A bicycle odometer (which measures distance traveled) is at vry oq;kkc7s6g 9rfokr g:.0sd8ez /3tached near the wheel hub and is designed for 27-inch wheels. What happens if you u.z 9 8g r6ds;qv0cfskokkeg: / ory7r3se it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on to -w.cs(t cra-;o)pdbhe rim have radial and/or tangential acceleration? If the disk’s angular velocity increases un od) -rpaob wt;(-c.sciformly, 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 angular velo nd+f)i1y1t6sendc-9s-qcp g4xb *bp city $\omega$ Explain.

Can a small force everp4c; qkfhj0j2 exert 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 do rn-vopv vp,63tq40alai;6vj a sit-up with your hands behind your head than when your arms ara66v- tviq ,p;0laov vj r43pne stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear u;q+o 7kns6 tgwheel 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 67 +tkogqu; snsmall front sprocket or a large front sprocket? Why?

Mammals that depend on kh :qc5s7g (jx/iu7 jf *yllfnlv23c6 being able to run fast have slender lower legs with flesh and muscle concentrated high, xc7g/c7 n*2 :q6ijl yfuh53( llfjkvsclose to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers 6v2i-hgtvez2:t5r ei (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero?j t/k5s ;k czdzul0gjn9xsafi ,4x1.2 If the net torque on a s gcjsix5sj; x u.kn,2l 1a/49fzd0k tzystem is zero, is the net force zero?

Two inclines have the same height but make different angles with :omy phz97v ib c9d1g6+ iosi13 t)hwxthe horizontal. The same sty1: oxgtbiz iv 7mdhc)6i19hs p+ ow93eel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) l0d clis. j+e* q5agn;down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energj;ilga ncld *5sq 0.+ey at the bottom?

A sphere and a cylinde .ya 5e-vbgu:0l+phh hr have the same radius and the same mass. They start from rest at the:-lh.b vahh u g0yp+5e top of an incline. Which reaches the bottom 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 angular momentum are conserved. Yet mo;p/k(*zcyqgqd ( xw /n r-a9dkst moving or rotating objects eventually s d*y/;nq(krk/(xdgc 9paq z -wlow down and stop. Explain.

If there were a great migration of people toward the Eartz;essuyt-u, gq+r34 m h’s equator, how would this affe34sqegmtr;sy- +,uu zct the length of the day?

Can the diver of Fig. 8–29 do a somersauloamz f /som7ri (/4rc6t without having any initial rotation when she l6/i74 sfro (czor/mameaves the board?

The moment of inertia of a rotating solid disk about an axis through its center9q-e2iw sqw kicb ghooys0 7(5p*ly+2 of mass iso h isq 5ceklw (y o-ygwpq0sb92i*72+ $\frac{1}{2}WR^2$ (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 holding6 b-xk yj*brx: a 2-kg mass in each outstretched hand. If you suddenly drop th-jx b6*by:kx re masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and havet4./h lmvu j,n the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is which/v ,mnhtj u4.l.

The angular velocity of a wheel rotp:wl..eahtdx(io4t b s: y1y7ating on a horizontal axle points west. In what direction is the li .o1s:7l4y th.pxb twad(:eiynear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely ro*:,j2blj iqtb tating turntable. What happens if you walk toward tjb2,: b jlq*tihe center?

A shortstop may leap into the air to catch a bala5elenjg94 * hl and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. g*he45na9j l e8–36). Explain.

On the basis of the law of conservation of aph, ,eqtr:cak*ky4e3 ngular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propelle:*k e,pk3ch,erqya4 tr can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 3i9l;dzk 2f,n p0 $^{\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 coinchsb:zr c )7bu4idence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Eahbb74: sz)cur rth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diver1 abmfk:4 rlgxo4j3808 gspa6vi. aurges at an angle i a03 fvsg am1 ba:48u8. 4rpoxl6kgjr$\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender ,jb7xm s-gy;2t w 5h :mvych5i6sp7xnrotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. yvm-7xwg i5b;nhhc57 sx6:yt2 jm ,s pWhat is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floori0w/ -3rc* yuf mfusq8lnc35j 3.5 m to another child. If the ball makes 15.0 revolutions, wrq3ysju w3 luf8i*fn/cc-5 m0hat is its diameter?    m

  A bicycle with tires 6 ;0 v r-2.etywsltwuu-8 cm in diameter travels 8.0 km. How many revolutions do the wheels maksr -twtv ;ewyu2 l-0u.e?    $rev$

  (a) A grinding wheel 0.35 m in diamet-)n4jd la uw+dsgb 42.sxk c3ber rotates at 2500 rpm. Calculate its angular v3s4clbd-bg.n sa4u2k +)d jwxelocity 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 4aggpc 70vr01e-2jh 8xv giqu; .0 s (Fig. 8–38). (a) What is the lineara vgg;r2uq x0ij1-8c0epvh 7g 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)p uf ,vhh7q37tyo+da) 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 +aikfc0- b wf)point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a partiy9ke6; qgwg 61m)p dtsdah,x.x l46cxcle 7.0 cm from the axis of rotation isy6kx16glmq h 94w;xtgd.d ,c x6e)psa to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its c : a*xhau*owd; g.pzq4enter from 130 rpm to 280 rpm in 4.0 uo* a za.4qg;x:pwd*hs. 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 radiu(;-v :*3/e*rmmv qdsqndy kjb s $R_1$ 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 Moonna wz:;.k2 g nxip-.gx, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, th2w :;npk n.xag.g- xziey 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 uniformlipf 7axxk( .s)y from rest to 15,000 rpm in 220 s. Through how ms(7 .xxifa pk)any revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 sex0t cz*8n sa3. 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 thepo 3e1 ls dr3yp/4p,xb4ux w5vga3v 4r stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1 1grxu x4 4,l pwer vv3pdy3poa/4b3s5.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 3f3th6d7ecd(9ll qdk .w -ur 1b60 rpm in 6.5 s. How far will a point on the edge of the wheel have tt-ucq bdfew(kdl97ld31 r6h.raveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turgw,5aywwa39w ns 1500 revolutions before it comes to a stop. y w,53agwwaw 9
(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 c6m(io2spbfrm.i yv ( ,ms2c ;as the car reduces its speed uniformly from 95km/h to;2 b 6(mr icsopyc2vm.,si (mf 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 make 65 revolutions ask qjk pox9r-qd- 5hi.6 the car reduces its speed uniformly from 95km/o - .j6qxk-p9hid5kqr h to 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

  A 55-kg person riding a bike p5o28 y)mfw pzu9cjz,*6au fn9mg w(oluts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radiu829w(w,6 upmgu f5manloc9 * )zjzyfo s 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. What ibi3xj6rpde3lj: /mab*l (;das the magnitude of the torque if the force is exep/baa x :j(ij3el dmr*l3;bd6 rted
(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 i zos*) 1( bto6+0nqwwvew8 w(q9mbgo fn Fig. 8–39. Assume that a friction torque of (6s(owv* eq8o0+zn tgm wb)qofb 91ww0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends ofkl:e+u u+ 3f/ko hn7 d6wy9scb a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then releasfl/k7cnu+uo9s :dbh+6wk 3ey ed. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tigo6st0bt5n .ry xg u;e8htening to a torque of 38. rto6b eyx05;8u stgn $m \cdot N$ 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 10.8npa3ifl/+ 2ioed u9c 5-kg sphere of radius 0.648 m when the axis of rotation odi/icp +u2a93nfl5eis through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycl- i(abt 2hve1ce wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mas-bc(21 aevhits 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 tlp+ nuby4:h 6a horizontal circle of rayp4lh+t6n:ub dius 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 co1,:)ccjo g3 uq:g vmp1heg3einstant angular speed (Fig. 8–42). The friction force between hi1cv3g: p1emqh gu j3og :c)e,er 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; qen;ka3giv oed q50: of the array of point objects shown in Fig. 8–43;a 0nkg5qvei;qd :o3e 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 consi+o8xgr;gmfkl fh v;3(sts 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 the correct (c6:4sus+k p6/;xs 2dvta bkv3 hsfgt 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 32 rpm in 5.0 min?+t36u6sd: psh/ats(kf4 ;s vc gxbvk 2 $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm anu tzrc qq0s6a./ y0i2zd a mass of 0.580 kg. Calculate zy0.i0scqzqra 2u6t/
(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, acc pec 3mwooy/c2tt,l b()y );jeelerating 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 tangx(foc2 u f5nux72 e)jlentially on a small hand-driven merry-go-round and is able to accelerate it from rest to al) jx2ffu7enx 2u(5 co 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 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 eventually brought-.ny .sbh at/g uniformly to rest by a frict a-..st/b ghnyional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball ;t.am rgvb 1p.q)s/ppat 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 throg9:nao/ 3bh/7t.u sno xz6 lzdwn solely by the action of the forearm, which rotates about the elbow j/s xbdz3uog6:a. 9/nzt7 nlhooint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a linrt/cef;e,pa 6q8 (djtm1/ yong thin rod, as shown in Fig. 8–46jcrqd/mtf ;t(, pny/e 8a1 6ie.
(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 mwa90j oxkkko8(7d qsu,n. t3r asses, $m_1$ 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 fucn (/rg 6ayr5mll turns (revolut rn6m rg/a5(ycions) and releases 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 momehq7sr ;;.ihhg( 4xfgb nt 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 ao4cm 76v 9yma9dm*4 vkpd*rv 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 slippiox 2 6g wfdsm:t 5a*sme3itu.;ng down a lane at *;ued iws6 amt5m3x f2 .s:tgo3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic0fjxfv;js 5gz :bms15 energy of the Earth with respect to the Sun as the sum of two termz5f vsfbxj: g01m;5 sjs,
(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 anex.4cax.gf+j(ip9s ilzy 93dd 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 cylinder4 ysil faizj+ 99egcx3d.x(p ..    J

  A sphere of radius 20.0 cm and mass 1.8(ocu q): vwslo2tvpn6 3z p80g0 kg starts from rest and rolls without slip3t2 wo qco6sp( ) lnuv:0vp8gzping 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 fall and its arre- iz*3jt)lowe - *jraz)rite3r end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating (h.dhjor2o8nkn2 wrv 1;d /nion the end of a thin string in a circle of radius 1.10 m at an angular speed od;1ko.d no( hi/r jv8wnnr22 hf 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentummc5;9k4hi codz g z-t0 of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at h9oz5c- i zd4;0 kmgtc1500 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 du ldx+ mls4.:xwvu8(platform that is rotating at a rate of 1.3rev/s (wl+:d4.xv8 xu dlmu sIf he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of inertia bif9fi k 8vci(d3;b qf,y a factor of about 3.5 when changing from the straight pokf3i(f,;i9 dqi8b f cvsition to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotat;u, dkjvzz)x ) 6f8uxbion rate from an initial rate of 1.0 rev every 2.0 s to a final rate ; v dk)u,)zfzx 68ujbxof 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 arobl5xz5ou*hh 4 und a vertical axis through its center at a frequency of 1.5bl4zu *hx5o5hrev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure s 8j lrj r3 ,vv8*2ic,(ee8tbgxsexw6b kater 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 tha 52wygc9 3a rh,qrscsj ufe l,-,k78ge 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 n*c.v9;5obs;e de cd oof inertia I is dropped onto an identical disk rotating ;b*v5o;e9 cddn.esocat angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.nsr .p0 8 s4ns3dbltn+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 centeb twp4k6+g1o vfl17ndc 92x ter of a rotating merry-go-round platformw1vl7t61 ngc fo94 ptekbdx2 + 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 freely with an a,33akx;(zurie6 qz c tngular velocity of 0.,3q t ;zazi6(rcx uke38 $rad/s$ 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 3wjbo3j+o 5 ppwxs *:kinto a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radwpo53j*wboxp j :3+k sius. 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 g/kxd/rsi e)m52w;y *w/eosy winds 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 )bv0g8v-nqrfu + gtv*$ 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 witgm4r7gp u4z3 n63azxcg h(b* shout friction. The moment of ine 6bnhracg 3z7*34g4gm(xus zprtia 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-m diameter merry-go-round turex(3m o5oksxekd5 ,b, ntable thaeme5, (,3ksxbx5ook dt is mounted on frictionless 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 rom:)c c9ou dy(7mu1jc*w jplr;pe lying on the top edge o:9ycumcu7;cpdwo r *j)jl (m 1f 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 such that the same side always f iwx6ifqt+6) jaces 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 Moon6+txf6)i jqwi as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ratml;onnp:2+qr:*hu rb iux a 8+e 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 thetoc 2fkpg ;i1pj0.vst 8*jez9 shape of a uniform cylinder of radius 0.20 m acquires * ogpzs2;fije89 cv 0ptk.j1ta rotational 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 0.050 kgouduk 3/rj:7f60um czj)4sjb 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 calculatrdukjjuj)s :uz m0 f63/ ocb74e 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 i9y 5ajy/5dohlprd)n/j4 733fwi igb ps the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, b vs a9f b;hloml-0q kuaqeo mc4zh014y)/e,0cut 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, q klbes -0fo0;lcy0m4 zqucva,e )a14 ohmh 9/and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-polbh,jc b /1 5jtzd;o3/9sqxczxlution automobile is for it to use energy stored in a heavy rotating f,x3x9q /oz1dc/jbc5tz sjh ;b lywheel. 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 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 illustratnb9ueg/ 6g-v svuhlujfl/s(d 0f:-w 1es 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 horiu.+l jhidko44 zontal 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 im4e-c,* kl r-muxt7k freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held hm*e-t xluk ,imk7rc4 -orizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radiuskyg e oqw.,gd xh99x51/e) yhf R. It is standing vertically on the floor, and we waxy1.hdy5xh9, wq og/9gk )eefnt 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 has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is maki/-lq xskpfb sti4 e59pc )q+-rng a turn with a radius The forces acting on thxepc bkqstls/ pr+4 q)5i9-f-e 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 1.5 mq4bx4zdzu. n(*/ jdesz ps1 ,d 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. Whatu zj.zq b/d4,(1 x*4dssep nzd 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 solid cylinder and her arms as thin rods, *nvx ahr7 s)drz0w0 s(making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightl)*(7av z0r0dhn rwssxy against her body.   

  You are designing a clutch assembly which consists of two cylindrical pl5vhu+xe(8jtuv- :kt nates, of mast+junu 5v8tx(:-hv eks $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 h:he)d 4t g8ior rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop withouthiet4:dgh 8 )o leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not ass,xfo85ct- ik,ardf qa ggw3c-:w h,x3 ume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the c/u)v9 9qq:ee(cuky db)o*vg x ar reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acqude9v) c:*y /9q(xvk ) eobugceleration 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