A bicycle odometer (which meam9;pfm(wqd.c aj;d.qho 2uw 4 sures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens i q d u9j.wfc (m.pa;4dq2oh;wmf you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point )q txz3 hah.9mon 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 compm.9 h 3th)xazqonent of linear acceleration change?

Could a nonrigid bods-f4et1ahl o7.4 lzdny be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expl:*lk,4a3xy6lr+wn n g3z ctilain.

If a force $\overrightarrow{F}$ 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 +wj ( 8;y-apbjb0+itcnh )kob to do a sit-up with your hands behind your head than when your arms ar bkij08c -;h+b(pwt )a+ynobje 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 t6yayk o8zmcm) a h +if4qb*jwrd 4+5e-hree at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gearfdbi 8 6 k-m5r+oq4wc*yamy)4+ zej ah is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend qp(ui278p- kruty5gerp5qf ;on being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distuf; pp5ik r-( u7ret2gqy85q pribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) q45 h1;twbyxg carry a long, narrow beam?

If the net force on a system is zero, is the net t8 ygfoj0 60 zdiie uio8ji0w/5orque also zero? If the net torque on a system is z50 0youi j6oi e80gji 8/ifwdzero, is the net force zero?

Two inclines have the same height but make diffemka.o bh2wl 41ak57 rb1ds2myrent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bott m12w 1a7k5o adysr.blkh2 m4bom be greater? Explain.

Two solid spheres simultaneously stn 5f kc)ms(xk0art rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there?)kcnm f(s05 xk Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start fb- ,1 ordigf2xrom rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which haoxr2f ,i-1 bdgs the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular mometpjw /v ,1ztna30j ,jjntum are conserved. Yet most moving or rotapjt0w t n3 ,vjj,zja/1ting objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, howpm8 w( egh0waei5p .k. would this affect the length of tg5ehwa e8.pp(ik0w. mhe day?

Can the diver of Fig. 8–29 do a somersault without havvn .oota0a7 qd:oj*w5ing any initial rotation when she leavo.wn d7 0qoajt ao:*5ves the board?

The moment of inertia of am9eqe )hjjx3+ rotating solid disk about an axis through its center of mass is j9hm + x)eej3q$\frac{1}{2}W{R}^2$ (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 siubz d fwfh0q6.72/zztool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular ub z 7fwzhdi/z6. 2q0fvelocity increase, decrease, or stay the same? Explain.

Two spheres look identica*jfc p:s+lovpe x ,t;9l and have the same mass. However, one is hollow and the other is solid. Describe an experiment to deterf+so lpt ;ec,j*: v9pxmine which is which.

The angular velocity of a wheel rotating on a horizontal axle pofa4 9:dujsemql6 0r.by ,6w7h fgx(ruints west. In what direction is the linear velocity of a point on the to xryr6b l q60am(g .u47hf:sfwde9uj, p 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 +sp91- oltnf kthe edge of a large freely rotating turntable. What happens if you walk tow- l+op91sf tknard the center?

A shortstop may leap into the air to caty)4p 0s.+gf6jz aabkthd g7d4.,igzgch 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 hi s7kg gj.d0) 4gf6z.a4 i,y+ztpahbgds hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conseib98rm64m xz shw g92pf7 xia8rvation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to kee8xbh8a2r4zmw 9mfi 7igx96spp the helicopter stable.

  Express the following angles m .i/8kxf,pphn 2. qnod( ;onmin 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 be:q-)yn*jz,ap c 0ubgzk 98wt6sbq;tecause of an amazing coincidence. Calculate, using the information inside the Front Cover, thjc9 6n- zsg*pu,w)8:yqtab 0zetbq;ke angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is direc4ve i,,hrt(l nted at the Moon, 380,000 km from Earth. The beam diverges at an t ir,e hnv,l(4angle $\theta$ (Fig. 8–37) of $1.4\times {10}^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a ra0) ntre)c.ayyyhi -3uq 6mhg9+qnt+xte of 6500 rpm. When the motor is turned off during operation, the blades slow to re y))ygu tq9n++0 e-qyrm.a6ch3xtnihst 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 ballf;h:am, y+vt:elzdi 5 makes 15.0 revolutions, what is its diameter?+,va5dyt: h;lfmi :e z    m

  A bicycle with tires 68 cm in diamenrlpf :9ztd6 e g/swr.0s6 b9mter travels 8.0 km. How many revolutions do the wheer z9. 9n6 fg s6et:dwblp/ms0rls make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. kkuec;u. d:oaoaey* 1h9 :p1j Calculate its angulae:uj. ud 9:h*coeak1py ak;o1r velocity 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 opuxw-ya6h+5aczj;) 9f*f a vene complete revolution in 4.0 s (Fig. 8–38). (a) What is the-x+ ehu5y)pj6;f* aacf wa9 vz 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 aa6ul w1hntj7a 5tp-w 9round the Sun    $\times {10}^{-7}$ $rad/s$
(b) about its axis.    $\times {10}^{-5}$ $rad/s$

  What is the linear speedmhkn)-/dt w b7 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 a7z t 0fj*hevmy7mk,5k centrifuge rotate if a particle 7.0 cm from the axis of rotation ik0tfv7 ,h7je5 mm*zk ys to experience an acceleration of 100,000 $g^{\prime }s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its cen hap:d7.6eqv7 ;g dnebter from 130 rpm to 280 rpm in 4.0 s. Determind;e vh :7qg67na.ebd pe
(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 radiuty5.)bdcm7r +rt ch9 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, astronauts aboard the Apollo spac1 j.+mi/wekmh5hv 7xdx os/w(ecraft put themselves into a slow rok51x jwseix (m/7h+d w./vomhtation 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 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. $a_{tan}$ =    $\times {10}^{-4}$ $m/s^2$ $a_{rad}$ =    $\times {10}^{-3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in5qq6t:-,,kn trlddt m 220 s. Through how many revolutions did it turn in :,5 nd drm-qtttq6,lk this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Cvyvs2r,8xvy8 g 1k q7dzjk.v1rhr-- dalculate
(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 irfno,j; i+v,wp0xl q -he -8fhighspeed jets in a whirling “human h wji f0l-vrfqn,p x+;o- ei8,centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/mi{n}^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpyvhm m,leterhaul/ nd// w9/r1o5.w1m in 6.5 s. How far wi/n vlwm/ 5m.o1dyt9a,w /1hruhree/l ll a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when *c ap/p u2tz4qit is running at 850rev/min It turns 1500 revolutions before it ctu2/c p zpqa4*omes 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 caxtau6da ;on+ k6 )hzn,r reduces its speed uniformly from 95km/h to 45km/h The tires have a di ;,6uzd+ 6tx koanhna)ameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduc11j(y.-y jw)dfz wgswes its speed uniformly from 95km/h to 45km/h The tires have a diasywyw )w.-j1 z gdf(j1meter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climb7: zt.( 4fa+akihxvpl ing a hill. The pedals rotate in a circle of (z7v. i h+atl4k:pxfaradius 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. mpv/k ao /t u1w8i-ym)What is the magnitude of the torque if ti-1amoty8 /wu pm) k/vhe 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 c8u aa ;0yaamr/k4f*h-m v 8lpin Fig. 8–39. Assume that a fricti8lv *kc/mar 4ah;f-mpyua0 a8on torque of 0.4 $m\cdot N$ opposes the motion.    $m\cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends oe1zw llfc h84n.7x y7z* f3riof a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then rh 48wy1orx7 cne7l3fl. z* zfieleased. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightenin-qp2j7 g zw r;sg*9qod(nfjv.g to a torque of 38jq qsgf(*dzn7pj v;2 .w-9rog $m\cdot N$ 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 eqzz :5:n qa,cq lxu3;of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its uz3 eznl:;:,qa q5cxq center.    $kg\cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 0tx/+.zz mygsxa6wv 9rd.u1q cm in diameter. The rim and tire have a combined mas1zywat6zr g9x0qu sd.x./mv+ s of 1.25 kg. The mass of the hub can be ignored (why?).    $kg\cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotayg1p* *cy950olk+ow5j qc xqk: lu cq;ted in a horizontal circl :j;x+kqc1 p9l*wo u l5qyc* yqkco05ge of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg\cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m\cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at conzm(m7khx g)-x.dffr 5 stant angular speed (Fig. 8–42). The friction force between her hands and tk. xxfh5-gm)f(dr 7m zhe 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 po7 lqp3w+i tbxl4-/ jbfint objects shown in Fig. 8–43 ab /f3 -tbjl +q4plxwi7bout
(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 total mass is a+y-8ckf*v zo $5.3\times {10}^{-26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $1.9\times {10}^{-46}$ $kg\cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times {10}^{-10}$ m

  To get a flat, unifori c0b rm7n+m2am cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown ii cmr720banm +n 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 radius of 8.50 cm and a ma ;,qpo/ro(xwoyebp 4d60qc6 w4v j i)ess of 0.5 /xq(qc o6p ipy6d;4jbvo)o ,erw w04e80 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 from ffw6pa /w1,ihrest 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 tpgsm7 eq pk 0w885si.hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform d0wpsek s.88mt5g7 qpiisk 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 eventuallpqi 41+c z-vvsy brought uniformly to rest by ic-p s q4vv1+za frictional torque of 1.2 $m\cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accele oazw9 xn(3(dorates 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 the forearm, wv,.wo avxacllie 556 lz-;/ wlhich rotates about the elbow joint under the action of the triceps muscle, Fig. 8–4c a5wvle;./6iollax-zl5 w,v5. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thqc8mqnra(18ljzaghl - .*r6fin rod, as shown in Fig. 8–48(l rfg.8nz chr*1qajl6 a- qm6.
(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 toe9qbinq) 9b0e o-/t xwo masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (ey .dwywdwjm kb9/sa 5- x,r+/revolutions) and releases it m-.xyd,ybw/a+5d w /9ker wjsat 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 in jpepn/y5fp0fg k75h8 x)w1eh ertia of $3.75\times {10}^{-2}$ $kg\cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine developimq7i7 p6 yvzp d8r03g;3fxmks 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 r;z 1qhv9 2+dwt ojsp(uadius 9.0 cm rolls without slipping down a lane auqt2odh+ pj 9v(w 1sz;t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to t;h(9olqwp pr3 he Sun as the sum of two termo;q3(w php9lr s,
(a) that due to its daily rotation about its axis,$K{E}_{daily}$=    $\times {10}^{29}$ J
(b) that due to its yearly revolution about the Sun. $K{E}_{yearly}$+    $\times {10}^{33}$ J [Assume the Earth is a uniform sphere with $6\times {10}^{24}$ kg and $6.4\times {10}^6$ m and is $1.5\times {10}^8$ km from the Sun.]$K{E}_{daily}$ + $K{E}_{yearly}$ =    $\times {10}^{33}$ J

  A merry-go-round has a mass obw ync/x/,e :nf 1640 kg and a radius of 7.50 m. How much net work is required to accelerat, c/b/n:ne wyxe 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.ia. m- i3p6zhi0 cm and mass 1.80 kg starts from rest and rolls without slipping down mp 36-iziia.h 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 vertic9iuda dw2x1,l 4 ++u6yhqcapi ally on its tip. It starts to fall and its lower end does not slip. What will be the speed of the ywdu6,d9p+i4 qaix+ 1uc 2la hupper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular 7k:pyay omwp6:8t2pimomentum of a 0.210-kg ball rotating on the end of a thin strw kpay6 t:mo2ipp: y78ing in a circle of 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 cylindrical l:hw d/a)8 cmigrinding wheel of radimwd a8:lc/i)h us 18 cm when rotating at 1500 rpm?    $kg\cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m\cdot N$

A person stands, hands at his side, on a platform that is rota./6y9j xa(hj ,nyuop pp3hca5 ting at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation h .,c6 p3j/5pyo nyh9a(xapju decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) uj lf32p1k/ezl22lvm.hhhk 8 can reduce her moment of inertia by a factor of about 3.5 whlzk/u 1llp fk.v3 8h222meh hjen changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an iwqs 4)gj glmt;6l4j3c nitial rate of 1.0 rev every 2.0 s tocst34l6);l j4gj gqmw a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg\cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its centert; : *i1azexjg9mt z)y 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 o*9jm:i y ategt z)zx;1f 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 a1iac -qo4:x p7tn izhf7u/d h7 figure 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 thq;4n c j5(v:y 6tf.eiez jfbv1e 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.    $\times {10}^{40}kg\cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an ig8 (br6kt pyx;dentical disk rotatigy8 t6pkxb; r(ng at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2j0wr n0ckgkc)h:( zn5.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-gp 1fj3xh6kv:ao-round platform of radi:pxa6 3jv 1kfhus 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.$K{E}_i$ =    J $K{E}_f$ =    J

  A 4.2-m-diameter merry/t: fg -a cn8.yqxvz3w-go-round is rotating freely with an angular velocity of 0.8 8 tycxzn f:ag- /wqv.3$rad/s$ 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, l9r q+c k-us7r (z-vpoxosing about half its mass in the process, and winding up with a radius 1.0% of its existing zck -s(9r7up -v xrq+oradius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$K{E}_f$=    $K{E}_i$

  Hurricanes can involve w8e fvlhdy0c. 3inds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $\times {10}^{16}$ 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.    $\times {10}^{20}$ $kg\cdot m^2$

  An asteroid of mass l/rzz0m+-xdoq (-hi u$1.0\times {10}^5$ 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.    $\times {10}^{-16}$ %

A person stands on a platform, inio: i( ngtms3dh2b -*nctially at rest, that can rotate freely without friction. The moment of inertia of the d-cotns:b3nm2* hgi (person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity ${\omega }_W$ What will be the angular velocity ${\omega }_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will ${\omega }_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry--n mo/whch d3a0 0pdonw8,7g/u be) ymgo-round turntable that is mounted on frictionless bearings annpa0ym-ho, 0ud 7/bwgh 3wc o8em/dn)d 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 end4xj;jv9( emr xy.3p qu of the rope lying on the top edge of the spool. A person grabs t(.y4 vjqrjxpxmu ;3 e9he 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 x7 bi ni(-ebc1lji*m19j d4 gethe same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat thj9je1bi bd(xn-gmc17 i l 4ie*e Moon as a particle orbiting the Earth.)    $\times {10}^{-6}$

  A cyclist accelerates from rest at a rate of ol *2oyxce-9j 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 cyu5p+deh1 w zk*linder of radius 0.20 m acquires a rotational rate of from rest over1k* epdwh+z5 u 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.gldgky- iy*6zi1b; b ,kmf,n, 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. Uyigb f6zik *;n.,dlkmb ,gy-1se 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 whee ui2gecm 02p8 ,jr0n(1 vgwjijl (${\omega }_R$) 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, 85 zoma;3e;mfi( r0gvg g4wb hwere rotating at a speed of 1.0 revolution every r wg;43m0e5;a 8hvfbgmig(oz12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times {10}^9$ $rev/day$

  One possibility for a low-pollution askp5x4sd6p 4+bi jz f)26m uluutomobile is for it to use energy stored in a heavy rotating flywheel. Suppos5+ bd44 slpu6)jz26pkx fsu ime such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a 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 $1.7\times {10}^8$J.    $\times {10}^8$ 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