A bicycle odometer (which measures distance traveled) is attach )sed */ mkiy0)g0r9v2ffkbdfk0 6 hsped near the wheel hub and is designed for 27-inch wheels. What happens if you udefi) f0p9hyk6r0mbdk2s*/) 0 gfkv sse it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a(sgj; s ebcnddv-v84o -un4it, c9u 70t9wmnm point on the rim have radial and/or tangential acceleration? If the disk’s nv0 idgt,e9;cmn 4bwnmoj7vt c4 -ud9( 8s s-uangular 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 angu-qm /rua7fb6. vq dgwuhd4i;; lar velocity $\omega$ Explain.

Can a small force ever exert a greater torque thanwx.e6j70 + ebs277wmqhr7 i m 4bnsacr 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 yy l bk:5d/z8;yo(3iac(vrpnb our head than when your arms are stretched out in front of you? A diagram may help you to answ;y :ok nz(l8v/5bb( i pcy3rdaer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pw u1w/v7(qwx q5ie0z da: u.rjedal cranks. In which gear is it harder to (widq5qu 07wjrx1avwe /zu: .pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast bffj7 dadz +:fu m-0.thave slender lower legs with flesh and muscle concentrated high, m:0bt7df du jazf-.+ fclose to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow blyje9rpl554b(agr*g h0s 5wieam?

If the net force on a system is zero, is the net it 8/-lq hz9x.6msajg torque also zero? If the net torque on a system is zero, is the .gamj6hxzs i ql9/t-8net force zero?

Two inclines have the same height but ggj9 5agz6c ,kh0vau2 make different angles with the horizontal. The same steel ball is rolled down gz2 aa,ghk60vc 5j gu9each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneo0fcgl1 z0d uby)o2/ qpusly start rolling (from rest) down an incline. One sphere has twice the radius and qlzp)dbof0 yu 1/g02ctwice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass.vgxd99o*rt2hs ps 0i2 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 greats v2o 0rhsp9i*9dgxt2er total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. wu6iw1*v*apg Yet most moving or rotating objects eventually slow down and stop. Expwi*1 6wpuv*a glain.

If there were a great migration of people toward the Earth’s equator, how21*/slyks r ze(jv7ys0 v/qj k would this affect the length of k/ qs7e z2k y/*jjyvr(v0l1ss the day?

Can the diver of Fig. 8–29 do a somersault without having aynz :ssc74 r, d76mei(p.dn asny initial rotation when she lsza (sm .c6ypinr77sd,n:4 deeaves the board?

The moment of inertia of a rotatiez7pn8 z9/3od9 yaimo ng solid disk about an axis through its center of ma7m9 yapo8/e3zni dz9 oss 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 onvne hmzdfq4.b /f3s*/ a rotating stool holding a 2-kg mass in each outstretched hand. I 4bed/nzmf ./h3fvqs*f you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howevms hss t.htjxfsa8hyu0*7 *6,er, one is hollow and the other is solid. Describe an experiment to determine wh0m8*f,xtat s*6 suysjhhh7s. ich is which.

The angular velocity of a wheel rotating on,ko0lj(j,vf:ewoo(;y t3 ncm a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point atj0c3j fk:oloe( nmv ,tyo;w(, the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge kel0*x lkn1y30o9a8pfhs7ax y1+ oytof a large freely rotating turntable. What happens if you walt8ha*a1y 1py3 lkokxy of0 e9+x 0sn7lk toward the center?

A shortstop may leap into the airwvcp-rbd 1mu mvj015, to catch a ball and throw it quickly. As he throws the ball, the upper part of his bodm5 cmvrp, 10 u-bd1jwvy 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 lawhttgl cw *x m2x*bc/,yfn63 z2 of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways,x t2fh2xtygl bc 6*z3wc*nm/ the second propeller can operate to keep the helicopter stable.

  Express the following angles in radianstk4f3sa(2hxpk;g2vte a * f3 w: (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. Cxn +ve *x:q8kjalculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as snq*ex+: vkx j8een on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The ;ggql3lr47p v beam diverges atlrgl4 3vq;pg7 an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. 5hz5 jea. (7 6aboz73ji rxdtlWhen the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as thehj reo7.a(75bx tl63 ajzd5zi blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anybys3n1zu// bzf.wu)other child. If the ball makes 15.wb)/u.zf3 ns1b yyz/u0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diametrwomm -db ru8lmwr2 /1kle -s5lc-2m:er travels 8.0 km. How many revolutions do the wheels markm u/5bow l2c-w12 mrl 8mrm-ls-:deke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcr.k6s; a)x cbculate its angular velockcrabcs.);x 6ity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (;7uxxx nk- sa4Fig. 8–38). (a) What is the linear spee4 sukna; -7xxxd 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 Ear*jroiir 8(7 id zp9s6yth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sp/t1d s vkj9utkemzk4x.lt; 89eed 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 centrpu x 2o)r.u6xyifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of ) xo6pxuy2ru. 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 ( (avmgq7 jzix35.qyl rpm to 280 rpm in 4.0 s. Determin5ay gqv 7q3(jm ilxz(.e
(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 radius7nc,j b24 adj kpprv-/ $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft puc5i(*+svi0 wdvf i4w kt themselves into a slow rofcwk (i04d* vi5vsw+itation 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 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 220 s. jp:j mqy .dx2/Through how many revolutions did it turjqj.:pd / xy2mn in this time?    $rev$

  An automobile engine slowsrah17ntuz, 8y(gy.po89ah h o down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying hiy5m9rvla9.gknp ww 6 ,ghspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching itakpw6v nm9w59 y,g.rls final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm: mxx +syys1n pe/pa9xbacu35:p3(oi to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this t:xs9 u5n(y pio xapb ae s1/ym+33pxc:ime?    m

  A cooling fan is turned off when it is running at 850rev/mir+fn tl(k 1 d,.civr6un It turns 1500 revolutions before itd,cl(.t6r+vukf 1inr comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as ongq v85o+, ia4-ofes the car reduces its speed uniformly from 95km/h to 45km/h The t gn -e4 ,+soiafoqov85ires 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 z kl*zy k/xdrn;fk)7c,h6vjfxs;d. 665 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires hy jd/xvl, 6k6h;kd.rxc7 znk s )fzf;*ave 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 0et8iap cyv 51a bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a cia5v 8i1t 0yceprcle 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 foi jl, )vji6lj8rce of 55 N on the end of a door 74 cm wide. What is the magnitude of the torlvi,jil8j 6)j que if the 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 n0 hhgc(mu24ff m9t /xk97 zqxthe axle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0m ctgh fmn fhx/2 (49u79xzkq0.4 $m \cdot N$ 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 piftsdm r9h0bvmz,- 6 6:ft9opu vots as shown in Fig. 8–40. Initially the rod is held in the horizontal positi:pv,t hd 0z669rmsbofu9t mf-on 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 tighth,.ye4 k45gm6 nvhthx ening to a torque of 38 h4v4 ,hgnm x hyke56t.$m \cdot N$ 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-kcrh2l/p :zq w/)zv51 kq:jlwcg sphere of radius 0.648 m when the axis of rotatio/52 wkqp:z:hl1jw rcvz)q/ cl n is through its center.    $kg \cdot m^2$

  Calculate the moment of inert lycxb;5g +jt*ia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignorexbl;j ycg*+5t d (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end opg28 fbtj 6t7uf a thin, light rod is rotated in a horizontal circle of radius f82ug jt67tp b1.2 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 a(-xuk7z2dwdkn um ) 0rt constant angular speed (Fig. 8–42). Theu2wud k-(k m7ndx0)r z friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objec0bd, edm;rh..1p d8ikz 7/zg6m mwuoyts shown in Fig. 8–43 abog. p ud1id. d6,mh 8rzk /7ym;omzw0ebut
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whmog u17 ,vq;zdak3-c zose 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,il pewb*+b 2f: 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, wha*+w: ipebf2b lt is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50qmf4rrml x tdu;+ 0)m +)x0vqa cm and a mass of 0.580 kg. Calcula+xm 0md ral;t rm+q)x)qv0f u4te
(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, acmduco b 4-r7fh6o):w2cdr:yr celerating 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-rounddequm g2lz5.hcl1,no o3: .zc 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. Calculate the torque required to produce the acceleration, neglecting friou .:gqn2.l cdz me51lo3z,hcctional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is82ptyfg, ;(o:1z2ixxpy (vue*zu dxu shut off and is eventually brought uniformly to rest by (:y* zf1 2p8tgdyz (2;e xu uixpouxv,a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–1b ();kwloekflx5s-f3 qa-ae 45 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 thrx- 1nw( *pibbuown solely by the action of the forearm, which rotates about the elbow joint under the action of the tric - inb*x(u1wbpeps 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 considere 3ba2/ny bgeb6d a long thin rod, as shown in Fig. 8–463 ebbnga/2 6yb.
(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 twot1k-27gimxj )m( vdk ;rpq t4v 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 accep: qrb,)5m6v;y u)w qk9z 2ksrikdr)tlerates the hammer from rest within four full turns (revolutions) and releases it at a sm5bd )s6r) uzvyk qw,9qi;2t: rpr)kkpeed 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 momenf:1hi 12 u*wylpffkb9 x5tbx1t 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 torque of s +bq2d1o8h-a3ba t sx280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of maz4oq s+si-tfn4e,n j9-anj i8ss 7.3 kg and radius 9.0 cm rolls without slipping down a lane j --z9eaonsq,48+tn i4i nfsj at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun 72a p)5ii1gslo3vlkw as the sum of two termsl5iao svg 1l7p2i3)kw ,
(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 kkp- + -bwe hsq6gbu:1pg and 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 cylinder +-w1bs6eubkq pgp:- h.    J

  A sphere of radius 20c.26cepist* k uh zue*+d63j7/ tv zpb.0 cm and mass 1.80 kg starts from rest and rolls without sl jbze7t6.* c+cutd *sh62vppue/ki3zipping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts to falwf)3d +uq 3zdfl and its lower end does not slip. What will be the speed of the upper end of the pole just before )f3z 3 w+qudfdit hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ba;m( 6(pqvpx m8ejeqg ;a)*ph8tog bk;ll rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 10.4pg6m;p 8q* j;8oxpgb)ae; e vt(h(kmq $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding : lmlppg .dh .)o7fdgse)u y5d8x he7-wheel of radius 18 cm when rotating at 1500 rpm .7)-sd)l8my exh 5o l:ugdef d.hp7pg?    $kg \cdot m^2$
(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 thau 6;bzxq84gf92 do d b+fj+iudt is rotating at a rate of 1.3rev/s If he raises his arms to a hori49;fj+bgd8xqz obid2+ udf6uzontal 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) can reduja5/yp *oym8rce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck positior*a/ 5o8ypjmy n. 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 rotas* h g+xsxz t9cr-)q5ltion rate from an initial rate of 1.0 rev every 2.0 s to a final rate9cl5 t x )sh+*x-zqrgs 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 rota d/;jghynpc0e 2-tco (ting 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. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is /e- y;hccnj0o (2ptd gthe frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure nwlh86m o,qsgn 0p3q2 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 momentum of the Earj,q fe-ey;er0th
(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 i:mqu0z 6n4qih j g,5 awl8j-ttnertia I is dropped onto an identical dis lj :tjq mh0q5,a6z-u ngwti48k rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a5vk-yeaft994gzq uon6, /y 2kwkeba1mjs :/at 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 rot v50iwe (qe1igating merry-go-round platform of radius 3.0 m and moment of iner1 vi5w 0(eigqetia 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 freer(cyn 9j e8y+uly with an angular velocity of 0.yy(en+ 89rujc 8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing abva+.zr a nj0b9/r (wfbout half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries awaynrrj+9/zw a( bbv a0.f 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 r:g0qm ek60g lcrby)8$km/h$ 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 6g2sx8-jep9i c3 z uxt$ 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, initia ldcy7fs9m6rec7 vp il0m75e(lly at rest, that can rotate freely without friction. The moment of inertia om56fdy707 cp r9l(mvsle7eicf the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter jq*(x e4u*v dnmerry-go-round turntable that is mounted on frictionless bearings and has a moment of inere*jxq4*nv du( tia 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 grouqhlb3-7 an+0 eyetov +nd with the end of the rope lying on the top ed+e ebhva3 qon 0l+t7y-ge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth sucq4cp j q9,ehukks3v58h that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as sj e34u8 q59qckpkhv, a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 3 aizmu1j v9i uh7,g-ym/$s^2$ 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(83 s zelhouyn9k3rsncls 4hu 8a2u/( of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s inter3chal83s2/ u(u h lerz (sn8y4uns9koval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two5bu*t(cm+yt h 2z7gzz 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 zmtcu*7hb (zgty +z52 of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheel z.g v oco5f;ex6v ze((1c6rc l($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, wer2+lo 7iz ga7pde 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 th+ad7 g7p2ziolat the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to uax jt/.tno oi+4 4ais8se energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km withj4i+ns xoa 8/atit 4o.out needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates 0u07uy-wuck i3h*/ wwlfr wy* 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:mpng4glf6ev 3l t/ edhn)i4;s. i.jz 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 (i.e., we ignore friufpqo thzn .z2h.;f*2ction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: q2f .;u.t2zhzohp*fn See Fig. 8–21g.]

A wheel of mass M has radius R. It i*a/ ,a gh 83z,beoy hk8an*tsts standing vertically 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. *z3 y t8a *hohsga e,ak/8tnb,8–55). The step has height h, where h

  A bicyclist traveling withosk,p qhbo45 1 speed v=4.2m/s on a flat road is making a turn with a radius bq,o 4sko51hp The forces 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 len r;zt:lko:o; agth 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 torque required to achieve this feat, and where does the torqueoa; z tor;::kl come from?    $m \cdot N$

  Model a figure skater’s body as a solid 05jlbnl5q j cb)ptx19cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculateb)j5j 1t 9bxp5c qn0ll 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 c43cw+gdnb2hbv bu6vgj: +3 f qlutch assembly which consists of two cylindrical plates, ofv2f+n b3ubhc 3dg vgw+:j4b6 q mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough t x-jcgj.e(v 1 r:jdodpbe1 re 7m0mc/2rack of Fig. 8–58. What is the minimum value of the vertical height h tha20:dp /ccr-11.rve ejdjmjo be( gm x7t the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, bvbf ;7w5x( rj6 y+kavaut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniflj 0l8 .ftff,h/oi6(;sbkf 3nh dcm2 dormly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular ac .8hhdd/ctf ;n,l2(m3ffbojilsk f60celeration 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