametehvuwaf ;)zrkglp-v h- 6/yq( 1r rotates at 2500 rpm. Calculate its angular ver) -(ga /1 p-vhy6wulq hk;fzvlocity 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;ta e5fl;zhk (s one complete revolution in 4.0 s (Fig. 8–38). (a) W(f;eka lzh5;t hat 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 (a)a6;80toj vha 3uaq-va /z(yrl in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poinl 1tqd x-fw 4vnw)s(/k- y-eaft
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a partvq n:.fnhp d 37p t1+:epe8r9rvp2orficle 7.0 cm from the axis of rotation is to experience an acceleration of :pn er13f29. o87 rtvpfphv dqenr:+p 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 13;nn 4om:fuls ;e9ih l10 rpm to 280 ri ul es1hn4lm:;;ofn9 pm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius2 +cb)/pn4oyxi(xdv o $R_1$ 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 Moo+3u *-gov d 5wlokc:i(vyr/jxn, astronauts 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 time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 i(xvo-yw:* u /5vgklr3d+joc m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in e hw 8ix vsa8etirq20tp2/p, /220 s. Through how many revolutions did it t2iet2,/8iswartepv8q p / hx0urn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in :,bf2 pq:a9iugzved 2l.f 7a6m r:l vthrsi*: 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 mqo7v0 b/gg c/of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its fin/g7cqvbogm /0al 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 unif*3vc gszhr :(jormly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time?z(vgh:r3 s cj*    m

  A cooling fan is turned off when it is running at 850rev/min It turnss w8n;eam kb qzfx8..q8xvj :, 1500 revolutions before it comeavq 8.sb kx8ez;n,.mfjq 8:xws 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 ud0 nicb:6),yn m,c8lh(lovgp niformly from 95km/h to 4v (cnmp8 :0o)lb lnichy6 ,,gd5km/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

  The tires of a car make 65 i8zg(pag 2ngv:jry ; ; *mwhx/u r/m7vrevolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diamete p a/ vwhvxzn iym8m;7g/;gr2jgr*(:ur 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 allvs kf 6:e 4g3)mbo+bzy her weight on each pedal when climbing a hill. The pedals rotate in a cirfz:6v +gbkbs4y o )3emcle 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. Wjq4n5 ,itd1f ihat is the magnitude of the torque if the inj4q d5ti1f ,force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about udt6*1; 1zs4f3wf pbbodi1m fthe axle of the wheel shown in Fig. 8–39. Assume that a frict6f1 ddp*1zobf w um4ibsft;13ion torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to oz9,x lfj,tjxw ,7-hz the ends of a massless rod which pivots as shown in Fix-,jtofl7 zh,j 9 zw,xg. 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 system.

  The bolts on the cylinder head of an engine require tighte6oc cl- fw10nmning to a torque of 381 -f0ncm 6wolc $m \cdot N$ 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.h: p 2sh x4qrhiyf)8: )n(aehx8-kg sphere of radius 0.648 m when the axis of rotation is through its center. r(h ) h :4sa)8fy2pxq:exhhin   $kg \cdot m^2$

  Calculate the moment of ine0mv pi61o7dohrtia of a bicycle wheel 66.7 cm in diameter. The rim and6vo0p1i homd7 tire have a combined mass 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, light rod is rotated in a horidinl ;:nd u2v2zontal circle i2:;ldnn 2vdu 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 potter’s wheel rotating at constant angulaqa(by/:hltu yf3y33 jgo- ;bur speed (Fig. 8–42). The friction force between her hands and the clay is jo-a/yq :tb(gb lhuy33fy3u ; 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 objects shown in ys ihe)o(mp9* Fig. 8–43oiy(9 s)h pe*m about
(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 consists4 nz uhx9t /h+t)h8wr3(ri ywb 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 at thzko3 )5d+dhnh.r,mo ce correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach ,+5hn m ohkc.3rddo)z 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm o0 aei6;a1zcm and a mass of 0.580 kg. Cao0;aam6e cz1ilculate
(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 swrzr-9a +shlj c14b x,ojzp- d3ings a 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 tangentially on a small hand-driven merry-go-round and is ab shv 5g.2mlg6nle to accelerate it from rest to a frequency of 15 rpm in 10.hg 2g.l n5sv6m0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is event19rp + pqb:r0 m+0e fka*lfkiyually brought uniformly to rest by a frictional torque of 1.e+y r9i1q f plakbrpkm+*f00:2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball atf+gu; az4mc 9/bplv3.w op wi2 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 ths (n bp1o)yiy 5p8q.ubqj pb6 x9p*u8re action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10pb6by u9 (spypn*)8jbp1x iruq. qo85 $m/s$ 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 roow: 8p5w .mac, jbt5rk:ft*51b zdt hsd, as shown in Fig. 8–46. * hkb:a5twordb51: 5cs.pwmf ztj t,8
(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 of two masm rk 2a2yu8vb6qq0i *ises, $m_1$ 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 witqffl d( op7u4cvm5 +m9hin four full turns (revolutions) and rc5mqufo9v lm+p4(df7eleases 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 of inertia o868 dhr2, 1jmsvokxee smg(:tf $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a tor o: w.pwo01a t0dqq-qdque 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 slipp*o;)ccjyqk; 7l(u0 wut hlt1 0z5hhj ving down a lane at 3.3 ;ck10j05uu )w7;hjvtz *yhqo lc l(th$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun aslv /yp.u jtsci1f b+mv)m5j /6 the sum of two1vc pv./jjm ly ) 6bmt/+5fius 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 q h).zxbewi(/a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylindw. zeq h/)b(xier.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from reso tdl-5rbmb qf; x24s9t and rolls without slipping dow 49b2;l-ro qmf5 sbdxtn 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. I6c 3eray aa/1k9jfp+b t starts to fall and its lower end does not slip. What will bbkja9 eaa 3rcf py+/61e 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 onbwyp6k +2.i cob psv89 the end of a thin string in a circle of radius 1.10 m at an angular spee 2. b8 kbipv9oyp+wcs6d of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angul o7 bb6xv3:6q 0ubp4w fux.xklar momentum of a 2.8-kg uniform cylindrical grinding wheel o6ub0x.b 6v kl7 wx:o 4xq3pufbf radius 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, hands at his sideab7c9-haq8ududt939kod b b (, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizonta73qt d u8baboc 9d9h(-9kdabul 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 ;3 pxu y.g(j 2ddjgg)wFig. 8–29) 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, what is her angular spe 2gjy3j.wx)dd p;gu g(ed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin ropm3xfr9ycv5:7) uk fy *e h,xstation rate from an initial rate of 1.0 r 937ef )fyr:h5pyuvxks,m c*x ev 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 rotatin fqs 2 b8vg;vm4y*th.ag around a vertical 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. Theyf;a bmt*h2vsv 4g8q. 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 o)c0x hw(7to nv8r1wxtf a figure 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 momu ia 4dn*kzsp4 rc((2qentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inert)kg y/,mkul;(h,3-sh kw;*pgfaxw uyia I is dropped onto an identical disk rotating at angular speedkasgw k*-p/m; ; ,,hw ghklx3uyf )(uy $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at mvvr6v, zb7o3 -8sqsn2.4 $rev/s$ 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 rota e5ksx(au-cat .i-l) fting merry-go-round platfor5(-.a )xkiatcl-eus fm of radius 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 rotating freelyf)extw8tdm/v v:7qm 3ka)w 5k with an angular velocity of 0.k5)t:v x7)v adwm 8qew/tfk3m8 $rad/s$ 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 a09w3x zohc6bvkci8w5e ouf 65bout half its mass in the process, and winding up with a radius 1.0% of its existing radiusc kx89u6ezv655 3hoofw i0wbc. 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 excess of 120 .fvrwnaswd8wo10 9 l9$km/h$ 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 03.dpugijcd.9vk: ds $ 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 ro;kmz8: gnqor-zh;shr v0 av1+tate freely without friction. The mozhshr;qo r zn:+ km0 ;-av18gvment 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-mx j00sr8goo7 m diameter merry-go-round turntable that is mounted on frictionlex gjr 80so70moss bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying onaa5+5f ng /vvfo m21 ugsc:aj- the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person withagn1jv+ ga5- cous:a /5vf2m fout 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 samabf1 s.n gv/n7oh d,w.e side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum.wf 7n.nv a.h1 g/,sbdo (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ratee1.+ s btzmm/ 6xbraeqj6a1l5 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 acquiwdgg /)stit:h)eb,b* res a rotational rate of from rest over a 6.0-s interval at constant / )dt ghi)sew:bt,g*b angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of twoy(c 6-yfug u0d ezn,nn5vv8 +m solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it isv,-u( g u ned0f+cmn 5y8nvzy6 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 -*/)/fer c j*tu8 ewt6yvry nqrear 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)cv:ej+ eux7y Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular +yu )ex:ve j7cmomentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution autoqkew85*03a ew mj.xx fmobile 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, andmw5akqj* .08 xe3xfew should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustratesfz .)jpfjmb 8im 9oo98nx9f+y 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 surface at sphxd / r1)0/0sr;/)w pqkrk tvd5iw cboeed 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 fri-dh yy/o3( z1is z1suz()tilb ction) 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 centeriyz(zo1 1 ds ) u3syzbt-hli/( of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing 508hm78nomx i x5q,kj)wlmpg vertically on the floor, and we want to exert pixqgnx l5m85m0 w k, j8)7omha horizontal force F at 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 flat road is making a hui2 -g,.t af:83x0blhweukw turn with a radius The for lwu 8 3txgkfub-.hie,20ha w:ces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.t7yhli+- pr k qet,7f45 m and begins whirling the rock in a nearly horizontal circle abo,7t7pl 4i-fh yeqr t+kve his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a sol:s bp-hmq( lgzjg7pu5:1)nyp id cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, agyqum::pg -zn 5b p1l()hps 7jnd with arms held tightly against her body.   

  You are designing a clutch assembly cyr7 ,noi 0m1om lo;8awhich consists of two cylindrical plates, of mas;o,oo l81yma 0m7c inrs $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the lt: 35)fpas vemen3 qin)*rl*jooped 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 the highest point of the loop without n3e5)jr n3tpel*av* mif:qs)leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do nonr4f-o:wv g-xejq n9,t assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the ca6.riycu -g9o*h e,kfgr reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of urc eg h6 9y*.fo,kig-0.90 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