A bicycle odometer (which measures distance traveled) is attached2hkpww m9ikh ;syfdjg 5u;pf)+7 *5yo near the wheel hub and is designed for 27-inch wheels. What hap iw;5g*hof 97k ; d+2yp5h suwpfy)mjkpens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rimt:z m1ojjt.v0tnz he7:i a2g2 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 compoio 12ae .tzjn:tzg0th72jmv: nent of linear acceleration change?

Could a nonrigid body be described by a single value of the angular veloc qbsb;8h)qebkdkuq. 3xw4 2* city $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force?xnlcbk6,b h*cjit yn/ +9;3hs 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 younyvms mk)5mnkc+xn(8 *lqy 1*r hands behind your head than when your arms are stre n185)nm+x(qsymnv*mk*klcy tched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprocketspd17y7sqgxy ) 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 sps 7 qpd)1yyx7grocket or a large front sprocket? Why?

Mammals that depend o8;xne 3+rfvaw nt.t2w hh-p6 an 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 86+vn.t f ;x repnhh32aww t-amass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beamil0) k6m5 0 ptjfpubn+7o; usw?

If the net force on a system is zero, is the net torque also zerocbul0t-gd i q-35i;hb ,5dfiv ? If the net torque on a system is zero, is the net forceb0-d i5vd u ft-,hcgb;5il3iq zero?

Two inclines have the same height but hep e6m0no7h1(*nwn amake different angles with the horizontal. The same steel b*nopn70wmeah (6hen 1all is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simulta me4zpy76w)sgml v+:hneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the :mep )7h 4w6 z+vsylmgbottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the-o k2guwxk8 l zy1:;s aa7c0df same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the gre-l x;g7ofcs 1yak2u:wzd k08 aater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that moment cox0(4i44ela+r -rnandp t g(um and angular momentum are conserved. Yet most moving or rotating objects eventually slow down and nac4 n0pxl 4(rda (g-ot4+reistop. Explain.

If there were a great mim ) pr,ffb*ml:gration of people toward the Earth’s equator, how would thibmp: f, rm*f)ls affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial roe/8;pqxw(jf 2x0zf qq tation when she leaves thp2q0ex;8jwfzx/ qq( fe board?

The moment of inertia of a rotating solid disk about an axis through its centsj/ 62qp bn;o )teo:oxer of mass is t2 s /eo)bjn;6ooq:xp$\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outsqw ee5b3jl::c xbk 5v6tretched hand. If you suddenly drop the masses, will your angular velocity increase, dek3vbb w5eq:xl:je 65ccrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, .1osfa-3isjt)l 2 f ; kcm(suocvo44cone is hollow and the other is solid. Describe an exper2as svsoc f;)cc k4ltm(ujf4o3 1-.oiiment to determine which is which.

The angular velocity of a wheel rotating on a horizont4 rad aaae)) kg-;(atbal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular accela-aa)4te gaakr )db; (eration 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 standingsyl *( *q3 e2brv4midw on the edge of a large freely rotating turntable. What happens if you walk tow r2dvembq*yi4ws*3 (l ard the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As jd5haqtlq+03t*gb e.+ z6nqu 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 ab0zd3 +hutel5q+6* njq. qgt direction (Fig. 8–36). Explain.

On the basis of the law of conservs38bhgkj xr f8q4, g.uation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate ju,g gx kf88rs.hq3b4to keep the helicopter stable.

  Express the following angles in radl 0,qajpoko55:83 rair 4cwgz ians: (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.uz/ tz-hjoq 6b90 .oai Calculate, using the information inside the Front Cover, the angu 0oobjtz9/6.iauqh z- lar 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 f;xous47)z hcbxbp g7 1rom Earth. The beam diverges at an x7s 4;guh)x7c zpb bo1angle $\theta$ (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 the motorxkh.5v sfcd13p1dgg4 5 4xevx is turned off during operation, the 3g.vhk4x5f1 c5x gdesvpx14dblades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level i8b4q 3g. addfc i aq/0bw4hf0floor 3.5 m to another child. If the ball makes 15.0 revolutions, whff4b00 dqc/wg 384 h.aiiadq bat is its diameter?    m

  A bicycle with tires 68 cm in diameter tpz 8 qhnnl20f 65c-lwo*x7r firavels 8.0 km. How many revolutions do the wh6fqwnx 8zlrh0of p* 2ln75- iceels make?    $rev$

  (a) A grinding wheel 0.35 m in diamen f;esmmwd5 .wr3+dy3.qz+ h gter rotates at 2500 rpm. Calculate its angular velocity in d msmg;z5 rfd+.nqw3h we3y+.$rad/s$ $\omega$ =    $rad/sec$
(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-rox2k o,5auv0cd und makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from2cxad5vk o, u0 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)q t5,z hw7qtnuw*/hl z;g gowv15ep7) 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 pkqldv2pr;7ys+kh k1 7 oint
(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 particle 7.0 cm frf,(uwfk uc n(i, k8a,uom the axis of rotation is to experience an acceleration of 100,0 ,cfu,i ,kafu( nwu(k800 $g’s$?    $rpm$

  A 70-cm-diameter wheel accer 5q,k2y vc(smlerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Detkcv(srq 5ym,2ermine
(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 radiuf0rmlq; 2sh6os $R_1$ 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 1b qmwv/mu q+1aboard 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-minwq m1+/q 1vubm 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 acceleratec7fc43 ztmp x7hh.n :as uniformly from rest to 15,000 rpm in 220 s. Through how ma7x mzftca.cn43h ph: 7ny revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5yboy5uw.db zfvb363)jp d74yr9 kax * 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 w;d *9/ qpxqj6qmd)2f jrk7wdghirling “human centrifuge,” which takes 1.0 min to turn through 20 complete re6x27q kgpd9 dr fqj/;djm*q)w volutions 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 diameteursks3 e2nrt38 )hs1 aco h*d.r accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. Hosdtehnra 3rckou12*)s38s h .w far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850r5b98s-h: h l x.pkfsjmev/min It turns 1500 revolutions before it comes to s-8hxkl:bsj m5.h9fpa 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 uniforml3ilaz mpy938oy from 95km/h top9a33 zio8 lym 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car maki;e0(zdau19 awfwmqw u1 1 qz8e 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The a8w1 ;zwq qfi(19z0w1ue dmautires 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 weigh0 2 h;0blmi t;prur,kpt on each pedal when climbing a hill. The pht0mpu0 rlk b2,i ;r;pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cmjp g+ wasbrksjcla386 29lq) 5 wide. What is the magnitude of the torque if thajc rl6lj8g )q2s+53bwskp 9ae force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39.+efei 2ua )0ky Assume thatfiey0kue2+a ) a friction 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 the ends of aes. zbzkyvpa6 nv-u6,s5 e jc(;9;eo e--uxrw massless rod which pivots as shown ix;-vn-u-ps bweycz 6ue9evo ,(rj6s;za.ke5n 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 system.

  The bolts on the cylinder head of an engine require tigh45h3xkm. p baui4f0 t1szn3e)m,nfe4f/nw wrtening to a torque of 38 pfe, b msfu43x5im1w)n4 tnzh3k4a./ 0rwfne $m \cdot N$ 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 th( trw )eto80-ifcgk0fe axis of rotation is gwr cef t)-0toi8 (kf0through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of aqlh, t(8) qalj bicycle wheel 66.7 cm in diameter. The rim and ti)lq,(j 8althqre 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 o h+)djae)r5gj b 79w) s 6wj2eane0jopn the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 mew)b a)nd+e2a)og06jh9 w7jjse5pr j . 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 wheel0hit7s 7 7*-g-3kmvn wqbgvkv rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay isvk btwghv-g*k7snv0m 77 3iq- 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 h lbs75d97 8q txw( mb34nevyiobjects shown in Fig. 8–43 y9dw7 n h qtimxb837svle5(4b 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 conw 0ae8uyq*r6z bbm /sbb7e)d1sists 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, uniforicydu*/ x ( ddmc*ms76m cylindrical satellite spinning at the 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 mcmuc* d6d yd s/7xi(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 wie r(eo4l:zc0h l(p1lhth a radius of 8.50 cm and a mass of 0.580 kg. Calculatec1h0z(lpelo:l4e( hr
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest n.6a:cvl f- ,lyfwm8d0wfg7fto 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 sm0cwkuw4w; 3h tlv4e-dyl4:(a q;ms v wall hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculat3q md 4wwwsklua; le( 4;hy:w4vvt-0ce 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 rotow3(w f70rkf nating at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.2o(3rk 0wnf7f w $m \cdot N$ 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+c3 wpvw6imf a8 /6yus accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thvlchy 8ei4pcs9; s 1w:rown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–8v;cw hc4:p i9l syse145. 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 lycu,mx83m40n :ah fr a long thin rod, as shown in Fig. 8–46.hry3 ,lcx:u f0na8 mm4
(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 corx6n0+ *rzowco7f /vt nsists 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 ful n*b+cju:9/) ; 5zkim8puvppef t x)vnl turns (revolutions) and releases u ncx ppk5j/tpu;8 ez9m):f vv+ni*)b 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 h3 uvkd2h*gu5,r ijrel ha *y3r6:xdw5as a moment 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 develops a torquu at/7c c r7)ol-qgo8ze 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 7neh nw1k4k7 x9p 7bhyradius 9.0 cm rolls without slipping down a la9h 7by n7h7w4xk1kn pene at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kineticzw3 t6m-.l9d8qb kl wo energy of the Earth with respect to the Sun as the sum of two ter. dzwt-8 wk l9m3lqo6bms,
(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 164otjgsh l2j6j2i gt4m; b+1ty 40 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rmjtl; 4gj sho tg41+jy26bi2t otation 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 kg starts *hafk4h 53bff from rest and rolls without slipping down f5f3f*a k4hhb 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 balant9:)zb n3i ortdj71dfced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before )dj9ofi :7tdz rtb1 n3it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thil d2 fzqcp.v*.n string in a circle of radius 1.10 m at an anguz *vdfc..q2pl lar speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg p+wt.c3-q zu8mteh0d prb71 m uniform cylindrical grinding wheel of wcebt0mmr p.+78qt 3z udp- h1radius 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 side, on a platform that is rotating a*1b) zq(a qu;iw hm7gvt a rate of 1.3rev/s If he raises his arms to a hov(wbmh u ga;*qz71)i qrizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29)x ytv8lp n-55,+ 7wfdov3a7zi)n prdy can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tufx3o7yy8)iw5 d,75lz pp nnv+rad-v tck 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 from an initial rate of 1.4ykp;k;mh9 tfgv/c v20 rev every 2.0 s to a hc2 p;;fvv49/ tgmkkyfinal rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its ce) yyt7fdncigb 25:4 mpnter 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 :)52b4f7pdmy nycg tipotter 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 pun64dvt +a1zw ( u1wkw3yrl5a 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 momentum71na +9e ooikj 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 inertia I is dropped onto an identiclfu3):adov0*b r yf*zal disk rotating at ang 0ffrozld :ba* u3)yv*ular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2 8uae0t j;*7rpe ff;rd.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 rotating merry-go-round plato.7paq c1aqp uf(o2. wform of radius 3.0 m and mom1(pwq.pqoocau.72 f aent 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 angular vel;fn g6 loro2fr gtm.0o0(+8yc.kmhqc +9ey cy ocity of 0.h c f.tmr+008(.foolrgk ;oy+ ygqyc9me 26cn8 $rad/s$ 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 about half its0k)jvb q2 0cuj mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away nu0j 02) bkjvcqo 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*+gm.wmi* pis;e h-rh in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass dc3z q3fe ,c ,cgp668gc fbw)r$ 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 rotate freely vnf2*egz7u ( c,/nlbpnz /t,jwithout friction. The moment oz vfn27pztnugeb/,lc / j(,*nf 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 ofig 6ksyscr0(h k23e8u a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment ofu32esy(g6 skc8 kh0 ir 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 r.;5vs4 8(k3acpukd -do. gb+qodnlksope lying on the top edge of op + 5snkbaqkg.4;v8dk do(d sc-3 l.uthe spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side alwayyr1zp v.zt20ds faces the Earth. Determine the ratio orz01 vdpz yt.2f the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 28cao* f +p l/x .su:nw3gkckim/$s^2$ 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 k buecv(s56 ,gshape of a uniform cylinder of radius 0.20 m acquires a rotk5cs,bg6eu (vational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.06oz 0gqpd 7jxv)e)br5 50 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-lonvg6zp70q )j r)d exb5og 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 a/;gchkx6 1 iyghw6k;ongular 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 ti )mwixo-w-tn/ fj6u0tt6fl18wfkv)6 w 0oexbmes 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-oxf twex61 )m)0klwow8/ -nvfw 6if -jb6u0ttquarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution autom khs:c /:eum 7kz v1hf7i-nh2. 9fyolsobile 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 y-e7scvkk usiz2.1 ofl hfn:hm79h/: uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and 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 illustrate9uq qukt9wy s0 o5ak+m.py8dm6l5*a cs 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 speed v=3.lsy3 irg6 8z(f3 $m/s$ 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 lef2q b3(s5o(cfror9o j ngth L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) thbq ((rf o jof2co3r5s9e 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 vey;w qx17anf 5frtically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step ;qfy7xan w5f1has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn wit qgo8)/kk gy)th a radius The forces acting on the cyclist and cycle are the nor qotykg)8/ g)kmal 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 o;/jvyfrv wuy9 b7 v: e8mt7m3bf length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torqu:v 3r/ jv7ftmuv97ebbw 8m;yye required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a f/o9* k x7nvffsolid cylinder and her arms as thin rods, making reasonable estimates for the dimensn9fo7 fkxv/*f ions. 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 clutch assembly which e 8 okszh93orxui1f,+dgn, g)consists of two cylindrical plates, of m o rg 3so8 ,1nidh+u)fz9e,xkgass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped ro.nd:r (q vx:5rbk7m aaugh track of Fig. 8–58. What is the minimum value of the vertical height h that the md5qnm avr(a .r7x :bk:arble 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 n84axxz/m vih-7i2 g(r;j qoimot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions asfyjr6n8j k ,s(m wo+sw6kc6 9s 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 acceleration of each ysf9mnr(sco+8w6k6,s j j k6w 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