A bicycle odometer (which measures distance traveled). lusdg 9iy5wv13tblyx,6w+ e is attached near the wheel .+l s16 bv9, 5wlwtyyudgxi3ehub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on thfa:qjphc , k ,x-0hr+0koz.fze 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 p+hzhkz.fq,f x0ja-rc ok0,:of either component of linear acceleration change?

Could a nonrigid body 1 rf5rp,-i kygbe described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than n44 wu.nf w9yea 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 thany ob , 0sox0 1xitmzf7d4 qkx0x.2+cab when your arms are stretc0x0 o.bb xyf4i1 sc7 z0 dxamkt2o+,xqhed out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and threeis(uq5edr2(:pxoc6 s 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 peda d(rec xp u52qs6si:o(l, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to pk7f2hm ko9xr+b * wq5run fast have slender lower 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 advantageou qmw r5+o* kfb7xp92khs.

Why do tightrope walkers (Fig. 8–35) cm9(cc:6x 6wlzwicvh6)5 y/-ya arojn arry a long, narrow beam?

If the net force on a system is zero, is the net vphof /7yby1mg( g )b)torque also zero? If the net torque on a system is zero, is the net force/) 1myb 7ggf()yb pvoh zero?

Two inclines have the same-i fdoam6qgb-k 5(mv9 height but make different angles with the horizontal. The same steel do6 qbv-afk- ( m95imgball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rsu9wf0 rinc z0/6t om l,;.mhsest) down an incline. One sphere has twice the.olr;0 wfc ut9/z6ss0mhmi n , 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/yvf m 73cigu3 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 gcf 3gu /imyv73reater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving ort: u)6j zpubl)ty2(ym rotating objects eventu2lty)u buyjt6)mzp: ( ally slow down and stop. Explain.

If there were a great7oz3 0hxzw-bouoyqh 1i1*hz8 migration of people toward the Earth’s equator, how would this affect the length of- hoo3 z1q1 ioby0hxwz7 u*z8h the day?

Can the diver of Fig. 8–29 do a somersault without havi + swnad*kx;mnv: msb3263 gkwng any initial rotation when she leaves the boardksanmvm2 bg6 kw +x*nw d;s33:?

The moment of inertia of a rotating solre :hmd7hre*:id disk about an axis through its center odhm*7re:e r :hf mass 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 holdingr8qdw:07, ig 3 sdgzf:dh3 ehw a 2-kg mass in each outstretched hand. If you suddenly drop d3dfg 07 gw:,8hirwd:h3ze sq the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howeveredf9. br3kr :mb3tpz1 , one is hollow and the other is solid.pk be1:z39r3fdb t m.r Describe an experiment to determine which is which.

The angular velocity of a wheel rotating *u/p c8ge0-qufj w 3bdqg+5 sson 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 wheel. Is the angular speed increasing or debu/jsq8 g 5g0*pqu-d 3sf c+wecreasing?

Suppose you are standing on the edge of a large freely rotating turntable. Whac1 -ta;7on ynzt happens if-z oy7nt1a c;n you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it qu z0cs03jgj--xz 2gpyl ickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 800xg3l-c2jspyz j- gz–36). Explain.

On the basis of the law of conservation of angular momentum, discus1wb+jf)t/p v .opafb)uagt 6/s why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second pro/1jata+ ) u p)fb t6bwv.fg/popeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30 jzyw29v93v1 xy9b3hayd 9 s4ygq5 cjs$^{\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 coincidenc1m9 9+-vp xt l)-w f5aaxhubgte. Calculate, using the info-al9 gu9t+v -)am1xtfbhx wp5 rmation 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, 380,0wrd 0 8f8,d sgn/9xafz00 km from Earth. The beam diverges at axr89, s0/gadzw fd8 fnn 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 rotatqkbfq 8w *v,aogce+9sk hg 32/e at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 vg/k9ebafs38wc+qh*o gkq2 ,s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a f6 z e/llvh4m 1n7 t*4e,zij:cmbyul,level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diam7m /tj4 ee,z4zh 1clf yi: l*lbm6,nvueter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutiog s7 + 5gjyt*i54rj uub1vf(cdns do ther*gys175+b(tj fcjvi54duug wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 253g3d( t /uuhxx gntb6800 rpm. Calculate its angular velocity in d ut(ut8gg6x/hbn x33 $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fq4za7-g 1byld ig. 8–38). (a) What is the linear speed of a child seated 1.2 m frozd-q 174bagyl m the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angulaovr1fe9cq, :g)v;ux/yw fy5g r velocity 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 speed of a4b 6wo 5fnw .jepejj:ny)v+.g 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 pa9 xe+y/en 9gfirticle 7.0 cm from the axis of rotationg +exyeif9n9/ is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates unifoyg3rz/ak+e6(nxqtr u el+2 re-- b7rtrmly about its center from 130 rpm to 280 rpm in et(rlr yb63 2t-ae n+r gx7-k+qz eru/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 radiusgp;zsjc w; u 09r,nos5 $R_1$ 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 ig1l( e*;4 0mz,-dlbjsapy ,gsjnwk,the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s enees gm0w4bl ylsjk n- ,*i1;pd,,g( jzargy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 2m l4kqf3)dg2ln * ,h5ki nxht220 s. Through how many revolutions did it turh5kllg*nnmht,) d4 k i22qf3xn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Cal1m vdv. 4j:.dec .8pq. u3 l:ppdc9porg 1pxzwculate
(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 .wfer jmm/qu0v ,;:wgstresses of flying highspeed jets in a whirling “human centrifuge,” /w,m.ruqeg0j:vwf ;m which 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 uniformly fr y9s0e/+x6iu- /edszmk v5qbk0cb-goom 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled i bx0 ie /ou6/ --kvebzs mk05dc+gs9qyn this time?    m

  A cooling fan is turned off when it is runninws fb-f;pwja9 +kyq5p; -/pi fg at 850rev/min It turns 1500 revolutions befo wqk9p-;w /pbif psfaj;-5+fy re 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 red ,ru4jj9x xz8 psdl4(fcf5eh :uces its speed uniformly from 95km/h to 45km/h The tires have a diametprxfs: x,dc5 f(lj ehju4z498er 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 revolution6 etff t7.jt2w/ytg(ys as the car reduces its speed uniformly from etjt /67 ty gwt2.ff(y95km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her 8(7q -vb fy,r(y feznlweight on each pedal when climbing a hill. The pedals b znffq((y8e-rv7l,yrotate 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 fo (zh r eadiggc0.7v*9urce of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force isv (g*au 0i.9rcegdzh7 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 whe94mcjvefn;l v:o b/.lel shown in Fig. 8–39. Assume that a n;. o/bcjf :vl4e 9vmlfriction 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 end m:p4gjjf++(t7l3tx o*u avqx s of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculag x4:j*x+7+jl3toq mp fuvat(te the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requires08 8p si k:0pakfr-jguq1yf 5 tightening to a torque of 38 8sf: ky5qu-jspr0 8 a0if1gkp$m \cdot N$ 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 t dg6alom0;m 4y 3xl1xdgm+s 4nhe axis of rotatio4sdngmgy d+ x3l14;xmal6m 0 on is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wf3/md utu:u) mheel 66.7 cm in diameter. The rim and tire have a combined:ufu/ 3dm )mut mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on ho (kt :i7esw6the end of a thin, light rod is rotated in a horizontal circle of radius w7h:k6ei(ots1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating sm+-. xbk:z;lv1phqdat constant angular speed (Fig. 8–42). The d1:qv l;h+ sxpm b-z.kfriction 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 i -/75(b2 ygra5rvgig z5amizkn Fig. 8–43 abou 5k-gzyivgrimazb2 75 g a(r/5t
(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 0asf i6 -ubgnq2e(l3uwhose 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 spinningpya uk31) utsri:f 86q at the correct rate, engineers fire fou1k uyp6ius: ) qa83tfrr tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mapns81 f o1i:w( zuvcvcu/-ww 9ss of 0.580 1 v:z /ups(1-vwww8ioncf 9 cukg. Calculate
(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, ac+ axfi4*be*xo celerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangjan :3krzv c:,entially on a small hand-driven 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 2.5 m and has a mass of 3rjn:ka :z,vc760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually mjf d+ h m9;(0dxis:gxbrought uniformly to rest by a frictional torque of 1.2 j 0fx ( ;s+gi9dm:dmhx$m \cdot N$ 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.a*12a3 yujx fec.f)fa6-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 thrown solely by the action of the zq)p e8:.2 loa pnkra2forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball r:.8a kpnqp2aozel2) 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 dg1f : 3ww1vt6g+ dah9sx-fi qcan be considered a long thin rod, as shown in Fig. 8–46.+ fw-i9 sdtqg1xwg3 h6:va 1df
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two m xt:i)/k +2kf 8ws 4lye0bwgo59nbupkasses, $m_1$ 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 (rev(v *ctiu4vi xr9tzd xbk;/3 u4olutions) and ctk/*;3z t uudv9 44(x xviribreleases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia 4nca9emxag*m)j*u6 vat hn8) 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 z2hl ctpqy6,1torque 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 slipr0nmdg0cv. j/9p(ooq ping down a lane at 3.j0qv/mo(90cpr.g o nd3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to2 a h1vsa:iy9t the Sun as the sum of two thta9iv21 y s:aerms,
(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 net 8y2f*d +ixf xxuiq10tfdurdd 9p6** cwork is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? u*x1 y0r2x8u*d6pxd+qfc if *idtfd9Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kgh 9vy2p+)j( 4/xu 0tqm l9mot8:dt 1bnkrftav starts from rest and rolls without s9a+n rk2uy htmtv91of v( ql:t8/t)m4j0xbd p lipping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall a0l h(,y hjn(powkf:/ gnd its lower end does not slip. What will be the speed of the upper en ph(l: 0(jg ,n/khowfyd 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 ballqcvy jitp61om3l- wp+ik :*t6 /pzi f5 rotating on the end of a thin string in a circl* : i+oyl/t5pq-fj 1vm 6wt3ipki6pz ce of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheel yehrp3em 3zd.ny ;mp+,* j-dl of radius 18 cm when rotating at 3;d-* m ehdprpelzy.,j+nym 31500 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 hib 63+qa9s wfbis side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms s+qba6w 3i9bfto 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. 8–2m z)v2 g gmry-;5(hk9eu ofx-+ pt3ksz9) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuckek-sm3 gk2;(hxg-v t ry o+9fzupm)z5 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 f*m2:zvreg4gn - p h+pyrom an initial rate of 1.0 rev every 2.0 s to a 4ppr+y h gg2nme:z*-vfinal 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 vertical axis through its a167z ) aes4qs ypno0pew,,ibcenter at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the ep zey,,)p0nwa1b assq 7o64 ifrequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skaterc06zr,d*n.xac ii n +o spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the jx1msgf r w728r2 xd1pEarth
(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 cylind2 p:jj4ap tbeixdo6.3 rical disk of moment of inertia I is dropped onto an identical disk rotating at ang op 4j3:ipdt jax.2b6eular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.9doze d n4j0k79tg v95.r rjkp4 $rev/s$ 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-r)ve-8 ,1vbie yf6ki ffound platform of radius 3.0 m and mo-) f evf16bi ve,ifk8yment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an an 8b maks :3lxwxyfj1)*gular velocity of 0.fx1lw*83bx:a sj ym)k8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losingm+2:py rtjel8 about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming 8e2+y:j rplmt 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 120f9 .gh( dh7szv $km/h$ 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 ( lg4- hf/itzd/ 5s2h7qaeh+swktrj6$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely wij/q296pd )2inf q t*j9q zxswwthout friction. The 6xfi/2wq29ts jq*9np qj) wdz 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 edz.yj)+j*; /u ffutby4omg.h,g+wq n sge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionlesyj oz/;. w)sf.t ,m*+f4uygnb+hgujq s bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of ropeq n xty)c.j9kr5q)lxxvh 0:/f4irz b8 rolls 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.)z5r/8 ktnc0bf9.qvji:qyh x )xrx4l What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. Do*yl 5 nzc+pt*svd6bw6wu 7h3etermine the ratio of the Moon’s spin angulvn7 *6plb3dotwzw 5ch*+ su6yar 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 q2p /l s2af*mzfrom 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 cylindeih+n g8x p; h7ew-7qlfxi+r95 kbkf-br of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular 7rf hq-ip8;+kw9b l +f5x-eknb7h ixgacceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.iid*uo 49rbzn -8di-5ygev* z050 kg and diameter 0.075 m, joined by a4 d*5zi98guyn o- d-e iz*ivrb (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 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 whjit, *z2*urehek .3jsrqjo(:fh58i qeel ($\omega_R$) 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 (k2+o,5b 33 xyurpjyxbrsg7 bas great, were rotating at a speed of 1.0 revolution every 12 days. I(o 33 gxrs5b+2ru7,bxpb jykyf 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-ro1r: *e idg-ipollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 k e*ir:i rog1d-g, 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 illustra67tulr87m9mtp0 tm fttes 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 (hooikyh(lj;eh 58y 1f8iksmb85 zp) is rolling on 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 uj1c a;l(on4g 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 ou o1l4( cangj;f 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 /-3dbdo/zqs t3 (wvnmthe floor, and we want to d/nds -bt3vz(qmwo 3/ exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with s4 7mhu4otg +nspeed v=4.2m/s on a flat road is making a turn with a radius The forc 4 +ohs74tmgnues acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a nj.n3c h).i um0.50-kg 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 torque required to achieve this feat, and where does the torque.3n).cu mhjin come from?    $m \cdot N$

  Model a figure skater’zo 82l/v323yvkagk7z3tfb mds 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 spinni3 kt87 2 3o2ym/vzlvfdzakgb3ng skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, oftd rd m(s0s(qzmt/2.l massmrtq dtm /0l.(sz2s (d $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Foquu+bk kk,jp . (7,ulig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it kpu +ulk7(j oq,ubk,.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 noqml u-5 1,bpdlt assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformvz-c87: ejttq ly fr tevjz8:q-t7 com 90km/h to 60km/h The tires have 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