A bicycle odometer (which measures distance traveled) is attached near the wheelt )l5w3(0j8.y;np uwmjz vz(s1s kznhsoh68w hub and is designed for 27-inch wheels. What happens if you use it on a bicycle;zwo8 ljk0n(6 yusz3hht5j. 81mwpw(ss z)nv with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a pou9k e1y:x pzxtb5x)4nint on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of eithern:z9p xkebx)4yt1xu 5 component of linear acceleration change?

Could a nonrigid body be described by a single value 9 *n)okbwm-jopq n2q(of the angular velocity $\omega$ Explain.

Can a small force evergps4(/l +;d uzezo p:m 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 wyrlb6kh/y ,ak3*9 ; csqo* svhands behind your head than when your arms are stretcq3*r/w *hs9cy k;l,s6oab vykhed out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the realqn ; nnb aaht9j)v05*r wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or n 0*; ajq 9bnl5nah)vta large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being5mq gmcit 6r( 99geso, able to run fast have slender lower legs with flesh and muscle concentrated high, close to the bgm5om qgr,e9(is9c t 6ody (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope wal ju40.g6zt ie(zx8jl4ufvhv6y gu +l3 kers (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net toreg4klk if8: a4ri jo-y2 v,8sbque also zero? If the net torque on a system is zero, is the net flayg4 ofbk ,2i -8 ev4rsij8k:orce zero?

Two inclines have the same height but make different ann0g p k2rexoge;7 lfs0,(ep5tgles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explaksget g,( 5e0xn;2lopf r ep70in.

Two solid spheres simultaneortcdo9fh 52d0 kp1we )usly start rolling (from rest) down an incline. One sphere has twice9pk5w d)ehordf 21c0t the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have thejd/ajl n-*qm( same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which hanl (ad/-j *jqms the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving u;t;r r av6ortj,42v 1qi8xclkg;s9ror rotating objects eventually slow down and stop. iv;xtojv 6c u;r , 2g4q81;kra9trrlsExplain.

If there were a great migratn m xqdhr/+6k fpqw3mk+88 -pxion of people toward the Earth’s equator, how would t+3+q6f8/rm8mh dk qxk wxp-pnhis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial roc fsp1uxi:q 3qf:k7t,tation when sh:u :tpq3f1sfci 7 ,kxqe leaves the board?

The moment of inertia of a rotating solid disk about anp6l/ r ujz-vc3 axis through its center of mar3l uzjcvp-/6ss 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 rotatza5 bi1oncf )(ing stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will you5bc(oi) n1af zr angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and hal53w1-purk+mjr vkg 2u;oi u0 ve the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is rim lu2;g3w+rvu po5j -u0kk1 which.

The angular velocity of a m,wew7 .wi0 qgow3 bi4x2l0zhwheel rotating on a horizontal axle points west. In what direction is the linear velwio,w qb7i z0m e.02w gxlw43hocity 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 decreasing?

Suppose you are standing on the edgj 1;8jb;r*fxsc0q agai93pb re of a large freely rotating turntable. What happen s bp*rb9g q;0afcjxj i1;a8r3s if you walk toward the center?

A shortstop may leap into the air 94wg:;q ge5)flz65lfwqghs;)aymze to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (z)fwl :e faqhl)y;mgw4z 55gsq69g; eFig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a helic8ce zv r56dv3a7 ,x x77zigfmlopter must have more than one rotor (ormz7, 8va e5 6ldc r37fx7zvxig propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following anp /an5ia,z d48hs/dlx gles in 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. Calculate, us)tt1k8p 4w dy x4sgxofq g/7a3ing the information inside the Front Cover, the angular diameters (in gyx438kwdsx/1 a tpqogf 7t4) radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,00+n8-tybzc:mk6 o gl 9f0 km from Earth. The beam diverges at+lfm86t9n c-g byz:o k 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 rotate at a rate of 6500 rpm.3 m0w-czf nd i;sg:9l1a;sels When the motor is turned off du -dl ;lsn1:;9z0ewscai fs3mgring operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball m 3y,;jpnp wfwz/4gdttj2l1v ; l; bin(akes 15.0 revolutions, what is its diameter f2jgw/lt ;znljpvp(;t 1nb,ydwi 3 4;?    m

  A bicycle with tires 68 cm in diameter travels 8.q ,p0*cl* 5ko a4wuugq/dq :w1ehy:hj 0 km. How many revolutions do the wheelqaoh/p0e4 :yw1lcu *u,wh5q k:j d*qgs make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate 9.y.*ye/nr c- oi .xbs;tv hwpits angular velocity -.9p b vh yx..oiec *n;ys/trwin $rad/s$ $\omega$ =    $rad/sec$
(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 revolw834(jlyud ly6 rad4y ution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seatedlyaydr y648wu 4j3( dl 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 velocitv wehpj -v64el3:xb5c8z2 csl y 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 v1 ;8we 1upuuo1yj r kve 6vd)(js.o5uof a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge1 m.48pmw zzsu; g2rg/ kyksw( rotate if a particle 7.0 cm from the axis of rotation irsmgk2pug/yz. 8sw; zk w14(m s to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly aboj(g;(ir7u shm 6 2y 4v lajlhl*,hbxi(ut its center from 130 rpm to 28ljir;(x 6ll ,(ihy svh4jgbh(72au* m0 rpm 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 radiuo -fwjk)9v0/6xidw pss $R_1$ 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 Moonfs1rl-l wxme*1npp d7va n533, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecra5 d37*sr lm3 nx1f-ew1an lpvpft 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 220 s. Throughj va4;gmrwrsr .0vq4e(du/( y how many revolutions did it turn inm . ry4urvd(jveq;ra wg0/( s4 this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculat ,0fxhv5 qv gow7dqa)3e
(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 thye zz z1n4gm+4e stresses of flying highspeed jets in a whirling “human centrifuge,” which tak1+ygm zz zen44es 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 from 240 rpm to 360 rpm in 6.5c kdm5m ;7t*4s:hpbnbgz3rei;c- *ck s. How far will a point o bki*:g e4ccn5s; -rk7 zt *bcp3d;mmhn the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runn)3sk o/, *abuh9 cejcving at 850rev/min It turns 1500 revolutions before it coaec /j9)ov3ckbh,u s* mes 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 reduc/8nu tbem.i l(k.l pho-+t:e ses its speed uniformly from 95km/h to 45km/h The tir . bi te:nos t8hll/+mp-k(e.ues 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 6hy 9yjxl a26z. 3ggsxwkw:u*-h wc.m.5 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tireh* g: j2wymya skl6. 3x .zc9w-uh.xwgs 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 2q+i/ v kutw/n+on1wphf)* m5j6gd kha bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a cir pfkkv)56wt2 h+gunjdm in+ 1/o/ qw*hcle 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 ofdinqo ;* m/:bpont/;2et6 5a)is wosn a door 74 cm wide. What is the magnitude of the tos;t6b:es ;i mtn/)d5n anwq */oio2oprque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. th/h0d0c 8 d thom8or;8–39. Assume that odh/c;oh8hr 8dt0m0ta 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 i5l;.bpz*7 ye;r p :1wsowmasto 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 n.s;sz7 *pyw;1 wblreop5 mi:aet torque on this system.

  The bolts on the cylindersk(;3s rftpwflsq3 l7j 56fx4 head of an engine require tightening to a torque of 38 3 3kf (4s7 ls65fsxtw;j qlpfr$m \cdot N$ 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 inertiapen.s-;0o cv(jgxx5i of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through vx ;e.(i5nxpcjo0 g -sits center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rim3psqn2ugg,4 whm(41syuej i n. op,7q and tire have a combined mass of 1.25 kg. The mass of the hub cau mgoyq1gsiw7 n 4,.squj2pe3,np4 h(n be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on0hwn0gx4efolei:mlod9 ) 3 n. the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calc)n ofn0.e3l9gx d h e0iw:m4loulate
(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 rotati- uec2nz.f.skng at constant angular speed (Fig. 8–42). The frictiks2-eunc . f.zon 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 er6 uuk.yvj6;in Fig. 8–43 abouy;uu6vrj ke .6t
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose totlhsf 4:yip i+n0y remk*n0.+ug i-ol2al 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 spinniiooh9th1xc.v. d4me *ng at the correct rate, engineers fire four tangential rockets as shown in ht1v.ex .4*9oodm cih 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 wy(yjd+cp xfky. kn 0pb/- p8z1ith a radius of 8.50 cm and a mass of 0.580 yp.yz8pn/ 1yk-b xf(ck+0jdp kg. 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, accelerating it froe(uh .g6k1igej t3+zj m rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round o)fm60 3ki 9dyxnw cr47f.zbg 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 k9o0b.d6nzw7 m x cfr4g)iy3fa 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 i 1h7:gj)aziens eventually brought uniformly to rest by a frictin e:j)h71giza onal torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kgh k;6stlwu6f . 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 solelf0osa6xe1 z1ny 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 uniformly from rest tf01nsxao e 6z1o 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 lvc1 ejd t+x51song thin rod, as shown in Fig. 8–46tec1 1+ 5svjdx.
(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 masseneo4h(bo/. dx karw e22d1(yts, $m_1$ 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 reso9 bqst3g *px-t within four full turns (revolutions) and relea9t-g s qb*xpo3ses 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 momedji+up 8r x38qnt 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 a torque a 7j:0gfhh. jnof 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 withoul;msc (am.jul. 7(sxnt slipping down a lane at 3.3l a sum7cl j(;nms.x.( $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect bkv; 0f8f*k (cuu97cfy7 ffgq to the Sun as the sum of tw8;7 (yu* gu7q ffkkcfb v90ffco terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg e0 qsmh d9od75and 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 s? Assume it is a solid cylinder q95hs70edmod.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts fromh/uele7kwc6 , z38fnfmcx 98k rest and rolls without sli,8lfz3efxn6 7cwm8 9 uh k/kcepping 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 and its ptsq,-1ybzf5dcnru5j , r h 66e3xl(wlower end does not slip. What will be the speed of the upper end of the lcn 6f6dj35yhw etrbx-5,r(psu,qz1 pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.2;ave77g+r k q15fls oxs*u6 go7f4jwx10-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an ag esf5oj*7x w1;o 4lvg+77fqx6au kr sngular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular mie h,dm0u3, qw 5onp8jomentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500,w,u38nimhq d j op5e0 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform , g01jz,rxsm pthat is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 , s,xzr1gp 0mj$rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–2 0e.5 jg9rurtz9) can reduce her moment of inertia by a factor of about 3.5 when changing fromjgtzu5r .r 0e9 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 fwq 8jv6mt h/qj9n-zg 2rom an initial rate of 1.0 rev every 2.0 s to a final rate of 3q98mwgnj h2 jvt6z-/ q $rev/s$ 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 alr1e2m 3w l+la 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 clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel3er1 wal+ mll2. 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(ai1iguu4mf6j : e(/wbi( * tgr6ygqnkhp 7 7c 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 cypeul :h p ,t)vi7b :/gam67nof the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inc/ q 59ggm+emgertia I is dropped onto an identical disk rotating at angular s+emmq gc59/gg peed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at2d j: 6vuezpm 0i(x/ebwikj-(/gjhs . 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;9cqar; g mt *2byw-re stands at the center of a rotating merry-go-round platform of r ty;meb qr2ac*9r; -wgadius 3.0 m and 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-round is rotating freely with ahb5 l p,9s9+g;jmck1 urxc5b- k6dia dn angular velocity of 0.9lj 1m56bi,9ks-u; cdp r5xa+c ghbkd 8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun event n +rx8c0y7dfuually collapses into a white dwarf, losing about 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 rotation rate be?(royux7n +f0 rc8dund 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 120 sq6pspdm l( q u5pf:ncr9/0x; 8sa+ue$km/h$ 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 z fdilx91: ,mz$ 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 withoy,x6w ni6o cwdp3n,q2 ut fric ,wqwicp32 xony 6,dn6tion. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter7, m2lzd9r: uv9fel wf merry-go-round turntable that is mounted on frictionl fm,llwe u9f 72vz:dr9ess 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 rop0-s y+4xg8sr/ srszd c .ymui2e 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 o4 g0+ /cssyr-.rsudy2 mx8siznto 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 Eaj+gml(c q) tbz5)r1r arth such that the same side always faces the Earth. Determine the ratio of the Moon’s spin arq)+r )gtlz(j mab15c ngular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 2rz4 9 9ymaj71kzdt :8wzj 1ijg1wz wi1 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 ujztz)+i* jesv-7 6r ycylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0- ze*z+ )i-67ts ujjyrvs interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two soly;awj wj20yx8r tyk7m ,/il j0id cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is r,yyal j0 tx8wr0k ;ymj7ij2/weleased 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 whk8ng (h+ksy skgq7n .h*6kzn/eel ($\omega_R$) 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, wi,*3rbw3;p ;/abc w;v wrjncu ere rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse top* bca3wb;;,wir; rjwcvu 3/n a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use ene( +vsm*el:tk ,,ou 8mlncp2gnrgy stored in a heavy rotating flywheel. Suppose such a car has a total masseko: t,n8+m,vgm l*u s2lp n(c of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an w p(cy:jb(;l1zci;+3 a6a9i zkh h gly$H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speed v=3.tgs *v-d8s /8x a(dkew3 $m/s$ 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 lengtl pc/y/wl:krwc : g8u,h 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:wwp:kc8,g /u /lclyr 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 the floor, andhg m*4tz ujqbvj(2x 1- we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (v24zh - mubjxj1gq*(tFig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a g8-x+ fuh(6xs aqtq: cflat road is making a turn with a radius The xg(t f86a-qhq :s+ucxforces 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 0.50-kg roc 8uqu3;6ozo0lk6ud xeuk/v. uk into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle 63k6x/eq kd luz80ovuuuu ;.o 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 arq,aykk y-ix8a 6+ q6h h.hdxk1ms as thin rods, making reasonable estimates for the dimensions. Then calculaty.i ax hqkq8,66 +h 1kxahkdy-e the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consis2z)7j 3 (v oc.t*ws.nl 1rljb(n s-cccive; nlts of two cylindrical plates, of mantinw*( 7bn-c2c3( s;1csv.v .rjj )l lc lezoss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 Fig. d)mxzyat9,7g 8–58. What is the minimum 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 d y,9t)a m7zxgtrack? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not9 k x;8ps5pztjmo,hy7 assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uni4zofuv: d (;xuformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of eacxo4uuf ;:(vzdh 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