A bicycle odometer (which measures distance traveled) is attached near the w46 u;a n ,by(mlshn )+zmzq(hkheel hub and is designed for 27-inch wheels. What hap;bh) nmlqz h (y4( kn6m+s,auzpens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angularnzjjhj9e 9-h1iirbx. -r.h 4 n velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does thei x-49njjbhhi1hr.r-en. 9 zj 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 demajz5w/*q ig.zl+uw xx55d)l scribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a grear,u hnymm58 w xnaz)2: 8jmcv;ter 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 a sit-up with your hands behind il )5x p9*tiahfrgac -726kqv your head than when your arms are stretched out in front of you? A diagram may help you to answer t7ilxa ar-9 v*gf2k) htcp6qi5his.

A 21-speed bicycle has seven sprrmop 4+-tfto)skz7ai 6.9hq )yltd+jockets 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 io lyok)z-dmph+4j).i +f7t 6trq 9stas it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend o,.lrrkgizo3n . gt+l 4n being able to run fast have slender lower legs with flesh r ,. gtrk.lgzno4+i3l and muscle concentrated high, close 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– 5 8yzf hfejx 0jo42sl1sq1elb *c2c*b35) carry a long, narrow beam?

If the net force on a system is zero, is the net to f3e ,vp eagls:xnnnczfx +r;*v56x0-rque also zero? If the net torque on a sy5n;-xlexv e+g*s fn,:xcr6 nz3p0vfastem is zero, is the net force zero?

Two inclines have the same height but make different an 6 ,c)feig75i5j) ovpg1vg robgles with the horizontal. Thec)5i7b 1)5govi, ggf epvj6ro same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simult:1xqp vuk6at)c k:ai6 aneously start rolling (from rest) 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? Whichku6x)::citq p akv61a has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same r0yj.4 hi orkn8adius and the 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 greater total kinetic energy at the bottom? Which has tirjo48y k n.0hhe greater rotational KE?

We claim that momentum and angular momentum are cons z0xy4abmv+:ef+3p + fa qvux(erved. Yet most moving or rotating objects eventually sla ufyvxam+ x:p3 bzfv++e40q (ow down and stop. Explain.

If there were a great mpdy ;2vb kx.i0igration of people toward the Earth’s equator, how would this a0vyp ;.k idbx2ffect the length of the day?

Can the diver of Fig. 8–29 do a somersau* yix5zrd* uw0)rui,zlt without having any initial rotation when * wir 50xd),zz uir*uyshe leaves the board?

The moment of inertia of a rotating soli,-gw ymqq-6mi4q m*epd disk about an axis through its center of mass iwp-q,i q qm *my64meg-s $\frac{1}{2}WR^2$ (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 sittin +uthuhswjx+0y7 9li:g on a rotating stool holding a 2-kg mass in each outstretched hand. If you sshw+9lhxt0iuu+ : 7jyuddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical)jlfb7ha wy4, and have the same mass. However, one is hollow and the other is yhj4 )bwfal,7solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points wesfci4 ecu-,: q4 i u91c9v5sk;aefptl tt. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describetstq fa9; :ec f15li 9e4u-u, ivccp4k 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 f ;hbf45 b:al z:a,sstqreely rotating turntable. What h:bz 5bf,: ql ahast;4sappens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw ittq //c3 ( 3uhnx )0ji4ydbeckh quickly. As he throws the ball, the upper part of hiiud(b)4hhnqk/0 t /c3xcey3 js body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momenty/c g.li c9:lwjrlm7u +wv (ji-thb1 +um, discuss why a helicoc h.y:(l1jlitw9g j i7+r-/lw+u mbcvpter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following an- atcx72d,)ken ;/qc baa km0wgles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of4cgsz()6msgv3crkt3y 6vx:b an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diametertcv)y(4 rc 6 s:3m36ggbvxkszs (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon,sr vjz/i2/sozc m.x):/x ,uza 380,000 km from Earth. The beam diverges azaz.s,/sc xr:u)2ox vm/ z/jit 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. When the motor is turned y(dr/d smem;rj:*u s7xo f-qis6v e ;4off during operation, the blades slow to rest in 3.0 s. What is the angular ae qj/s:mr i67-xeydd o *; fusmvr4;(scceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m)a 6gnyt7 i5cx to another child. If the ball makes 15.0 revolutions 7ctxng 5ayi)6, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km0db.;ck nlxwqfl7 ;e6 . How many revolutions do the wheels makek.bwf0e cd; lxq nl;67?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotatcf+r38e+ b.b,gyngf pes at 2500 rpm. Calculate its angulacpb+geyn3fg.b+8r, f r velocity 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 ingcbt 2/v*ufyub;(6 tk 4.0 s (Fig. 8–38). (a) What is the linear speed of kt ;/bubf*u2t( 6cyvga 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 o1:7hy qa: s.wht r;(je1m2ivux+ sybvypdn29f the Earth (a) 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 tm d8xtwn +4 qzlcje):i6m49 zo3sc:t 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 uxro+8:gl8v+w ql 67;gcyi exrotate if a particle 7.0 cm from the axis of rotation is to experienc8r7:uqvg6x l xiy8+c;g+e w ole an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130::,hi..+jztdtf p r rd rpm to 280 rpm inr rpz j::.,thd+dt.if 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius p/y/ xwg,8.fr7 2jp mmxv2v ll$R_1$ 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, s 4cuxg9;yh,a astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min tim gcxa uy;hs,49e 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 1/h rpvwr)0rrza /d: 3p-d zd(gcmjt 905,000 rpm in 220 s. Through how many revolutions 3r/0jr )09dphmw z-rg cd(/:ad pv trzdid it turn in this time?    $rev$

  An automobile engine slows down from 4500 nrfa z. a2f*v8rpm 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 highspe*; uzwg(s . f*g6r px3irwlw,1iper4red jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its wp prr1i34ri6 grw (fgw;.es*xl*u,zfinal 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 diamx0l+sqf x9 ,cqdsx- 0jeter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of sxqjdx 0sfq-9c+0lx , the wheel have traveled in this time?    m

  A cooling fan is turned off when it is r,y k*9, sa8t61p 8;auo omdmknbxyji6unning at 850rev/min It turns 1500 revolutions before it comes to a sto9d smy 8xjp m bo*1y u,n6a6,kt8;aikop.
(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 unifor6j k +n)p6oe2iam2soq mly from 95km/h to 45km/h The tires havei2oj)ma6qs p2 n6e+ko 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 zu4q*dg05 ;.mddsf*a)w ywa; wh clg .revolutions as the car reduces its speed uniformly from 95km/h toqw;ymdhsd;g.a*w .)w dgzu0*cl 45fa 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 puts all her weight on,)jaujk 6 l4ao v:b9)wmz.fn,24 -uaemfwsu l each pedal when climbing a hill. The pedals rotate in a circle ofajlamz2eabffjmv.u 4, n:s )9wko4)w -l,uu6 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 pg1x-xvi 1eb 6ig3. lz55 N on the end of a door 74 cm wide. What is the magnitude of the tgxlb .6eg1 vii-13 pxzorque 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 the a 8pfth*/rb-bdo)r h2 jxle of the wheel shown in Fig. 8–39. Assume td*28rrb fo p t-bhhj)/hat 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 tr-kx1 gvo .s ovli852zo the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate t5s-k irvo8 1 gv.xz2olhe magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to amvhxaod : 9ixvtn,8p* e b2:t4 torque of 38 :dbi t49,2mxta:n ovxe 8p*hv$m \cdot N$ 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 y(-ds u3u // e4hoyxdg10.8-kg sphere of radius 0.648 m when the axis of rotatih/d geuou-(xy dy43 /son is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 c0cqkm1u6 e3i*wqap5q m in diameter. The rim and tire have a combined maseq*ac0i k3m w65q qu1ps of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a h 9g1 ;sl6u wtfctv)p3norizontal circle of radius 1.2 m. Calcul; w 1g)t6ctv3lu npf9sate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angular spgv6g8 ejn 0gs6exakk gq9h;.5y 4 jgx8ie7rc+eed (Fig. 8–48qc 66 a50 9kjgi e4yregh gvge87j;+xxksng. 2). The 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 objects shown in ddk8i 43i .jp9,w6krdsey m*w Fig. 8–43d48jr,.w k* 9iime3pkdwsyd 6 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 consists of two oxygen atoms whose total maotn/o i ns-.ygd(rs2q v +)+z d j,7rgqxr4cp:ss 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 i +rml;r:h0pacorrect rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the sate0 i;rp+hl rm:allite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of ;xpusywhtn0+5)n biil (8 9pu8.50 cm and a mass of 0.580 kg. Calculi x5pnb (h;pw+9yil0uun )ts8ate
(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 7tj,ukc 4a;n-zjp5a.lpzm-r y),r xi bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a smxssg87xy5d ejst. f-:all hand-driven merry-go-round and is able to accelerate it from rest to a freqejs 5s d.:xx8t7gfsy- uency 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 ubz16 ) 7lu -kqsp :hskha+156lrpfyaeventually brought uk : l-p zy66rqu huk5s 7sap+ba)11lfhniformly to rest by 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. 8–45 accelerates a 3.6-kg b-c zrz/ylb4uu llwbh 9,l,0;xall 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 tt.;vfna 7hduq/dn+ qc 9box3+hrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. Th;qoc9.n+/q ubh ndf3a+v dxt7e 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 consi1 h269 dbopc 6l*alqmadered a long thin rod, as shown in Fig. 8–4l l6c6 oq2*b9mpaa1 dh6.
(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 twyl tb1 cy5, mjdsdqw419ch- a3a:4wbto 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 hammerpd c:+k-7 k6.w*c-cv np lelnf from rest within four full turns (revolutions) and releases it at a speed onfevnkcdw6c.-k *l+:-7pp l cf 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 0 zp53q bnqo-ji1q c+(sc 6zgxa 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 developwiielon+qh.,/b 54 5i 3hcahjs a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cmrdf)zl3sqx/ qvo -*)y rolls without slipping down a lane )v lfz oyqxsq)3*/ rd-at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of gx+sylwe9. us w g62g-the Earth with respect to the Sun as the sum of two g6su+ww-yexg2g.l 9sterms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much e(qk q1pcdh9.net work is required to accelerate it from rest to a rotation rc .9dkp1e(qqhate 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 )2n( q;tf ibf0yb:6:+1ytgwagqnxk pkg starts from rest and rolls without slipping dowtb: f f1wn:+tp ib0yxky(n2 6;gq)qgan 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 o t7,rd8 7lr kdpn95lh:fh4sbto fall and its lower end does not sl 7rf 4l rdl,:h7nhpt958dkbosip. 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 on the e vp 2w/yu6c6mbf+it 8gnd of a thin string in a circle of + bt6wiu2f yv86cg pm/radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular moment7zlk7ry in9qjv7: xi /um of a 2.8-kg uniform cylindrical grinding wheel of rj 977il/vynzix:r7k qadius 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 uk.y/8( )5o*sazmg 2d httmexa platform that is rotating at a rate of 1.3rev/s If he raises hisho .5uy g e*/tdzm(2t axsm8k) 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 inertik4q) ez/ul) rma by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s)) zeklqu/4m r 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 b-8r:rwn.t5 6cs78 nu et/jso tb 6zpxrate from an initial rate of 1.0 rev every 2.0 s to a fina: s-tctr tujwb76 n x6e5/brz8s8o.pnl 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 3pqr -hylq63x around a vertical axis through its center at a frequency of 1.5rev/s The wheeyq3 pl-q 6xhr3l 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 mz+d3r)tt o yj pak 5rz--cfe36omentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momen2 s n,em)e7rlvtum 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 ineethwiq0tewm)s 71p:/rtia I is dropped onto an identical d7mpq: )ee0wtw t /1sihisk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.u v/uedk0us ;+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 platfx :lg9f /e7vrxorm of radius 3.0 m and momenx: g9 7rlfevx/t 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-gofj5xzt.ok ,n4 -round is rotating freely with an angular velocity of 0.84,5zt. xfonkj $rad/s$ 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 col ;vx,y:nbi8 ijls0d sl;*fgl h1 6a.nulapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0%vd0h:lila* 6jxg.y 1sl8f;s uinn, ;b of its existing radius. 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 involv:;io:p8 b+ rd)cupe7(etrt hhe 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 y:0e //ddatw y$ 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 roto ry*y,uz d8-cq05pv xate freely without friction. The momentyrup*cd05 8 qyo-zv,x of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person s 6mtkrd0rhp6va n:pid(r) .f9tands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a9rr) vd0(f dr ahmn.t6 6pipk: 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 z5ah7s9 k (gbjthe ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s centek 9(j 5s7gazhbr of mass move?

  The Moon orbits the Earth such that the same side always faa9 s q4/-uuiuices the Earth. Determine the ratio of the Moon’s spin angular momuius 4i u/a9q-entum (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 fromp3j5o;rm8xe)je/krm6v zyu. z1u k1zz k87 fj rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acq;td6efbxh7 4f uires a rotatf6 hxdf7be;t 4ional 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 dis:r7 )zwzxkq+ aks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from7x)q:zrz awk+ rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the a4gy1oe wq9 pa2 o3 +aae,pd+ffngular 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 massslcy*l;+4pg 6w 4 o4qzphe )uu 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 4u64zuhcoe4sp )y+l p ;gwql*days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energ ff5pj ilm:y+ d7*i 04k+mq72rltqdvsy stored in a heavy rotating flywheel. Suppose such a car has a total mass o4 0yiqplm m+dvrti7qjsdk*l2f5+:f7 f 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 illustrates bkdr / .ydh jkf,**6aemdw39v 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 spkqc64 po2wrcv; x0h q.eed 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.eqyg;ns rp5y /8; m+dys tl(6(rlbiha6., 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) the linear acceleration of the tip of the rh b(8yrpr6/lnqm t;5adgyy(;i sl 6+s od. 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 havq6g41 -g zotns radius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will14go-tngv z6q 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 flatwyhq-le;;zfc f171t e road is making a turn with a radius The forces acting on the cyclist and cycle ar1c;w17tqeye fl h; z-fe 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 lengtfdk nh- ql,v3kxmpm0o,14cy2h 1.5 m and begins whirling the rock in a nearly horizontal circle abovecmkx,fhq,4 d3p- nomk0 yl21v his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, o d/lz7a e/ 78*hzesyumaking reasonable estimates for the dimensions. Then calculate the ratio of the angulazydo 7z/ h/a7lseu8e* r speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical pl e dwpv*yx-9a5ates, of mass -dawp 5 *9yxev$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rougyo3cs8 3jd/yv(hr /2 kbkh lb+h 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 orb d3 2schlyv/ k8+ok/3hjby( f the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not a )h y*g*c(hfkbssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolut09tqh :, p f6p6ju.xrze62ncbx5nye k hg w8.tions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have9g2nq6etpw y5zxh.cb 68jne u60t kh f:r, xp. a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s