A bicycle odometer (which meas7.ae ;fdz ld5dures distance traveled) is attached near the wheel hub and 5d. a;zfe7lddis designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant o: (bmusg/hj 0n+gbq* 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 m0jghq m/ +bbno(: gsu*agnitude of either component of linear acceleration change?

Could a nonrigid body be described by a sinv7w 9mdhv/ unw.xt q25gle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a lajz.hu be .bgo5 (u++porger 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 beh:j5odjj a3/b sind your head than when your arms are stretched out in front ofos jaj3db j/5: you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at t0ig1(n7 p s rjgs-4sybhe rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front spgs(i r ysgp47b-jsn 10rocket? Why?

Mammals that depend on being able to run fast have tl t.z xue933ys9.pnvm7nn -x slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis.pt-nx n les793x3n. vymt 9zu of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fi,.o +u qhhv-lhg. 8–35) carry a long, narrow beam?

If the net force on a systemqk+icm5a/ jxt86*pf d is zero, is the net torque also zero? If the net torque on a system is zerofxk /q 6jdm8i*ap +tc5, is the net force zero?

Two inclines have the same height but make diffs g5a t 91jkxvp0vo gk0nm895cerent angles with the horizontal. The same steel ball is rolled down each incline. On which i89nkjk 0a tmcv 5o1gvs 0x5pg9ncline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start roll nv gv+ag2urkz,5b 12ving (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? Which has the greater total kinetic energyavvn2ugb+1zr, 25gk v at the bottom?

A sphere and a cylinder have the sa*c9:z tdn2 +m,qpu mc r95apoime radius 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 the greater rotational KEt+au*9: mrc9m, iopcn2d5 qpz ?

We claim that momentum and ai2b 0ocqwdazju 8zr0sx 9(k 58ngular momentum are conserved. Yet most moving or rotating objects eventually slow sk9zu0iz 82rjdo c baq85x (0wdown and stop. Explain.

If there were a great migration of people toward vnopf:(o1w x.s-tu s) higj;9 the Earth’s equator, how would this affect the lengtho(.;uf x91s:o v) ghn-tj ispw of the day?

Can the diver of Fig. 8–29 do a somersault ze f(w:ndg*v u+6ay5qwithout having any initial rotation when she q65w*zye ( +v:dnaugf leaves the board?

The moment of inertia of a rotating solid disk about an axis through itkza u6s1e j.bxl)z.j7s center of maskse)6..alzu71 jjz xb s is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstr9 pjxa:*1 mdw1x,kg yj8e i0vretched hand. If you suddenly vr9*ad1xi wjejg 1 0x8y:kmp, drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and 7tovq ,ju29 i,-jvuby ptme53have the same mass. However, one is hollow and the other is solid. Describe an experiment to det527pt q,ymvte3vu, uij9 b-oj ermine which is which.

The angular velocity of a whuh.yl ya:h4 i,l, vp0irvlm4(eb:bx* eel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheeley: a.m0 l*(ihhl, ibu4,r p:vylxvb4. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating tur7s smge j8jvrq3r(79 sntable. What happens if you walk tows 973mrjs (7gqvr8ejsard the center?

A shortstop may leap into the air to catch a ball and throw it quick ) qv:p9cuol8sly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that hi9lo s:p8 uv)cqs hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law sm21 q af .vaoob,xrk/0i8j r/of conservation of angular momentum, discuss why a helicopter must q. a0v/rskixjomrfa,o 1b8 /2have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a)4n0k7y 1hlo xdls l;j1 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 coincidm(e) zd:sov a ak*lwx.y.6y/pence. Calculate, using the information inside the Front Cover, the angular d) :v . kazaxld6m.ew(ps*oyy/iameters (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. Thy .b: *n( owun)rk+uad2dx c+me beam diverges at coyw2*n ( xdm +udna r+b.:k)uan 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. When4;zy x9kivm1 3aib*cf the motor is turned off during operation, the bl x bc34izf9vm*k y1a;iades 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 floor 3.5 m to another child. If the bnlnxpdih w3b,/m( x0y5rcz +0s gf( w1all makes 15.0 revolutions, what iswwxm idc3yp ,n0blf/rx1hn0 (+ z5(gs its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutio *ew* zyqu ;7;v6z nx+hw.p mqjf7w-kgns do thwmxf6. w yg77*jqqwp -;zke ;n*zv+u he wheels make?    $rev$

  (a) A grinding wheel 0.35 m5v ;zy qx)cv4bt8u 1zr in diameter rotates at 2500 rpm. Calculate its angula uyvz5;4 czxq)tbv18rr 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 wymc:;o rur8 *wtiq3 *in 4.0 s (Fig. 8–38). (a) Wmq8 r*yc;t* 3i orwwu:hat 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 ,wy1zb35pa o olly 9v1velocity of 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 speha rd3r;r9 l9eed 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 particlte,xqr)w74eorf6; m y e 7.0 cm from the axis of rotation is t7tefx; eq6 r r4omw)y,o experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly aba at yx3qm0,m9out its center from 130 rpm to 280 rpm iayq,3m am0tx 9n 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 s nn .g*:-mort$R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put themselvm0m1z/ rm dog8es into a slow ror1ogzmm 0/d8 mtation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from li kc3c-e71b 04pkm rgrest to 15,000 rpm in 220 s. Through how many revolutions did it turn in t1 mp4k70ie blcg3 r-ckhis time?    $rev$

  An automobile engine slowoz1 d9 pga8;tq5ri;l js 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 highspeed jet2t;crr d8ou8c4clmg0s in a whirling “human centrifuge,” otr80rccu4 mc d2;l8 gwhich takes 1.0 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 unif:d+nj5u8 xidx1vw )vgg f2y+mormly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have travelenyxf: +vw8jgi)um d5 1gdvx2+d in this time?    m

  A cooling fan is turned off when it is running at 850quz3.nrr cy( ,rev/min It turns 1500 revolutions before it (3, q zncr.ruycomes 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 re3vtd4c9zh,q8 u bt4zeduces its speed uniformly from 95km/h to 45km/h The tires have a q 9eh 4tbu48z3,d vtczdiameter 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 as the car reduces its speed unifzu4 yag7hkazd fy7s -wzvql,8 2p j2.ds .r7:aormly from 95km/h to 45km/-v aldqj.47,8r yfy.z: sa 2sugwzz7ha2k7pd 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 each0 k3,+frbwew lt(vdh i3*.w: w,uavio pedal when climbing a hil,wfwv*o:t,0 (di+v l.hb a3rewk 3uiwl. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the enut9mvj:k 7* dj(t nt-qd of a door 74 cm wide. What is the magnitude of the tor t9tjn dj: 7-mvu(*qtkque 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 shown in Fig. 8–39. As) akpb7txtc2tm 4, nf1sume that a frictionb ckn t 4,mp12)fttx7a torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends 0n, jxbo7hh-cof a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on,0ohb 7jhcx -n this system.

  The bolts on the cylinder head of erlbvorq *oeyp9 p;k,f44 (*)oefi;jan engine require tightening to a torque of 38 q4* y4* kr(feoje ;, r9iflobevpo);p$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when thed656u x(cuxe f8gh,n g axis of rotation is through its ce e6u5c6ufggh8x nd, (xnter.    $kg \cdot m^2$

  Calculate the momenta5xx dlbix0,+ of inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ign ,axix+d5lbx0 ored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rot 7 n 7 m,lohpqqt;okfcq; yxhc3 t5ot75,:hh1mated in a horizontal circle of radius 1.2 mtt;37k7,yh qq:oloc1 pxh7h mfqc t,5n o; mh5. 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 constan( kvwe. ye0xclkz3(x,up7lh-s x n .0kt angular speed (Fig. 8–42). The friction force b,sll yep . -7kwk3e hx0nxzux k0.c((vetween 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 ivl+tuie5 ke:.es0 fd3z*lh * fnertia of the array of point objects shown in Fig. 8–43 affl0e3:*i heukt*+ e.szvd5lbout
(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 s g koaq i9uh+12uy0*0s+nj grmass 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 ram.h3wfl z7r3sth32 p30kvynq te, engineers fire four tangential rockets as shown in Flmhrs2v nf 3.yhk3p7z0q 3t3wig. 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? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a maszl ox)c.s6hn0s :8-grq 6ixb.nsf 5xynl2g9hs of 0.580 kg. Calculats y6hl9:is.g h0o q-cfb8gnx56n2xnsz. )rxle
(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 itjgvf(k 81d(zaj fdv2(* 3qsd w from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven (qz5rsi+ua u4ln6li;2wr;msmgd z, 7 merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5q+ ag,6w;lizrz u(;lmru7sn 52sid 4 m 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 ofn t+adte14/ ,fl 4cpcqf and is eventually brought uniformly f/,4n tt e qlc41+cpadto 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 bv:k*pjuoxa/b wj 5p 4:all 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 thrown solely by the action of the foreavouuypvb (b-7 .;v-fs rm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated unibvfs;u7 vp (bo.u -y-vformly 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 long thin rlke*u o0+ 2odfod, as shown in Fig. 8–4k* ul0+2ooefd6.
(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 tw3o7 (-p*cu ft- czskhco 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 0s1 sm oqvp*h,(revolutions) and releases it at a speed of 2s qvp0h 1*m,os8 $m/s$ 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 of inertia ofb8n*w () jevns $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine developo-sv. c5zr.(.tbhm :v ylycj4s 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 cm rolls without slippik bx*v.*d gq4qn -mj*3yc*trung down a lane at 3uby.j-gk43rq td *** c q*nvxm.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with resp4 q (5;crem,z xruqh;m;) 8rsynoxb9x ect to the Sun as the sum of two term;sb8(; r zyxqoxeuhc9;r,q 4mn)xm5rs,
(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 mu p+a o3 s.ibnj(7*a1xeuwfhs. ch net work is requir7ouxs.f*iajsa(bp3e h +w. 1 ned to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm aohc3o73 wd,a wnd mass 1.80 kg starts from rest and rolls without slipping down a 30.0hwca3oo wd73, $^{\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 (2serkg0s2pretc r on2)wfm9 8d,.ln fall and its lower end doesne etns8g2.r lmr0csdp9, )okfr2w (2 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 0.210p - 4zgtc0 nzqn)suqh+byl5o1skc 7) :-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an ak5)7)pc -40+cu n1syog lshqqzntb:z ngular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momen xz 5.2nshg-qgtum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating - zq.5n hggxs2at 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, rofg hd,-bc 0k.a,(5ruqi 8ojon a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotationd,b ,(aroi5u q8 r jfkh.0g-co decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the9kcx oa0h g *t)h2 rkv ln5),2.nkqahj one shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 whenvna,x 2tqnokh.r j)l52 9ackk h)0h*g changing from the straight position 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 rotatio zb:uwjj(9 l,yb6h0iec4: dm nn rate from an initial rate of 1.0 rev every 2.0 s to a final rate ofzj9mblb,4 :0ujd w6 :cy hi(en 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at a fr*:a( r ok6qzbpequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel.bq:pok (*az6r What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinw *jhnfo5 8.qbk*;jmn; s3ix hning 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 momentvn(onzxlzl(8 u t ,9 3-b9nxrxum 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 inertia3bce -m hhaex w(u. 66sqge:l-uy2ot0x hmh38 I is dropped onto an identical d:xh6m e2wys ml hu eo3g8-hu-b( h0q3.cx6e taisk 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 )x9k -qxl o .latyyt m6e-qf,*2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rota,e: (woi3eyaf*jz2zfe y m j.-ting merry-go-round platform of radius 3.0 m and m(wjyzm-i:ea3y . ef of*e2j,zoment 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-hxl5tr5shd ( 2o o(xg:go-round is rotating freely with an angular velocity of 05(sx gt:2x5ohdlr(h o .8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwar/ cypor;u0 0snf, losing about half its mass in the process, and winding up with a radius 1.0% of its existinnup0r c0s;o/ yg 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 e hofpuv*h(g) fg *ph13xcess 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 pt1nxtr3w; t9$ 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 ref33rbumd1 /r acw cr1-st, that can rotate freely without r1wdcu a/3c 1-mrbr3f friction. The 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 stands at the edge of a 6.5-m diameter merry-go-round tuq; gqqfge1)po+hv/l-ouo *.o i kqg2c,wa: ;brntable that is mounted on frictionless beov:.k1g*guoobw;g,q / oq) ia;+h qpe 2c-fqlarings 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 groundzbkcz z7 7w2 p9kqe4t5 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, h9 q ck5bzz4 p7tzke2w7olding 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 bj1:zj z/::6m fyfr* ombc(ut the same side always faces the Earth. Determine the ratio of theff*j 6mm (zuz ct::j:bb/yro1 Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rat)auz em0l( zy)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 the shape ,j+ csi0 cf;au2bvhb7 of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval atbbcfh a7js u2;,icv+0 constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical e5 t zcr;cl,;19zi azvdisks, 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 thec;, zle9vzr5; taz1c i end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheel ( b xtuixgr s+v.h6srp8pzp lf 510n665$\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, weco6q2e0mlyef3o- gt*y/ggoecs(z m s82 p47 mre rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neus6 37/tmoceymfy qsg cep4o02ggz2 8*(oeml -tron 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 use0 vej8wzgg6t98zno v2 energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needitz9v vnge6j2w8 go0z8ng 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 an:xc2 o4mdl / 9 ic29t4)aplgd megp5uz $H_2O$ 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 ond jo:bv ;ly::i (;iisr a horizontal 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 qw n2lvu/df s51, g:7bjxqfr,can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as i,j:fg2q 71/un bf5vdslqx ,wrn Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on twj)qk u+iev:6 he floor, and we want to exert a horizontal force F w:qie6kj)u + vat 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 making a t0w1(qq km()sf7qsup nc c ;(tturn with a radius The forces acting on the cyclist and cycle are the n7 qq)0mqc(;tnsft( k scp1uw( ormal 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-sp4 hcz82aq 0okg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the to82hp z4qacs 0orque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s(ju3x uew 33)r:wj /hsylqkmxh.x e(. body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstr.wxs xu3:l hy()k r3/e.xm(jw3u je hqetched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consit likz2h2e40 z;cac l*sts of two cylindrical plates, of masshcie l*a0l 24ct; k2zz $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 roll1 /m)-yzrtvx is 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 p1-x /viy )mtrzoint of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but db*r qcwmrj .:* :nrib4o not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spe5*f7afgkzz )y ed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. fa)kfzz 7yg 5*(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