A bicycle odometer (which measu( keav8-j24tquwoh*-w. bls cres distance traveled) is attached near the wheel hu*jkasbuw2t le4w- 8-v c( oh.qb 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 con1:oy kafnzh27 uiz1 7nstant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the dis7zh a1znnyi:u o72fk 1k’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 angular d 3u v4iunu*./fqtv kvk/,3qp,+ku ehvelocity $\omega$ Explain.

Can a small force ever exert a greater torq-yv*-,kdfdo, onjm07 x w)-ka mt3 df:ia- lqxue 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 ngna6p m:kp)ch0q8 yob5qk/-do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer thi6q: )c-hmponga/kk8q5y0nb ps.

A 21-speed bicycle has seven sproosm jwj)3ib0 ,ckets 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 front sprocket or a lao0 ),3smwi jbjrge front sprocket? Why?

Mammals that depend on being able to run fast havi hfyep1)/mhmu ilgt oub 4b3+b)y;lz/m;.b ;e slender lower legs with flesh and muscle concentratem;fb) b myi;uto1iu )bh/;l m4hl.by z+pg3e/d high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carm/jrt3fi. i d0j-qcfyvx, l ;9ry a long, narrow beam?

If the net force on a system is zero, gtj9objb0;cs 9p m:j5is the net torque also zero? If the net torque on a sy:jgb9 m;pjcj o s9b0t5stem is zero, is the net force zero?

Two inclines have the same height but make different angles with the ho7oy) sdc5.e t;.vg6 j pbfu-1qk)yobzrizontal. The same steel ball is rolled down each incline. On which incline wi vu)dg67keyp. c-tfo5j 1zbbsyoq ;.)ll the speed of the ball at the bottom be greater? Explain.

Two solid spheres simu pwoxg-z,qg l *+mce4my687arltaneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Whichzgx8mm,co6r 7-+p ayq 4g*wle has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the sameoxexzm. )+hi pp 4s05j 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 hasi mhx +4pj5).z pse0ox the greater rotational KE?

We claim that momentum ann; mao 6mj*5yod angular momentum are conserved. Yet most moving or ro*jn myma;oo6 5tating objects eventually slow down and stop. Explain.

If there were a grea3demoy06,b v vi.zka p5234lh dfuh0tt migration of people toward the Earth’s equator, how would this affect the length of te vpi6kdv4y,huoz .t 30bdmlh03f2 5 ahe day?

Can the diver of Fig. 8–29 do a somersault without having m).ykn c8r::qoef4)x etz ,gh any initial rotation when sher)n txmcy),k: :8qefh.ze og4 leaves the board?

The moment of inertia of a rotating solid disk about an axis through its cente;irxq-6i.ah/ 6n;0ld/3jq l )q0 d hxcqrdpk kr of mass is qd -j)xn ;k3 6 q.dhqkrldqi/c 0;p/hr6lax0i $\frac{1}{2}WR^2$ (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 mayn1:nxqx2 ;m kss in each outstretched hax1 2 xknqnmy:;nd. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identm135 qqbe)ih-y7pukv ical and have the same mass. However, one is hollow and the other uy b-5)7 ekqi1mq3 hpvis solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axlea1 6t -z5j6ffsdovbn-4 wrj d( 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 fs w-v6rtbjd jfo6nz( -145adthis point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of aa05 qdvt 8f6ny large freely rotating turntable. What happensta6yqn0vfd8 5 if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw ;v) ,rol;bjxtit quickly. As he throws the ball, the upper part of his body rotatvl;ot)rxjb; , es. 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 osp/yyhd:s(nsg6p7rjg)e 3: bf angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways tgyd:bnhss3r: / y)(ge 7p6spj he second propeller can operate to keep the helicopter stable.

  Express the following angles in radians,9x16 3cc bq) nqm e0hsahlkw,: (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 coinc.cwh-wm o. j.uidence. Calculate, using the information inside the Frontw..wh omu .-jc Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Ear6oho/j 5d a0gfth. The beam diverges ajaoo0hgd/ 5f6t an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotasj4 scs-pu 8 b vmvh8i7c1hf1,te at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow do i1m4csf1 -7hvsv h8 jscu,bp8wn?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another childl0j747p 4q wx1 eyfeomzzf *j:. If the ball makes 15.0 revolutions, what is its diameter*1l0jf4xz7oy4jmwee :qp7 zf?    m

  A bicycle with tires / aukkgnfq+; (68 cm in diameter travels 8.0 km. How many revolutions do the wheels make? ;kf auq(kgn/ +   $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its .tu dk ml:8lq2angular veloc l:qkd8mu.l2 tity 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 s1ubd, 1dr19gs mg1hm makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed o1g r,hdu1m1g1b9 s sdmf a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit aj.u+y;o n2lauround the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poimm8+:6h en3) pb .hb:gqpavpf nt
(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 2yb/ w(3/d kxhy+bz aaa centrifuge rotate if a particle 7.0 cm from the axis of rotation is za(x b/+kdba3 2hwy/y to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelpt: kyh,o(tuyx4( jp *erates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Det op,yypt( kh4:t(xj*u ermine
(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 radiusvs23i1r tc6q8mps tn 6 $R_1$ 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 themselve3ab1a/ y3ga ous into a slow rotation to distribute the Sun’s energy evenly. At the start of theirobug /a13ya3a 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,q8q6va8 -pdm(w3n01a smcraxdkb h( rest to 15,000 rpm in 220 s. Through how many revolutions didhak6da,mrm q((-81 08q spvbwda 3nc x it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate;rir, yq;oe0* ,tean8jie1gr
(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 flyini2z2q 01 7m- lyjq-seg,npa erg highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final spme-liza2 pr ng2q7 ,j1e- qys0eed.
(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 diameterdjf)4h9wn ; w/:ncsb j accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. Hj:w9/sdwn jn;)fhb4cow far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turbid wx *vj,yj,(35xpvned off when it is running at 850rev/min It turns 1500 revolutions befori(dv*5,pyjx wbj ,3vxe it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces ik brbcp, -).cqts speed uniformly from 95kcpq-bkb,.c )rm/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

  The tires of a car make 65 revolutions as ;u/ w(okc- *zng tl2- wsj6xtethe car reduces its speed uniformly from 95km/h to 45km/h The tires have a dian j2ulsgwe tc/- k-tx;o*6z(wmeter 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 clim6t2 qsy3epjuswh0.y.gq c.v 0bing a hill. The pedals rotate in a circle of radv..s.gejcywp0 uq0326y ht q sius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a forcsm .4 l+wa7mtup57kgw e of 55 N on the end of a door 74 cm wide. What is the magnituuakw4gm75mpw .s t7+ lde of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the whb2w4q y24/eto x69tws5hy ra heel shown in Fig. 8–39. Assume that a friction torque of 0.4 s byty442a29wwotx he 6hr5/q$m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attach f.(j20:ikwtdy g zd6ged to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.(dkj:wfg0 zd t2 iyg.6

  The bolts on the cylinder head of an engine requir-a vl9a,ufg2ge tightening to a torque of 38ua ,f29al ggv- $m \cdot N$ 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 inerttj7cdzra6 atam ,8jmq2 c40v*ia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation0 mtav 84mar,6zd*ac7j qc jt2 is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diamem u0 u0g sar7.tql. rm2l(h59en *bfjkter. The rim and tire have a combinehru*0u2.a5fek9br(q t g7.0nslmml j d 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 hor22.:m i( jcoyridx-fw izontal cc row-2x.ijm:fy( di2 ircle of 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 a bowl on a potter’s wheel rotating at constant angular h s ia;rzs(mj0c6/gs,speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N total.sszahs6;r j(m/,i 0gc
(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 vc. ub5o qk) +;saz*sb wwd5f;in Fig. 8–43zo f+c 5) sb;5aq;db*w ks.vwu about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxy/zn6eag941o is* r s6 m4yznx8pa +zcngen 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 at the correct rate,kza0w zc:v f58 engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steac0zaz vkf85:w dy 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 massgfrwn5on ay 2bs,61*ps ze7g1 of 0.580 kg. Cyr,n*1g26nbws es zog f a517palculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest tb5y3t0o/gf dj89 ,gdkqc9 :rgp2ncb eo 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 tangentiallyz( ,1 iy7zg:bxy v:bfz 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 haszfgv:,bib:(y7zx1 yz a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventus /f/pik3a)i sally brought uniformly to rest by a frictionk3sfsi /i)ap /al 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 accel k55ms1ocehrp1qr 73lerates a 3.6-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 solelybg,cwgk**x2vdl 9dq0j*k,j s by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformlcw2,xks jj9*g0g* *l,d bdkqvy 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 (l) 4.cp2y t flieqj.o7)qezabe considered a long thin rod, as shown in Fig. 8–4z(y )a4qqeefci .jo7). lpt2l6.
(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 masec6 ejjp+yexal 6o/8-q,fo/eses, $m_1$ 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 tcj gt4vfhjg*h* g,z9c a)n-i1he hammer from rest within four full turns (revolutions) and releases it at a speed az hgn14h-v, g9fij)tj*g* cc 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 momen bkv)oi,pkq9t z05o(g k9,qdn t of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops qi+y5 r3fnstuj(d 1 h: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 slipcz p)5dhc6,ab ping down a lane5aczdchp6b) , at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic enef.vmb 3p*8p,k;wf kpfrgy of the Earth with respect to the Sun as the sum of two t3pmwkb;v.p*ffp, fk 8erms,
(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 rad5 u:3d- ; px1cjidzq:qwdl/zdius of 7.50 m. How much net work is ui13 xzd pz cq-d/l;qd:wj5:drequired 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 and gikc gj :tr*ctv 28tp nscd0j32;26kzmass 1.80 kg starts from rest and rolls without slipping down a 30*nck;8drktt vpcjzis22362 : t gcg0j.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 g(uoo v12ci w8;t6qqeand its lower end does not slip. What will be the speed of the upper end of the pole jgwoo;18u2c(q6i qet vust before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on theei. r5h+o o2obrb f1g3 end of a thin string in a circlr.2 1rfo +b5ebohi3goe of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular vuokm- q8 b(j: nti0(umomentum of a 2.8-kg uniform cylindrical grinding wheel of radimjb :t0o uqiuvk8(( n-us 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at hisbydzb yy 4 q90dlye3/, side, on a platform that is rotating at a rate of 1.3rev/s If he raises his e0 yyyz4dydq l9/b, 3barms 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.yopzdn*u;vgqc/g 9 03 8–29) can reduce her moment of inertia by a fudgg*/ p3 v0cyz;9o qnactor of about 3.5 when 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 rotation rate from akp;/z(n(k o7; b4s naxo8dn 1p6nquaz n initial rate of 1.0 rev every 2.0 s to a fi1s8 ooba4(u6n( x znqkn/; zka pp;dn7nal 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 center at aec 5/czy42feb 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 cy2/cc f4beez5 m, 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 ska;l8 rsglsn0mmb.te( v e2(b- pter 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 momentuqlx(n xn ,n6 9.y.azude(3dmjm 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)a:y-2l oj1 rf-fx.be)vitl d of moment of inertia I is dropped onto an identica-rfl yb)te fdo -j2)vi.alx:1l disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a za7x34n*rdl) 7zexzxcpj k 5b. e7ys8t 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 rotating merry-go-round platfoyc6eeolk1 );x/, cv0e oe 46qo xv2nkwrm of radius 3.0 m v2,1 evw;eeocx )0 ock6e xky 4l/o6qnand moment 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-round9bdo5apclee3:0rcq ) i/wj g6 is rotating freely with an angular velocity of 0.8b el6e53)po w0:qdicr a9j/cg $rad/s$ 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 collapsesc cymg.tk3 7e::uo 6ne into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its e :ycun7koeg tc 6.em:3xisting radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involv,61ncy 3fzewv h9e0z6a7 * xu5ahzf xfe winds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass zc08 s(86upxw8ivy yd$ 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, lvrf 1n( z:7ns*/ebhi that can rotate freely without friction. The moment of inertia of th/z:sibeh7nr( 1f vn*le 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 diazq*8 hbbm4(rp meter merry-go-round turntzr (p4bq8*mb hable that is mounted on frictionless 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 with the end of the rope lyinga: c 4ivkaom ofam.+ +sr8q87g 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. Whatcv ikao f7 +84ramq:sm+g8o. a 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 / rmu 0vq+lyfjpj,g56side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a parti+l/0qm yg,p fj6 5vjurcle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate o/0 6cdp5vd srs,/s;nb c8:0vl tnsjlqf 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0 tekch bt2 f7y*p:(-nr.20 m acquires a rotational rate of from rest ovet(e:nf2b*k h yp7-rt cr 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 ap;gk4fxr 0-xcylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when itgk0a-x4 frx; p 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 s gv 8y-n6wqq5angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times asr,e x/r x01errh*c(sx great, were rotating at a speed of 1.0 revolution 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 sperx( /cr,es xhrx* r10eed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy sto g9q ,*xr8l5xycoqlq 1jw2+bwred 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 needing a flywheelq2wg bq1,ocyljx+qrx58 * lw 9 “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 illustrate le yl,r1v:1sd; ruml1s an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is5h *o32kgcryj m7 dy(x 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 lengxzg1rm( - u,ez0 cvio;th L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the forcm0gvzez rc(xo ;1-,iue 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 st 5unelb7ew( ;fb6 9eovanding vertically on the floor, and we want to exert a horizontal forcene7efwe b6 (b ;59vuol 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 speed v=4.2m/s on a flat road is making a turu i.svx87 w+lb/y3t3c5 ql ptdn with a radius The forces acting on the cycl+y5q utwsvtx8c/i l7l.p3b3 dist 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 0.50-kg rock into a sling of length 1.5 -czoo)v 4 kzg8+hna;x,m2ppn:*qdel m and begins whirling the rock in anzaz+clxpn;pm 28, hkegv:dq-4o) *o 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 come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, maki1b:k elhtmp-v+9 4cnyng reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skecpn4 :k +1-9 mlvyhtbater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plate90.bw c+jx+hd/q hp: z8webr fs, of m/+9.pe0z:+cb wqd hjr b8hwxfass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 o8byy6 4l.lkev f Fig. 8–58. What is the minimyl 6kbly4.v e8um value of 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, bof/mxp m* d+qn;m l,i+ut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 .t+ khcxqv(s r-q6-n ,cj9lkaoz1l 3v revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of-+.n6l t(kzo kcc1qq9s jhr, 3-laxvv 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