A bicycle odometer (which measures distq-la3fk;soovdgjw -.- 9mm1oance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on mo3 9oqw a-j sdg;--kl m.of1va bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poitw(i.qaygr i5qb edx*jo*0 za-v1z:) nt on the rim have radial and/or tangential acceleration? If tv z 0e*)qai:d*(zri1 5-yatx.gbowj q he disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angularn58+ovmzj i qljmyk* 7ndjf(2 mng2*8 velocity $\omega$ Explain.

Can a small force ev1aw 5ltj-8nyy, xgc1/+ oxutyer exert a greater torque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands +c e xc)kg.60a5 lv.y7uo:j9 lsthfirs wv7w* behind your head than when your arms are stretched out in fgtsvix+y s7l0ol. a75j96cfhv w:we*)r k. cu ront of you? A diagram may help you to answer this.

A 21-speed bicycle has * +tgiz m5 i+rp.b4be6e23qe1 aiydps seven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small 2rmy5ez64 b i*+p iti+1q3eabpd gse. front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fa j84b6:2ngmoov -kkru yn* dl7st have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of m*o6gdu7k8 ry-bk n:lj4 nvo2rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) c(/7ojk ;cyhw 2iimduky*qmz(ov2zhl 8i4/k)arry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net3zsxgo2gy9: fxja ;too) uy9( torque on a system is zero,y t9 o)xua(g;oxy 2z osg3f9:j is the net force zero?

Two inclines have the same height but make different angles with the ho/km(056sfhnvgkqp 6 irizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom befq(6gs 5nhp /i0mk6v k greater? Explain.

Two solid spheres simultaneously sta1:b :osfgzrq7v p 9bn.rt rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energr9v p1oz: bn.7:fs qbgy at the bottom?

A sphere and a cylinder have the same 9cnbxj97uu i )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 b9x7i9 u c)jnugreater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conss3xz2l5adrkrxz1 + z8b :j5k cd)1ijcerved. Yet most moving or rotating objects eventually slow down and stop. Exp crrjkk5)+xi j:d zl1 8z5x cd13bs2azlain.

If there were a great micaaw0s2q :d -mlt*2crs229jx cp c.cs gration of people toward the Earth’s equator, how would this affect the length of thep2c*s 2 st0-scjcl2wx : acracd 2mq9. day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotat1g7dnukp )i4-qo xc vx;cx (7sion when she leavekxni4c 1xx sv7gp ;q-doc 7u)(s the board?

The moment of inertia of a rotating solid disk ab ys mr16 ,9,bb) sm*2yxtphvgyout an axis through its center of mab2)y9 ,t xrhg *s1ms6, vyybmpss 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 sittinvui6 :xs o72vng on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity incr2x6iv7:os vn uease, decrease, or stay the same? Explain.

Two spheres look identical and have the sa6yho ,a/ntxh *me mass. However, one is hollow and the other is solid. Describe xyh*/n ,6taoh an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. *p+wey2p;l9pcofn1x 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 wh;c*+xypl o 2p1npwef9eel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edgckg5vmb7a1o 7lp, u( fe of a large freely rotating turntable. What happens if you walkc57p mu1 vlfk (,abgo7 toward the center?

A shortstop may leap into t*v.micl7 0e/t sdpolq3f 6we4he air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates.o37c0fevmqw etllp*. 6s d/i4 If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of an+tuh)3e db1gx4t gs0 tgular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller ca u4b d0+t xs)gge1h3ttn operate to keep the helicopter stable.

  Express the following angles in w u t:-0laqy,bt,ks+s radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Ch m-,pva p. iz0jc,*u; nzz0mqalculate, using the information inside the Front Cover,q0pjn-.zmz vcahu0,;*i,zmp 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 Earty xowlt:h je++g8t:4hh. The beam diverges at an angle lwej hty8x4:++gh:t o$\theta$ (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 rpmcft 6y zm4w z2y,m9a3i. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the bladescz,mfmi4t 2zy6w 3a9y slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another chi5 4orkuohzo3il2y)tfk *hdxy1 1jvr3n8 s2 t5ld. If the ball makes 15.0 revolutions, wt 2ovl*k1hoh3 4)r18n yo32uxr55dji k ztsfyhat is its diameter?    m

  A bicycle with tires 68 cm in kyh . oeb d-40wb:cg2og n5g.adiameter travels 8.0 km. How many revolutions do the wheels make? 2-b.o40 .cgbghg a e5do: ynwk   $rev$

  (a) A grinding wheel 0.35 m in diameter rotates a*.lsx 4-zmhsj t 2500 rpm. Calculate its angular veloclj-hmx.sz4s* ity 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 s (Fig. 8–38). ( i*:k6kshapkx u9 5wk/a) What is the linear speed of a child seated 1.2 m from the center?:pikkhxkk5ua6w /s 9*    $m/s$
(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 its orbit around t +d3bzjjfz*n* he Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a 4k-gisyak:- j; y2ltvpoint
(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) mustb--7 s6 h1inanxl jig( a centrifuge rotate if a particle 7.0 cm from the axis of rotationx-a g h6lin1jnbs(7i- is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its centu;heqc 4 (n wd c;4(+ik bjih2j3prm3ser from 130 rpm to 280 rpm+2(4n3 icmqekj(rwsijh 3;pd4 u; hcb in 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+fnb27;amo jb-xd wk + $R_1$ 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.1epvfdgwohz7z g98w +:2ibe the Apollo spacecraft put themselves into a slow rotation to distg ezow2v+h b7p1w if8 g9:e.zdribute 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 rest to 15,0bf jr1,,b okc*w ;k6cb00 rpm in 220 s. Through how many revolutions did it turn in this time?,cfb k,or6; jw1c*bk b    $rev$

  An automobile engine slod. ho kvf.r74; siy:ijws 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 w/ opoq6wjq al-hr001highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through1j w-pr wa6/0qooqhl0 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 accelerzye .3jppg uc,sn*y-6 ates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of th,6zpc -en gjsp3y*uy.e wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at(5c0tc-o eb;:o f9cosp orgt l(+d 3qt 850rev/min It turns 1500 revolutions before itoc;tcc0b o:r+o5t o-( e(9spg3f dtlq 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 revjx(v4r32u zdjv q6u4holutions as the car reduces its speed uniformly from 95km/h to 45km/h jx4jv qz(2 uru46 3dhvThe tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces w83ux ssmb,. ,nyx mq9its speed uniformly from 95km/h to 45km/h The .m, x93umbsxswy8n ,qtires 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 each pedal when climbins eg5-iew9 gzr9s3w9 bg a hill. The pedals rotatesw3 r ibsw5g-e 99gz9e 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 end of a door 74 cm wide. What i9 pu *iu;bet1os the magnitude of the torque if the force is exertedbitpu;u 9o1 *e
(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. A 6z78ma2q3 h-8lvv;fyy web8,fjkrxkssume that a ;vjkby3 kv-f8 ,6ze8hamqr2x7y wlf8 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 the ends ofy ose ty h0n*4hj/v1;p8zr f7f a massless rod which pivots as shown in Fig. 8–40. Insy 1vhh7 yftjf 8 *e0p4nro/z;itially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylin xci-va wp,o y59v4mc2der head of an engine require tightening to a torque of 38i-xcvcyop49, a v5mw 2 $m \cdot N$ 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-)a sxrsx.,i*z kg sphere of radius 0.648 m when the axis of s*iz., s x)axrrotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in 3zuohf *(r9fudiameter. The rim and tire havfruh 9(zfu*3 oe a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a h3x c:7jip h8qeorizontal circle o3e:qp jihcx78f radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping aa*( ++lzf,oxk yy*p vj bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force bexya* fl (oz*ykv+,+ jptween 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 arra7i:g b6;sqi+f/ v (hei)td: cbipxs0n y of point objects shown in Fig. 8–43 aboqg/p i cbiv 06t;d):fhn i( sbeix:+s7ut
(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 cons02tsus4u i1wp fm+ew5hc 6waq/. 0iwiists of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning.y wov;u kk((a.*-,zcelso 2acp1sx t at 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 r u( l(zo v paycasswc2ek.o.t-;*1x, kadius 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 cyl7(yhnd j6l wq/inder with a radius of 8.50 cm and a mass of 0.580 kg. Calculathyjdwnq7/l 6 (e
(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 fromv 8 diqw(xgg6. 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 lq0c* c:.h x .b2babdasmall 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 760 kg, and two children (each with a mass of 25bhaabq *. xc0cldb2.: 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 atkcvrr1z6s 1r-d w0 rp0 10,300 rpm is shut off and is eventually brought uniforml0w0rv1rz 6-dk cprs1 ry to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3:k- yx4/bbyd6y2t blu.6-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 1bgxmip88) b jwht)ou*ty 55 eforearm, which rotates about the elbow joint under the action of the tri8*xj8b)to m 5)upbt gwi1eh5 yceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin ray;av6qn(0 cb od, as shown in Fig. 8–46.0a(6; yabvqnc
(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 ofwag9:s 7uj1cv 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 tl e 1 p6pu08, d+pp*-e;ptmpj4qoftfwurns (revolutions) and releases it at a speed of 2f optpm4p t-j p+ *ufelp6;0 8p1dq,we8 $m/s$ 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 inertiat2ve0en v3sp7 of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 2yew6lnqq)js) 1ldhp x kgn.8 1nns,*75mdp 1e80 $m \cdot N$ 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 sli-3yipkb jpg 3 +e2(nt++vkm.tfa8khg pping down a lane at 3.ti 83j g+v(gpk++3a.ek-fk hm bpy2tn 3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sunmsx(;: cwcq1a as the sum of two teac(1c; q :sxwmrms,
(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 164acrw3 q9xfv:e()cwq * 0 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 afe3 q:*(v)x9rccwwq s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kt759jc8x ij + +wtbihlg starts from rest and rolls without slipping down a 30.0hx b7+wtct9ljj8i+ i 5 $^{\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 t(r 03fqvdtl c7bq n4g j-u*;0,mlnpuyb. xd2to fall and its lower end does not slip. What will be the speed of the upper end of the pole justtpn0-*x mf(.3g uq7lv2bjc rndld; utb y, 04q before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular mom*( ycmp l8askl +4mfe63 .lscjentum 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 sclsp4la +s3jl*8mmefyc( 6. kpeed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical 4:ibg4hlhjr 84hkq1j grinding wheel of radius 18 cm when rotating at 1500 rpm r:hijg4jb41h lk 8q4h?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a ra2trtg y::hmmzr npi6t c( /p-oa:q5: rte of 1.3rev/s If he raises:t( :imm:z aqyrtr:oc2 h5/pt rgn6-p 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 reduc6q hl*xv:3wdhmyow,t*f; e 4ee her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she mah wwo34 tvfe yeq6*;:, xml*hdkes 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 spinm,n*m aqn h/k0. ae(uq; sl*vk rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of *aknsle/ v mu.q(h ;m*k0n,aq3 $rev/s$ 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 )e335qn knaz9vh 9kqta vertical 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 clayn3 e 5zk39t)kqq nva9h, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.elh;mds;du d.t, rr2j50 w+if 8+neme5 $rev/s$ 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 angularcn13 7wyo4ij t momentum 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 cylindb ux)2hgz4v8drical disk of moment of inertia I is dropped onto an identical disk rotatin2duhzgv 48) xbg at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2bibw+;hbf * evco4ehsp+-n ,b w9r n7;.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-roun a/,xk 5kfp zy92ccn) ze58fprd platform of radius 3.0 m and moment of inertia 92/npf2 ycfp 9,ek5xc8 z)kraz 50 $kg \cdot m^2$ 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 angular velocity of 0h n(jz3wm4y (30 kyhvh :jva:e.njv3h: hv ejh:3ma w(y40z(y 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, losing abs ,9 db(khs ozd4woepv ,z ,*-srk96biout half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotati4dw6k9zk*9ps ,h(ooe,s b - srbv d,zion 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 excesmj*c qczk,oz8 + )ha+fs 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 qyo7e:3r auh0$ 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, initi ppp iq)no 56uv9 0b6d-y6bnilally at rest, that can rotate freely without friction. The moment of p66pp bny6qbi0 d)ol- i vun59inertia 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 tu30g ywkyvq7v3e6; wrmrntable that is mounted on r7vgey63m;0 w 3w ykqvfrictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground, wu wx e)y7728jnmqiz with the end of the rope lying on the top edge of the spool. A person grabs the end of the roy27we 8nji,xq m7wz)upe and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earttgi y2zt)c1c; yp33r qh. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. 3y tc1i;rq z 3p2t)cyg(In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of kv 1u6lcylg.mzrirke30l,; ,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 shapefn *j m ow+.w*+ui/5e5ntzwxi of a uniform cylinder of radius 0.20 m acquires a rotational rate of from re z .ifue5owx+tw/mn 5wn +ji**st 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 cylindrical8h 7zez7hnynf kad i8c3 601r1j9zrpl 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 anr 1kz7n h e3r08z91 n8 jlip7hc6yazfdd 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 spee) yt74v mbghv/e+-m ahe8.xokd of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, wer8-omexhmt+; de rotating at a speed of 1.0 revolutot8- ;hm+medx ion every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low+ta mpw;9fl 5w-pollution automobile is for it to use 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 travelwl a tpm+;f95w 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 an phf-h72uh wg b1l q8r0$H_2O$ 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*2h0deupt*q d9rk (p / v8fydgru.b+il d31es 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 can pivot frei41 c) 9rsgagmqf5/ 5bke6q(jjr r f;fely (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 6 )i 5qgqkjf/s ra91crb5;(mef4gfj rthe 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 the floor, and;(g7:j a.wue9 uxeha)lf sl 0p 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 height h, whereaglflu0 :x ;.9eh7p(sw )auej h

  A bicyclist traveling with speed v=4.2m/s on a flatqv+2i pcfpf/ + road is making a turn with a radius The forces acting on tifcq 2v/+f+pphe 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 abi3l9l7:fyi i :cy4g i 0.50-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 yi3lf7 :bi:cilgi4y9 where does the torque come from?    $m \cdot N$

  Model a figure skater’s body cok*o5a5 jzb+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 ou+okbc j*5oaz5tstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindroawe5 u,g9b hcqbjz )y3g*p)3 1xoa5eical plates, of mgaxwz,9*eb)3co ha5y1g )bjpqu5 eo3ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ra6 kyn/sk s fd;5 ae-lc:7hqcm7dius r rolls along the looped rough track of Fig. 8–58. What is the minimum value ofe/ - k7ylcdf 5a7sc:qnhsk6m; the vertical 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 not assum5)y9/lldwpno (e;xui e $r\ll R$ h =    (R-r)

  The tires of a car make 8+kb ,l)s4h eec5 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. cb+ ,l sk)h4ee(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