A bicycle odometer (which measures distance traveled) is mt)ztgi-t+a7 attached near the wheel hub and is designed for 27-inch wheels. What tit +7gta -m)zhappens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. 4ze7fi6 7losp Does a point on the rim have radial and/or tangential acceleration? If the di 6slf74i7opz esk’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 singlet(sy j:f (*djwy.d37espct *g value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger g3zky .6p:hh8ofc-s r force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head thanj4p7 )j:utbl*b 8 vzkt when your arms are stretched out in front of you? A diagram may h)*b4lj 7b 8 t:tvpzkjuelp you to answer this.

A 21-speed bicycle has se587x* o7b46e3nmuflfxq v nxi ven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pe*uxi48 x 5 q7oebf 3nnx67fvmldal, a small rear sprocket or a 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 being ab1+wk vaw 7xuv(le to run fast have slender lower legs with flesh and muscle concentrated high, close to the bodx+k1a w7(vu wvy (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, narrow bea2abn,: a v0urn deqddf8 --xm3m?

If the net force on a system is zero, is the net torque also zero? If t fuybl+,rp0r jbnmj i/ q227is;,8evche net torque on a syste2 qu2b 0;fecivjpn8,l+r,byms/7j r im is zero, is the net force zero?

Two inclines have the same hei4 acf6 khk;t+kh0 b.du :pjhc,ght but make different angles with the horizontal. The same steel bkcck4upa6hh bh j0:k.;d ,+tfall is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneousl.of60pqm6 f( jucyv 1qy 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 greufp.q 6 fym(01j6vqocater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mas:7ry e/ jsc 04-idl+lmvx cky1s. They start from rest at the top of an incline. Which reaches the bottom first? Whijermvls/+xd: ic 4lyk1yc70-ch has 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 momess ,70ra jbshq/qj6 m:dze-+qntum are conserved. Yet most moving or rotatin-:zaqq+j es 70ssd,q 6hrbjm/g objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how woulmro5yq:8 ,kdj*fq5xfd this affect the length of the daox5m,jd:*kfq rq 8f5yy?

Can the diver of Fig. 8–29 do a somersault without havinvd6k k w8e9rj0g any initial rotation when she leaverw6 j08k vd9kes the board?

The moment of inertia of a rotating solid di7+t s vpj173dqa* a vk,(vzsehsk about an axis through its center of mass +7a 3edpv(1,7v zva q jhksts*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 mh0cy xoylry 221a003vbdpy* u7c7wm on a rotating stool holding a 2-kg mass in each outstretched hand. If you sudden 27wvu*rxlcy db2 oyya1 p0m0m7c 0h3yly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass.85y+*gvhq p rj However, one is hollow and the other is solid. De*yvqj8 5phg+rscribe an experiment to determine which is which.

The angular velocity of a wheelymcf10l 7+ximk8ldo, rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?x k oc8+fd,71m0myll i

Suppose you are standing on the edge of a large freely rotating turntable.4qvgh9o:ia- so: dynvd.69 kg What happens if vvyo:oq:gd4a6 g hd 99kn s.-iyou walk toward the center?

A shortstop may leap into the aird 0pi)gpz.diwj,df*/ew z. (b 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 hipez(,w p0idg f/dw)dzij.b* p.s and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, disu0 lvz ws;iqt9bw2. s1cuss why a helicopter must have more than onb2uzwilw.q;9s0 s1vte rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angl3 kjg z-5a)t6jk/xps(h a0idbes 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 coinckpasi.w3+fg :3b;axjidence. Calculate, using the information inside the Front Cover, the angular diametersaw; pi+3gkfb3. jx:as (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directe6jw1 zbfn 1 zjk.bqyt( bl-68pd at the Moon, 380,000 km from Earth. The beam diverges abq8jkjz6 f n(1pbbzl -16w.tyt 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. When thj88a 0*;el xo -tcyvm4bz)pd qz.x :jke motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration asc*)olmxbe880.ja -yxz;p qz:vd 4j kt the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If thepkvc+ i7 e2v-k ball makes 15.0 revolution2vcpveki- 7 +ks, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revol xo nj;0qaw8 81+oupd jb0,lpeutions do the wheels makup ;peljo, o 1dnw jq+b0a8x80e?    $rev$

  (a) A grinding wheel 0.35 m in dia9k ikhgd y s71oyhbrbfsu:7 f(86+ .znmeter rotates at 2500 rpm. Calculate its angular velokk:yos.9is h b68g(rdu7 1hzyb fn7f+city in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0ws8e,fn)ho6g j db .:e s (Fig. 8–38). (a)bn ),dfe8 wogesj.6:h What is the linear speed 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 td:)x3svpu 1cp he Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of r kc10lxprku2s 4ye52 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 cm from tb,7+mx5r21nxm sm emwhe axis of rotation is to experience an acceleration of 100,+ emmb mwxn2751ms,r x000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates un -k n/v.8nzytniformly about its center from 130 rpm to 280 rpm in 4.0 s. Dk.tn/n8v z-ny etermine
(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 radiu u3s+r 0gxzy7ps $R_1$ 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 Apollo3e5o8x ldyw1q -wou 8b spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. Atdy88e o1q5boxwu 3l -w the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly 1wfs.yif ku.pw5l/ 6l;t5zrefrom rest to 15,000 rpm in 220 s. Through how many revolutions did it tu. f;w 5syz p/iurf65 ltk.wl1ern in this time?    $rev$

  An automobile engine slows down from 450p4tl vx a(izj j2f17)575v cny ;5fwenlc 2tkv0 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 strs2qnrqvq04 k/ 0rw gg7esses of flying highspeed jets in a whirling “human centrifuge,” which trrg42 /q0q 7vn sg0kqwakes 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 acceleratvdbsg* :wbb i81d8zah 5.bj*tes uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheeg.ad1*ibbvj :h w5 8b z*td8sbl have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns u6g, xw0biebftg z5*v 3c*0w plzu-j*1500 revolutions before it comes t pe*0gi 0cwxu*jb3vub-zf l zw*65gt,o 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 c)4gyvy ym 7q4t0e 0avoar reduces its speed uniformly from 95km/h to 45km/h The tires have ea0y myv gt44)q7yov0a 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 rz5ejnz g4 es546prb9 sevolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have asejn gr 5569 ez4pbs4z diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a biked-) loj,-kc d, ds:cfp puts all her weight on each pedal when climbing a hill.psc dfokcl:,d j,-)-d The 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 of 55 N on the end of a door 74 cm wide. What is thw 60q1w 1.;h 5 a:7qdfc7lygnznyzfvp,s6yuce magnitude of the torque if the forc: .1 1qf gu06v5dznwnh6zsqy,p cw yyfl ;77ace 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 aaw/8qccakf;af+ h 4 z9xle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.4 a kfwq+49c az;caf/8h$m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m,h7 6tie/fea2 -5fyhh, chpa4z are attached to the ends of a massless rod which pivots as shown in hha a p6cyi/f 7ht h2e4z-fe,5Fig. 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.

  The bolts on the cylinder head of an engine require tightening to a t 0 kiszz9tq ))hyu/kk/orque of 38 t0 zhsku/)9kzykiq /)$m \cdot N$ 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 inertk/90zov n k6apia of a 10.8-kg sphere of radius 0.648 m when the axis of kn/9 v 0kazop6rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a brp7 t,+5nm khaicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be k7 ,nmha +pt5rignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a hoqt6 l7: ;2(ee giclss2m c xg przcm*ug*4td64rizontal circle of radius 1.2 x6t4 m;u(l r:pidlq2t ge *g6cc ces4sg2*zm7m. 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 wheel0r9pscsvwx ,h hi6s(1 rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N to(196svcis,hx hs0p w rtal.
(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 ofcbycxi+b3dgg ; 0t5x) point objects shown in Fig. 8–435xbc;+g cixy) gdtb30 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 coej, xd1y4fngn50 m*bj;cp r7dnsists of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical sate89hxrwzzp:/gq 4t ym7llite spinning at the correct rate, engineers fire four tangential rockets as sqt7x 8m:y 4h gw9zp/rzhown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a rul ofze.-u52 -m3vmef adius of 8.50 cm and a mass of 0.580 kg. Cal5u.f ml- moe23uzv e-fculate
(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, accea 030op2 td,- udbwoh *4ulstzlerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentialp1;8pbg , hppzly on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm1g8;ph zp,bpp in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 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 brough rr53xsm6(hjj t uniformly to rest by a fr3xj r56mr(sjhictional 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 aci5ak6noxd) qkh p6y4- celerates 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 bylc8h3lac z/+p: owt8uz,az /b 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 hu+w a//8zozc :actpl ,3z8blrest 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 bladeumrn8y( v7n3 whk 5a6h:2luhm can be considered a long thin rod, as shown in Fig. 8–43 28av uum7mrh(nnlw 5hhky:6 6.
(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 consle3le jclx -62zv :6raists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from res x2ni+ 0yz:whq-jk hl/pi*+twnj i)3z t within four full turns (revolutions) and releases h-)*zxlw tk hw:/+0iijnyp3j+ 2zqinit at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia w,sbtreyo )0- 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 q3ay yn*2htd5a 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.;evx(optb( lc lao;:,3 kg and radius 9.0 cm rolls without slipping down a lane a:xe t;,lc(lo( aov;p bt 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic eneg8 :c9x+ 7y0bupm(c gmug)ufs rgy of the Earth with respect to the Sun as the sum of two terms,u u+px 908 bmg:g cu7fgs(y)cm
(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 kg2pdx 2oml )a2jphmx3n3 ./ou4 m0f fug and a radius of 7.50 m. How much net work is required to ac.32f l24 o2o xhu p0guj x/d3pmmfnma)celerate 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 mass 1.80 kg starts from rest 4az. v bqu t9rb;mi-0m5ie,lw: riio-and rolls without slipping down a, i. im;v4:9l -wrq-eaiuimbr 5zb ot0 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 t z0 lhta82qoo,o fall and its lower end does not slip. What will be the speed of the upper end of the pole just beftlq 82oa o0hz,ore it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular zs;p ,uw ft+h(momentum of a 0.210-kg ball rotating on the end of a thin string in a circle ofwz ;ps(+h ,tuf radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylind 13pppl6j li-brical grinding wheel of radius 18 cm when rotating at 16p1li- pb3lp j500 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 rotaqaz a3njc v,x4 2nqn6,ting at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation dq3ajq 62x n,cnnv 4a,zecreases 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 reduce her momen sqjdx3z1 8-fuedgu66 t 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 angular s6su6 -z8 dfxjq gd3u1epeed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rot 3u)xndr +ug,zation rate from an initial rate of 1.0 rev every 2.0 s to a final ratedgzr ux) +n,3u 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 a0,anycz/xc 2 dt a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg ,c2n daz0/xc yand diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning a eh4kc49 rp mnfc;oyo;ammuc+(p/4t :t 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 o9cz8l ;l:utmvbx 4 kd+fe* j,bf 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 inertia pd9niq2:2 jgi+w cux -fk6:;l zf9wuwI is dropped onto an identical dis 9l d2n:2qciuzu96wxf gw-+ j kpi;fw:k rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.48d.clzf1 l 9zi $rev/s$ 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 cegbg7ypri5x ;fk;w 7u0nter of a rotating merry-go-round platform of radius 3.0 m and moment oxk g; r07fyb5g7u ip;wf inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angu5a-xcejx.2mj x )e i6gcq3kv-lar velocity of 05xa.c-e)6xc2 jv3x -jq kgmie.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 eventually collapses into;sjhk aj-+/vybwj d- 5ux7o 2o a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assumin-uyob52waj /;7 jj vodxshk+- g 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 invol: afigfkxssok l3i,:j-d +d;8ve 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 ap)89h py /+hr sgop9kf de3f8$ 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 without mu3tz+m iy6:y fri3+uy tym z6:imction. 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 edg2je..73gm5b ; ybns7 qs k2rwrtuncy0e of a 6.5-m diameter merry-go-round turntable that c j.3sk;ur.yst0mr 77wn neyq 2b2gb5 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 fv f(3f ;ss8rday0(t6b,s uwg of the rope lying on the top asgt,6y s sfur8(3b(vw f0f ;dedge 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. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Ea: l/ pb6e9hiaiww8pb 3rth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its op9i/w3bhe: bli p6 w8arbital 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 1 xqoaqjb(865bm/$s^2$ 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 brv;2u f*xm5n a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s intervn m 2bf;vxu5r*al 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 0.050 kg andajmmj.11j6a/ qdjpz z-y ; qb6 diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diametemdm1- qj jajzq;1 6 /.yjpa6zbr 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheeb+(- y+q.xp-9z)8tep0j4pcl emgun7tm n yo el ($\omega_R$) 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 :hlw7bf 6gb,t our Sun, but with mass 8.0 times 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 uniform sphere at all times, and that the lost massbfb,lh g6t:7 w carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy skho-joa)+nhu)uhc3q/b/95gbbs l , xtored 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 a9solugqubkx- jhn35)+h /bch)/ b,okg, 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 illustratesq4+9k ;rbr9j8sl8vy vpqp bd 7 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 rodzqy 2+ lifl4v8,ki9v9k j k:flling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot xr 6q1zk4-axav ql6*yk/ gj2,3cm 0qx)xn kcgfreely (i.e., we ignore friction) about a hinge attached to a 2rmq6z)0/x-x x a3kylkqq 6vgc* kngax4,1c j 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 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 us+8ly6wf2 x 42k+tcqhmd-kmradius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step agxsydm++w8lkk-t2mhcu f 26q 4ainst which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling aoht2 te( 3ko.vaet9+7zz rhp .2hgb)b-l6zwwith speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal force h2 t 7 -btko+rzveao2pla.( 9etz zw3hg 6)b.h$\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 omm)n wdp(/ wg0f length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. Wn0gd /w )wm(pmhat 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 ai * .emhc:qzhwf/rop4o8+ou / solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skat o*. e u+cw/zq8ipm f4rohh:/oer with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consistsb:dt +wre) q,nel 3ryky *5,-wn4brij of two cylindrical plates, ofdykj+-b5eel 3 n:tr, r w*)ryn4w,qib mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 -c10k zd4 5plqj+wiqu4a6r j: hm,cin along the looped rough track of Fig. 8–58. What is the mhqi6 014m4 -ccn +,a:u5qijkl wjrzd pinimum 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, but do not a1 78(pb/z hwrcar0zdlml +y5j ssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car r flvw: 60v61x j-vtauxeduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular accelera6vtu 6 avxxj wvl-:0f1tion 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