A bicycle odometer (which measures distance traveled 8spo +zj9y5yq) is attached near the wheel hub and is designed for 27-inch wheels. What happens iqz5yopj89+y sf you use it on a bicycle with 24-inch wheels?

Suppose a disk rotate o4z7lh /rxks+s at constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of eithesoz+hr/l 7kx4 r component of linear acceleration change?

Could a nonrigid body be described by a single value of the angul9 24cqkz6kbj1ctuv 0car velocity $\omega$ Explain.

Can a small force ever exert a greater torque fj v4n2psn8)kt;hs8 uthan 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 your head than w* tn:gdbgf c1,hen your arms are stretched out in front of you? A diagram may,1nfdc b :*gtg help you to answer this.

A 21-speed bicycle has seven sprocket/)uw4 tjizl7 k0zn1tds at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocuk 0/t4 zjwt7zn1d)ilket 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 have slender lowe0yj aqpa-7d2 lr legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is adva2lyd7aqjp-a 0ntageous.

Why do tightrope walkers (Fig. 8–3 .cqyym ,piiqgm /4/;k5) carry a long, narrow beam?

If the net force on a syr0uju8zo 4trfjc; f)(:bk )fwstem is zero, is the net torque also zero? If the net to04bjfuk ;jft :r (cz8)fow)urrque on a system is zero, is the net force zero?

Two inclines have the same height but make dyb:5wo-3zwsyn z+8 hv ifferent angles with the horizontal. The same steel ball is rolled down each incline. On which incliby sw :y8zw-+3n 5vhzone will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) dowl7 ;0s tlhlxed(,lhw2n an incline. One sphere has twic2hld t(ew7h0ls;l ,lxe 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 energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start from 0 ewgpsa: 6d a.*jgudkz228fk p9, bzarest at the top of an incline. Which reacheaw6zk2b:j k2f. d,uds0gp9zaa8p g e*s 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 angulam dhhheup3fx.;7 4es* *j+kpsr momentum are conserved. Yet most moving or rotating objects eventually slow down and st;s h+kepf*3xjuhdm s *p74.heop. Explain.

If there were a great migration of people toward the Earth ,rk.(bte-kt4n ifh+ z’s equator, how would th+ tfrit kbe(-, zn.hk4is affect the length of the day?

Can the diver of Fig. 8–29 do.anpb * 35rebr a somersault without having any initial rotation when she leaves the board?5pr* .3 ranbbe

The moment of inertia of a rotating solid disk about an axis through its cenhvx )u8b if nmjo*6/(pter of mass is hxb8i v ()*jnp/u o6mf$\frac{1}{2}WR^2$ (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 holdingfv:6tmg4t jp1y0r /*ly8dj k o a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angulajo 16ry 0 k/j84l fgvm:*tpdytr velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, udn*e-x*, zgluh y 8(kone is hollow and the other is solid. Describe an experiment to determine whidu-(xu*ghl8 zn *ke,y ch is which.

The angular velocity of a wheel rotating on a horizontal axle points west. 4 w9gqbmyueww e88u*+zq a5u /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 at the topw/ 4aweu59u mye+8b g*quq 8wz of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotaty4ydob23u* w rg.1tmaing turntable. What happens if you walk towa.ayo1tgbm4y u2* r3wdrd the center?

A shortstop may leap 6pgbtgi9 /ed5+ibs*:hsxyo8 into the air to catch a ball 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 hip/b*yg+:5xi6s dphgbosiet9 8s and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular x+c+mjikflp:al: s jm588zb4 momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operaa zi flpcj+ + blmm5s4j:88x:kte to keep the helicopter stable.

  Express the following angles in rad:nll3h:sjm g.zl30mi ians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coyta+zn-zpnq7 ko- y )w*v v1;kincidence. Calculate, using the informat-) 1ynzanyko*wzt7 pq -vkv+ ;ion inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beapp svavui:iw8( eb. ()m diverges at an av:i8ba( p.spivw( u) engle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the mvd(rq .yf --njotor is turned off durin(yr.f nqdjv-- g operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level flo;v9 bn5odtpf sq7m89 uor 3.5 m to another child. If the ball makes 15.0 revolutions, what isfpv5u7m qbo;st 9n9 8d its diameter?    m

  A bicycle with tires 68 cm in diameter travelbs+lded j) vga 0( cfu7l :2sa.fq;bj-s 8.0 km. How many revolutions do the whee+jfa2(v) 7sddqsjbue b:0c.f- ll;gals make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Cal:0rfvb/f4vgpjsw cq/ (z n m-0s(b-n* oijyj,culate its angular vegn i-sz( j/nf/ psr0 f4vm- ,job(w:bj0v*yq clocity 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 skhrq; )u1f*r j (Fig. 8–38). (a) j 1qurhr ;*)fkWhat is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in it2c,dq vx luv8/f9 o+wqs orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear s-j5)h r5ezb -nesckrg)1ov w+peed 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 centrifuge rotate if a particle 7.0 9f2n nne +xnq8cm from the axis of rotation is to experience an acceleration +8 nxn efnq29nof 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130i)5 ows bb3 i/,ia8tci y.zbe9 rpm to 280 rpm in 4.0 s. Determines38tibb/y)5 aw,e. cb iio9zi
(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 uut6i0m99ntmcs : c g:$R_1$ 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 spacecr vh7.j8qct0;u 5ih1jstb g 6sqaft put themselves int .squ g1t0jhscjiq v;t687b5h o a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 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 accelera; v;y -z 88rk/ldkaiozar6b:etes uniformly from rest to 15,000 rpm in 220 s. Through how many reva vk r6oz8: de;li/b ark;yz-8olutions did it turn in this time?    $rev$

  An automobile engine slog n f4pd) ,lghr 84i:wmsbw )mwj1 lm.,mr6j:yws 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 highspeoywjgb+ 7 he35ed jets in a whirling “human centrifuge,” which takes 1.0 min to w +3e5h7gy bjoturn 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 diametl44 lowmd t/uf.cpj 2w371 jjder accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. Hcdw j.jl3d fo2 w4lp 7j14/mutow far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off f)y (bt2p qew)when it is running at 850rev/min It turns 1500 revolut )fe t2)pywqb(ions before it 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 the car reduces itss5r+ ,xviog 4l-q.fay.*qcy x speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.y,var lxxs y 5-i.4f+*qcgq.o 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 revollthao(ue )3w: h.f kx(utions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of( h3:.f ( oa)htxkeulw 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 each pedrw.9qkt ov3+d 5rjixjy (,2mq x j(dh5al when climbing a hill. The pedals rotatvm rq o9(5tw dx25hjrq3idx.(+y,j jk e in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a for u//bnvy rd 3.tb462ei ffj9zfce of 55 N on the end of a door 74 cm wide. What is the magnitude of bj9ib 62dv4.rue yz / f/nftf3the torque 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 axle of the wheel 1*6/,wv 3xkj96h9eltj cmmecrw7 j fashown in Fig. 8–39. Assume thataemv6e 9kchjft*w 61/9jwx r ,m 73ljc a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to t (s9mi92uorjqf(ysb hobix,c /74 v+j he ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held ins, sbv4oriq(9h i ofj27( +/mbxc yu9j the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tighti+*wfl a eg;t+ening to a torque of 38 *gf+wlai;te +$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0gds c t5+iqi9(ippoo8d2-)xb.648 m when the axis of rotatioi+t bpi2-i9 gp(qcd)so x5d8o n is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. Th /ldh vjsg5 3y33fr/;mzixvt7e rim and tire have a combined mass of 1.25 kg. The ma;yfdrhgszj3 tv/7 v 3limx3/5ss 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 aufyl- ;eu1 j0-t52 lk) nqefqj horizontal circle of radius 1.2 m. Calcjlut)l-5fk y1f-;nq ee2u0jq ulate
(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 sp+lf f j)ci+ed(c( f(p1jfzz+i;/ wgt(e9qviheed (Fig. 8–42). The friction force between her hh+p f(+ +j)tv f ;1((wf(ezdezl/icf jic 9qigands 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 Fig. 8–4xtj).- b 1r:1i:irq y txvwvt63 jbv) trxw1i1xir:yv:-t t .6qabout
(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 who;,m2v4 cj37t ej zuvigse 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 ae v5b7h90y vfdt the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of 0f9 by v5dveh7each 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 un7,,*sz v. mmrpj;kbw zb zr.(qiform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calbr;zm,qzs pk.z,7vr*j .( bmw culate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from r 2 ci 3vdu3bc)n*rar,y3pvo 3aest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and is ( m pbuyypn*h3-ug8s,h1ut 8zh9 q.k lable 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 (eaclmuq(ytg zhnp p1,8bh*s8yh9u uk3 -. h 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 z97ho1 kdw:chz*0 eq( 9o8n gtg0nblq eventually brought uniformly to rest kw otndnlbzgg: 8zo19c ehhq0*7q0(9 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.y2(o478tza r5 w faung6-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 throwny,r,/,yu: yibs3pvvkl m ;ow* solely by the action of the forearm, which rotates about the elbow joint under the action of the tricepy: vv*wri, b3;,mpko ,y yl/sus 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 coz1wnj,( +njtbnsidered a long thin rod, as shown in Fig. 8–46z ,w(jntn jb+1.
(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 o/4xc y+t7 tgc:;hor dvf two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (r,vp qnpglo:;8+ drs5 qodc3bl++,lwxevolutions) and releases it at a speed of 28 wd,5b; ls:qv pqcx orln++o 3p ,d8l+g$m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment ouaayt: igfjb)ff1.2) f 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 t,g+xf2)xpfv3spu*hvg2ije-5 fv5 gf orque 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 c i7 ublr+z5jx d*vwbtn.e:+/ em rolls without slipping down a lane at 3.3/ jb 7bwdzvn.+t+e5e uxl*r :i $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as de -d,: oo1v .xrq-d17yvbxshthe sum of t qr:d1 7 e1oo,-vx-dsybd hxv.wo terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much neq;vkk/ ldfjerx 1(;no7nnz7)f a e07ut work is required to accelerate it from rest to a rotation rae 71q n;(v)k /e7j70n olfrxd uk;afnzte of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest . k4*7hbxr q,ff vj48kpepk+sand rolls without slipping 4rse*pv k84+bp.7kx q h,fkj fdown 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 s7 pg0me+c o)mutarts to fall and its lower end does not slip. What will be the speed of the upper end ocgmo7u+0pme ) f the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentu e/ tkbn bk(3-xs-8jsvm of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 10.4knse-b- j/xvtk sb(8 3 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of 09qgkidkb b, ; uug,b.,e-kka a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotatingib;, kg-9db0, uge.kku, qbk a 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 h 6zry )m tmju-au+zs ,ok09.j cenj6.pis side, on a platform that is rotating at a rate of 1.3rev/s If he raiczj ae -0tm9ur.6 u6zsj.nyk+m)po,j ses 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 her6vn gn w0;3ack moment of inertia by a factor of about 3.5 when changing from the straight position kvcg 06;wnan3to 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 rotation rate from ac v4 y;js2u.ykn initial rate of 1.0 rev every 2.0 s to a .yk usyv;42cjfinal rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertica3 )nw8mlyk z a/rm+m5ml 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 cent 3na m5my/8kl+) rwzmmer of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momont1 l* mn )rvk;bz(h/entum 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 momentum of frw(h gnn,s iqj(fw,, 4n:8vythe 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 cylind 9nb7qsuq-opd :vcn0;rical disk of moment of inertia I is dropped onto an identical disk dnupb; v9qs:7c0-no q rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ligx)+ci; 7agat 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 t8 u)puek y6 l.8wuc 7g-ut6vyche center of a rotating merry-go-round platform of radius 3.0 m and moment of iy e 6uc t w-c).vu8g8uulyp67knertia 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 free34czdiv o6a 1fly with an angular velocity of 016 3cfzv4i oad.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 white5u,jiy0t -q +m1qedec dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its exiduciteqmj 5ey 1,q0+- sting 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 involve winds in excess of /:6imj 7vdqbwbf ny- 5120 $km/h$ 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 0bge4 ljr397q by -rdn$ 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 platia)9(-ud 5e +5 rqscaen yp0mg0zhuch61dro( form, initially at rest, that can rotate freely without friction. Thedzeaocneu 9as(r0g ic1h0u+(mpdrq - 5y6)5h moment 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 st6(vzgc)08.n; wvsaanx gt 2ma ts,ma2ands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inerticwtm 2. v2nma a8(gsa6a,n);g t0vz sxa 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 roli71/ epk3ggdwe ni3+cls on the 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 i3p n 7gwe1cki+g3/edof rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the zrh/dz6f b ffz ub-ukj -j-,)+same side always faces the Earth. Determine the ratio of the Moon’s u- z,bfr-) kfjfz-huz 6d+bj/spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 f e9/oswi / tiu/ny;t-g 2a1xom/$s^2$ 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 iouf- ewe/ ;)qc:r0 gnen the shape of a uniform cylinder of radius 0.20 m acquires a ro :ee0ewqfg -/)o;unc rtational 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 cylindrixte w, ff3rj7ts t 32mu,k7v9rcal disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of it tt9 xtv3jr,uk2w3fsef 7,7mrs 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 thexdja vt*) jwm/, yc1-l 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,gq-aj3v)q kv+ but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days.kvqg+)jv3a- q 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 automj b wt u789ln+oo)m7ungfl62mobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass87 utg)+mlo9 fu olbnwj6n7m2 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 illustrates a*1suls/jc 6 rp jbg+9an $H_2O$ 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 hory:s5 do5luqg 3izontal 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 andj590okw;z ipnlfo 6 1f 3w.hji length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force ofkwn9i.p3 jlh ;wf 5oizoj10f6 gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius 50vv9rbb hylc8cap95R. It is 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. 8–55). The step has hei v08l 95hrvc9ab5pycb ght h, where h

  A bicyclist traveling with speekv44d0pu0 sh g.hpp5hd v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal forpvdh 4g0. pp0hk5su4h ce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 m1aj4o7 kkq2zp and begins whirling the rock in a nearly horizontal circle abo j4p7koqz12akve 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 bg dg o)i27ji96g kf-kwe5c6qmody as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensi5kjmicg 26g-kqgw o76die)9fons. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly wf29.c,xrrz v( cxyf e6hich consists of two cylindrical plates, of 296xy c. zrxr, (ffevcmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 looped3z v)/ lh8tumne0u 6xx rough track of Fig. 8–58. What is the minimum value of the vert0h/t8 ezn )ml6xuvux3ical height h that 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, but do n(mto:d59 mvuij,d9+z 7 bp vjtot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces ic td+i 8j905yen:xm u9- gmolbts speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tirc8- : mmtxnbje5d+09oig lyu9e? $\approx$    $rad/s^2$(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