A bicycle odometer (wh2pkgwkxqtfacbk j( 4: gsxtw56p2 0.*ich measures distance traveled) is attached near the wheel hub ankq4cgt2 w xkk(fstb. 5ap6 : jp20*xgwd is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Doklt5a 0fiwuctps;p-a3 tq4/p3b+ )nves a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either b)icv53 p fna-attlwupk 4/s+3pq;t0 component of linear acceleration change?

Could a nonrigid body be described by a single value of thanm+x 8t4q6wey3u.g z e angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expla 1dvd p.(g hyp;h4st7yin.

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 withnj0uxilhb 3vb 9u01t. your hands behind your head than when y3.t0uxuhiv bljn0 b19our arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and thre9no*z hjl20qj gb te37j ljlsd7k( 7s,e at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large tjln3 gsjd ,l(29*0ezj 7jsb77koqhlrear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to-n r d8nwk y1f-0x.pyc run fast have slender lower legs with flesh and muscle concentrated high, close to the bo.fc-yxrp1dk n n y0w-8dy (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, nar b:86xttxke3cqxh )2rrow beam?

If the net force on a system is zero, is the net torque also zero? If the net2r sg5p xwzn31..gk8 av rjdf. torqrnd 3s2vrkzfx1w5p.a .. 8jgg ue on a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizoop* f /kss/g1rntal. The same steel ball is rolled down each incline. On which incline wilp fro /s*/sg1kl the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. cir6x5.*h / tbuwo :olOne 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? Whii w/lth5o6u*x.ocb r:ch has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start froci lwr6; fcx 94nfw9rkc7+*z+spz:mbm 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 zzn+ mr6wl 9pc7fcwx:r+9;sc*i bfk 4kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. o qalpc/771 aikzyv)9mtze+-Yet most moving or rotating oti zm e71yap+aq-9z/c7k vlo)bjects eventually slow down and stop. Explain.

If there were a great migration of peop.w wfbklb;,+mnl2 +ro le toward the Earth’s equator, how would this affect thm2 .nwofbll+ +,;kwbre length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rota1/7yasv+uzfvf4 6 lbj41n1g uh.ev c ction when she1nb yj/e17fvuhv4fa61 + us 4cgc.lzv leaves the board?

The moment of inertia of a rotating solid disk about an axis through im vy7 gne(z;m8ts center e y8v ;zmgnm7(of mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstry;eobvfpz731 etched hand. If you suddenly drop the masses, will your angular velo b1;73oz vefpycity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, onf)gj e1k2 xe0xe is hollow and the other is solid. Describe an experiment to determine which is whiegf x0kje2)1xch.

The angular velocity of a wheel rotating on a horizontal axle nr0i( d,cl k2r k g mwf8y8d8+;ns6rhbpoints west. In what direction is the linear velocity of a point on the t 08d 8,wm+syd2ck6gihrnnl8f( ;r kbrop 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 edge of a large freely rotating turny5q -ztkpgq qa88tpzv8 71sd*table. What happens if you walk towarg z qps8pqt8a 7tyd1k*qz-8 5vd the center?

A shortstop may leap into the air to catch a ball m 6ii9-6ismgc and throw it quickly. As he throws the baliic9gsmm- i66 l, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss v-5u rn.(-zy,anv yuswhy a helicopter must have more than one rotor (or pro( vs yu-u rzyn,a-.vn5peller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following anglk/-y7, tpsth4 a.au yves 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 a8h;i8h i o1klryb7t f+mazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, tlb7oi+1;yf hkh i8r8 as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from +htjui y1lp r9hej /,3Earth. The beam diverges at an9tlp1/rh +3 juj y,hie 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. When the motor is turned owak (jasfs ,6t-ptxl8o-8 a 7eff during operation, the blades slow to rest in 3.0 s. What is thl f 8--atexa(86,7sakjtsowpe angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level yuc6hisy q 6v iqkg)338dk1 w3floor 3.5 m to another child. If the ball makes 15.0 revolutions, what c 86i3q yu1)3dvyhw3ki6qkgsis its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revoy *ig55w p6pbzlutions do the wheels6z5p yib*p5gw make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its luym032l 3fa7 j pub3gangular vel2yjm pg7ul3af 30b3u locity 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 /( u,3l kfmtjhrevolution in 4.0 s (Fig. 8–38). (a) What is the linear f3muth (kj ,/lspeed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around t;gn,+*hq nzss;j w,wthe Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spev2c6lk tc-n 9ked of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 43evx6k +d7ulo xjaa*cm from the axis of rotation is to experi3 4kx+aol6jdx e*7avuence an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about4h o2.j +pt vugw-p8ka its center from 130 rpm to 280 rpm in 4.0 s. Determ4uppkgvhja2-t . o8w+ ine
(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 radiuexcbk7, 5ba( ls $R_1$ 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, astronafi v1j *w:dk1huts 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 vjh 1wfi:*1k d12-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 f5n9wtebll 4v:emuo)+ qb 0ol/rom rest to 15,000 rpm in 220 s. Through how many revolutionqe+o0/otl95lm)vn eu4 :w lbbs did it turn in this time?    $rev$

  An automobile engine slows dow;4sb yap3fj j5n from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirlind 9h.q(6cwo5ac.0siytvu 7 qng “human centrifuge,” which takes 1.0 min t ot.7y si95 hn.uwq0 d6qcvca(o 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 240tqn:lc5vl-(ks6 m,x c rpm to 360 rpm in 6.5 s. Hoskct :q l-6cm, n5(vxlw far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turnedgwer16x qve) ) off when it is running at 850rev/min It turns 1500 revolutions before it comes to a sto ervgwxeq)1)6 p.
(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 ax4vnwqqj9 . :fz*zf*se xa(0 r-se g7vs the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.8 f-z*:4geq re s .7vnqwzfv9*asx0(jx 0 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly fr5:gik++ti- qs+((t)t edh7s xrdhz axom 95km/h to 45km/h The tires have a diameter of 0.8i7dgt+5r -+)s(hqxa h( :xt+zsk edti0 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 liq;y 1cfot7 8climbing a hill. Th qofcti7y ;8l1e pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force -inv m;,lfglvy;f2v 5 of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exerte-vmf;ig2v fvl5y n,l ;d
(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 ay:guups zw /)g xkm 8f3z/a7s0bout the axle of the wheel shown in Fig. 8–39. Assume that a friction torque 8u wfx//y)azssp z7:0 gmu3 kgof 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 of 5 t5wq9v/q 9y1m: owjo;l(kqw;npd eva massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal positionqo lm( ;n9oj:wwe/kv5yw 5;vdpqt19 q and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylindew7w m3sc yj1,o142rttpaj*qw.5 cbgu r head of an engine require tightening to a torque of 38 1w,*mr tj .74cow pw1b c35a2tqjs uyg$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere ofb2d 4vqi928j cy .qmh1jp310 kj jizlm radius 0.648 m when the axis of rotatio0cjjmzkj iqm4 9q1jb23h8pyd.2vl1i n is through its center.    $kg \cdot m^2$

  Calculate the moment a2xlb wntbs:u6f1 0 sxq/c-ylz/,oh ;of inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1./- x2 1t lw/qaby;h, 0sn:bloc f6xsuz25 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 mif9nw2w+)f ihorizontal circle of radius 1.2 m. Calw +9nwf fim)i2culate
(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 const wunmfl- 7tq78a+qrv)ant angular speed (Fig. 8–42). Tq -78tr u)qmn af7l+wvhe friction 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 in h arx/2xnck 60f 44.7 jsdsg7fgr.rhiFig. 8–43 jf47gh.rnr 4c 2x6hik/ ssr0 fgdax7.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 oxygen atomsjbt1d8 34+b5epjxxue .s-nbm 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, ejz*auoct14(h va5r1ej : v6 aengineers 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 steady force of each rocket if the satellite is to reach 32 rpm in 5.0 minta 5c4av1z1e au(rhv 6e j:oj*? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius ofjk/ 8q y7zw l5hr r1b:1:wfskd-f1p ns 8.50 cm and a mass of 0.5nywsf-w1d5rjfk8 p 1sr h1lq:7k /b:z80 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 fpb*gh; ,( -wcostt -dfabxa ..rom 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 sma p6k h 0*8+;cnefu(kltdy8ft+za xsd2ll hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 sp 2dkfut dsz;cf0h a txe+8 6y8l*k(+n. 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 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually broucb iprc;* q1a+pkcs1zq 4 ),cdght uniformly to rics,)k1*ba+ rpp qqdc c4c;1z est 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. 8–453 w ok3,ymtw8q accelerates 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 solely by the action of th+dgs+3yn(5pbjnup,j cj ; m2ve forearm, which rotates aboucnjvnd+y( 3j5 jsp+, g2bmp;ut the elbow joint under the action of the triceps 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 l a-wwd 8rpm)o:ong thin rod, as shown in Fig. 8–46.w)-dm8or aw p:
(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 +yy2w:: het bl)+rqmnmasses, $m_1$ 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 hammrag(v7 * 2txsi3 5 ,evabyn-fcer from rest within four full turns (revolutions) and releases it at a speed oriys7a(nvbxtc53, e g -av2* ff 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inerthn f a0nv2yq6p*6 mm-ky ge00xia 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 deve2/ iy(wy9q. qb4(wuxv r ygyh7lops 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 rokudj)ahfi6u 4.,2ma3+l b g/rgbusp1lls without slipping down a lane at 3+r ,g.34 fl12 6bubhaaum s gpku/d)ij.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect t2xtu /z-eks6 1m kptc-o the Sun as the sum of two terms,xme tk6zs -/-1cutp2k
(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 m .*ssma)o2yhuu85 d)a mqy*o dass of 1640 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 s? Assume it*m mo5asuaud *.y 8q 2odh)sy) is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg xqz s-*ajtgu ut(3+ b-hlwt0;starts from rest and rolls without slipping down a 30. h3*t-xbzu lag 0qtw;tj +s(u-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 toho5n-anzz ;6r2+ l mb ghof9wtjr/ t2: fall and its lower end does not slip. What will be the speed of the upper end of the pole jm-r2 z+n2w zhot6r:l/nboa ;fg5 9thjust before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentuh j 1pj7he)upfq1u i.mte,omzuhgz9 k*14 6z0m 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 speed of 10.gzo1u mm 4p*z06kp1hj ,9jte71.fhzuei h)uq4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindricj z6n:tk mq u6+n1r,somrlm4,al grinding wheel of radius 18 cm mkmn nl:m,4urs,oz1 tqj+r66when 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 his side, on a platform that is rotating at a rate of v5leac*h wtsfwjp5r/7fr*-ym -tp531.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreaelspcf55rvftr-w pty */-w73j* hma5ses 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 rox8(5lvzq jtv-ov9 qdn-h ej -rt8 .v1educe her moment of inertia by a factor 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 angularz9d .qq5(x8vv8rt h-ojj- otnelv-v1 speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can in* ngx9kt)r* vnkmk55g3s:gg gcrease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate k5 9v 5ggmtxsg *r3:*g)kngnkof 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 throu 9t au7inq*v(k w(yqjyqj 5p:4gh 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 s(y n j:uy5t aqq*(vwp47j9qik haped 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 firv(x ime-u -k.zmg ):ggure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Earik4 q,- ux,r,p .yckokth
(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 inertia I is dropped onto a :x+ 0z apsj4hc,nz:oun identical disk rotating at a+hpzx:, 4s 0jo:czn uangular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at f:rolgq anqs6 ,,x7c )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;-j lh+n( z+d/6z rtv-ylggyv stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 920 l-ylg+6-d /znv(yztg;r vj+ h$kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an an+42:fuo pbx v av.ya7kgular velocity of 0.8apybvvo+uk x 47 af.:2 $rad/s$ 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,cw-v /obch6 -.jr9ycr 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 wo-bj / rhwc9rcyo-c.6vuld the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winxir 7l9;ou2qzixl e;, ct*qz9 ds 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 +dbv86e;* qs1 i j,bbvtt0glk$ 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, inkcrpuo7u- (-h h w5w,trlpd/ bg l+/m,itially at rest, that can rotate freely without friction. The moment of in odppl,muucr-h t(+k r/bw h5l- ,/7wgertia 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 di63w quwj t5ho9jo8a,h ameter merry-go-round turntable that is mounted on frictionless bearings and has a mjjwh9uq 68,ah5towo3 oment 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 5ebi3vluz:dxrq y.2 3 lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the pers23qr: . iu be3yd5vxlzon 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 sg igo07 gmil3*8k.; ,rcnry ybame side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own ax8bgyg; rnlyi 7cm0,g*k ro.i3is) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates (mnphg6r 4nlhc8 ,l o)from rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acquires./ gty651 vpgpu 0zgwnr:acb8 kx0m, j a rotational rate of from rpz :u1k0vg,bpy 085.gw xga/6njtr cmest 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 cylindrical disks, each of mass 0.04cwfnkvf, ;f /50 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 tocfv /fw,n4;fk calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed p4m0 l4j.1h9 n ( m gylod5-jg8aigc+a+pllew 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 tim 15 goh4xd7:**nnmgus yqv, woes as 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 speed be? Assume that the star is a unif nh7gwm nx vq uood1g*5y,s4:*orm sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for ax r7,iv98yqslj ;ofq7fgrs .2 low-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, u7x7osy . j8lsfr9;qgq fv 2i,rses 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 illustrahvcd5 6ym2h e01 adva/tes 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) is rolling on a horizontal frh)fj1,( +ll1 -e3hfqkim rd;vrgd)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 n5s-cz4cl1rv,s 3tfw length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Ftlsz rc cv35-sw,f n41ig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertical: z*xw8cq1g eekb(ae8 ly on the floor, and we want to exert a horizontal force F at its axle so that it will climb a stepe1 a8x*z(g w:ec8be qk against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed veg54k-2v avzf khmb10db; v+u=4.2m/s on a flat road is making a turn with a radius The forces acting fvukav bv0-5d 4bzkmg 12; he+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-kgw: ow+nj es/jm28uje06 p2 ars 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 rem2e wau es6/:+2nj0w j prosj8st 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 rvaeixfj n9 0sao3x31/ods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for xajf sxvai9e3/ 10o3n a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutrrn 2k-a 8f2n cgof8b.ch assembly which consists of two cylindrical plates, of f.cro8 gbkn- n r28f2amass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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. 8–58.xxglwx n9 (l (q7gb2vt 4zyl+w2i;da8 What is the minimum value of the vertical height h that the marble must w(lzl7xn x2vw+xl4t aqg8;bg9 2iy (d 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 assu lnjxyx1e-x(3me $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spb 58v y8r2s54b+nu c xts)dcvteed uniformly from 90km/h to 60km/h The tires have a diameter oftbd8)y+svvtccbrxs4 2 5 u5n 8 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