A bicycle odometer (whik ;a 1r,:ht l+yt:l1yhuzt+ qych measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. ltu:1z,y1lt a;kq+hy:tr+ hy What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a pyigr 29oj,u8r9yi ; nnoint 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 component of linear acceleratii ;ion u9rr28nyy,j9 gon change?

Could a nonrigid body be described by a single value of the angular veliwavdo2) 1 i4gocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger 2ig+k hezjz 0.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 hea6fvuyr6 2 l*qsd than when your arms are stretched out in front of you? A diagram may heqf*vr s6y2l u6lp you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pe3 r7g+qe0k n p,frde8jdal cranks. In which gear is it harder to pedal, a small rear sprocke+jf np gr,re38kdeq 70t 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 able to run fast have slender lower legs wit 7eftpm9y(t8qh flesh and muscle concentrated hi87t9 e ymp(qtfgh, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beameh a0g+czml+6 ?

If the net force on a system is zero, is thpba,d o fo(n5,e net torque also zero? If the net torque on a system is zdo,opfa,n (5b ero, is the net force zero?

Two inclines have the same height 1 0:jhvhl,ob k h0 ms0f*va)imbut make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed ofs:0,vhi* bh)00 ojkml avhf m1 the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (fr2loc egl z7m,6q4-bwrom 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? Which e74 wclo-qz,r gb6l2mhas the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. The)r dz m)b*-jpz+auhq +y start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotatio*bj)qz + phuzrda- m+)nal KE?

We claim that momentum and angulari3 mf) nx*q tfn6))rkv momentum are conserved. Yet most moving or rotating objects eventually slof36*)ntx qr) k n)mivfw down and stop. Explain.

If there were a great migration of people toward the Earth 0gi pjr:d)a9a’s equator, how would this affect the length of the 9)gra: 0ijdap day?

Can the diver of Fig. 8–29 do a somersault without havinesenk4 pqbq1a3cf- 8.g any initial rotation when she leaves the board?bs4k3 q-q8e1cnf.e ap

The moment of inertia of a rotating solid disk 8q pwy de-f:* eqrz3)iabout an axis through its center of mass i* wr e:ypi-dqe8 )3zfqs $\frac{1}{2}WR^2$ (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 outstrw-s no:uwfka/ l07i3uy w.xl (etched hand. If you suddenly drop the massesk u 3ifxon.-ys:u w(a7lww/0 l, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have t euo*bt yux 6-:(nqxov (k/*pshe same mass. However, one is hollow and the other is solid. Describe an experiment to deterv:uop(o *tx bx-k(*quy6es /nmine which is which.

The angular velocity of a wheel rotating on a horizontal axle points wext aq7z98hbhj6 mt3g tgn6(/jst. In what direction is the linear velocity of a point on the t8txjqh6 73 tm6an9gjzbg (t /hop 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 l ytv0z98)1 e8agkll fof a large freely rotating turntable. What happens if y 8v k1lylg) 9fa8zt0leou walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quicklq-f zy 5gykor)f:fm3c- .i .bly. As he throws the ball, the upper part of his body rotates. If you look quickly you 5--3foz mfrqy:b. gliky).f c will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservatmm mdh4 tghkll 1/. 4u95x4bqkion of angular momentum, discuss why a helicopmhglu9/m q4 m5 kxtlbk dh144.ter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians:zvx mqqs+n, kbf :-8j22-.2 ig7zcrfjzjswx ) (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 E: c/pbu;5 vxuv 07qwgharth because of an amazing coincidence. Calculate, using the information inside the Front Cover, t;v/ghuqp05:b7uc xw vhe angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km fromt, h(;wwpr a9p Earth. The beam diverges at an angle (,h9pw atr; pw$\theta$ (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 -c.s y3-sles )mje29to2xynva rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades sltoem2. svs) xe-s2lcy9y3jn-ow down?    $rad/s^2$

  A child rolls a ball on a level floor6yppyl7k kk-+ 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diam-k7 py+l6ypk keter?    m

  A bicycle with tires 68 cm in diameter travels ix x 0z)sr54fkyc *(os8.0 km. How many revolutions do the wheels makk)osf05xirz4c( sxy *e?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm-t5lr:fs b /yt*vgn y-. Calculate its angular velocitsy-*b-5fr /:t lgy tvny 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 revoy.c(wbk 6o, 6fjssgo4 lution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from thefy6o6.ogs(w,4cb ksj 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 Ea9l7i r8 ; tdt.xtscj7orth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sb/bt+,j::swq 9dp vcopeed 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) mus71, lqp ho0ewtt a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration ot o,p1lq 70hewf 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center fromuw 7q(autle* c nx8y(- 130 rpm to 280 rpm in 4.0 s. Detexnu-uay7q(8e (t*cl wrmine
(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,6vcat+ fndf 5s $R_1$ 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 Mo-mvensn n.bj kh:az/). 3mih1on, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min ti)nk-j3 sa:beh ..n1v /mnhmi zme interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Througm5i r4z m)ldz+h how many revolutions mlmr +izz)54d did it turn in this time?    $rev$

  An automobile engine slows down 2dakw6f ol65zao: .rrwtek* :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 sn9mf *tvo 68wutresses of flying highspeed jets in a whirling “human centro wv8mn6ut9*fifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uvl5am-f2uu.5j b(iuni, dua 6niformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this ti2 5 -ii(56j,uulnmua .vdbu fame?    m

  A cooling fan is turned o(;m xci1gb92lf +spxwff when it is running at 850rev/min It turns 1500 revol+;m clig2px sb xfw(91utions before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car ma e6zjm7i)u xz/g vw)r+ke 65 revolutions as the car reduces its speed uniformly from 95km/h7i+vx)mjwzg /ur)ze6 to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions a 5c q)0 xb+for -pw:9l)dhbow yhozu) *5l+atss the car reduces its speed uniformly from 95km/h to 45km/h The tires hzwahwftd+o) x *l5qsb :)9)oob 0yh-up5r +clave a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike a t tv0xv0 6(u(5 dkyuuly 11crqhr6+rputs all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radiusc(5(qu vlhv 1rr06 +01 uraduyyxk6tt 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 cjuvttbqrb :pem30q::, uu( 3N on the end of a door 74 cm wide. What is the magnitude of ut::ucb erq3buv 3jp:(, 0mtqthe torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown fxsz3 nf e2kti6a(-u *znz *6nin Fig. 8–39. Assume that a friction torque of 0( *fak niutzesz-6xn36 2nz*f.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the o1v7)oamc +t x+5otbsends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of1 v7saxm oo tbt)co5++ the net torque on this system.

  The bolts on the cylinder head of an ensv .nr6t8pm2zgine require tightening to a torque of 38 r8n26svmt.pz$m \cdot N$ 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 of radius 0.648 m cjkzpmgtx j-;ct1085 when the axis of rotation is through i1 mx0cjptc;-kg5jt 8z ts center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicyc-x m2hr+y y*:tchbpdh.4sms .le wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg* + mp t:yscyhr-mb.h 4.h2dxs. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thinc4 rhcg jiec3):- g8irq17ceue5hq izljf58), light rod is rotated in a horizontal circle of radius 1.2 m. Calcqrfeh 4z- 8:ri 1e iu 8lcgj35cecq7hc5g))jiulate
(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 pottehj s,ljl;r*l0 vr2n :wr’s wheel rotating at constant angular speed (Fig. 8–42). The friction force betwv,lnhr;r js0ll*w:j 2een 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 poin: t a4.cww,+c+fr .yk)vaguabt objects shown in Fig. 8–43 ab. kr),b+ctgaya.:cw fuav+w 4out
(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 atomso)9g,pw 2w unc 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, enginau ydij 0-,iicoe0 x:3eers fire four tangential rockets as shown:iud0oai xi-, 3ej0yc 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 l :e *h(crf,k.5zlmlpa radius of 8.50 cm and a mass of 0.580 kg. Cafk5z,l.:ple(mr l* chlculate
(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 swingat2ai* l brlt;0m5h*d5 i9whrq )x7a ms a bat, accelerating 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 tangentially on a small hand-driven merry-go-round and is a*9-wq1tecer0 8ig bh xble to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, 0eei9h1*8wqt-rxbg c 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 atzv( qzh njmeo1 *p:;l* 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional to:zq;mje1 vohn (lpz**rque 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. 8–4qkxc1p2 t )kk+5 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 sold s.ih)gh-l o5xst e;0ely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelxht5i es)g.l-h0ods ;erated 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 consider ,9rlt3az -gbked a long thin rod, as shown in Fig. 8–46-zk,9 rgb tal3.
(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 masses, y q75,ces6s ox$m_1$ 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 dju,9 d/)7qvd ehww,zturns (revolveh,7wu,zdq jdw)d/ 9utions) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertiae;y2.t jj0sw-,r 8gsg4c2jc puqd4 sr of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a t )zygxnn4/e)0wxeu:e orque 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 radigshbmt(.8)mz;fhy1 p. d;bl ius 9.0 cm rolls without slipping down a lane at 3hz ( gfdp 8. mhtlb1ybs).;i;m.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum c 3/qnxwu uql27f-w5fof twou -7 l2uf5fc3w q/qxnw terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kgx9qtigy w 0 3t71i3ukg and a radius of 7.50 m. How much net work is requiretit g wg9i30uyk713x qd to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.kkw5kye7a//edx; r.yo.a * lo80 kg starts from rest and rolls without slippinxd* rokea y ya;owke/l.k7. 5/g down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall a qda-rb7hb: y2nd its lower end dorb b:7-ahqy2d es not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum o; 3orj;5 m(j ohybr/(84 ffcyv pp:axhf a 0.210-kg ball rotating on the end of a thin string in a circle orj8y xofy4/ 3v;cmj;(o phb5 :aprf(hf 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 gr6vl,8xl7 j9kfc j92dwrbnl 0qinding wheel of radius 18 cm when rotbcjd02 w lq 9njkv ,698rxll7fating 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 hi9la fud1rqxrxli 8 f8hw+yq,cld2 p,07;te3 zs side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotatioewxyf 8rxap,l d3flut 7q;cq8,+l 9di2 r1zh0n 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) can reduce her tzuguzbp b-x6v7(+5 h0*xkmn 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 angulm +k0gp*bnx7x6(z 5 u-bt vzhuar speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spiocg09 4xh p11y2 wqmksn rotation rate from an initial rate of 1.0 rev every 2.0 s to a final 1x2kywoq p1 g49mc0sh 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 around8: nny fotayz d692qi3 a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it? d:9iony2a8 tzfn36 yq    $rev/s$

  (a) What is the angular momentum of a figure skater spi vbf3dl*vqm0zizg)js;7 :,lf nning 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 tjr-hsbwx t+f p.q4k9- gpl/ u4he 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 momen .bejyc,n/7r z4fy5uxpzv3.x2j gl4 at of inertia I is dropped onto an identical disk rotating at angular s j4a .z35cy,lb. fz xp7/2v ujgxr4ynepeed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at+ s s)pkd-b0ft 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 ste 0 *anw1godwy0gc:4dands at the center of a rotating merry-go-round platforc dw: 4ea0go*wdgyn 10m of radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angula;c vchpjl61af s p-,8tr velocity of 0.8 f h pt1,c c-vp8aljs;6$rad/s$ 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 5; c2p)o gog*yx 9;.uynzermninto a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existingox c.ugmne9 yor z*2 y;p;)5gn radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in e4pff eu.ot-*f xcess 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 5plvkextd/c 7y n*n06 $ 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 rotat+b .d0p*i ulyme freely without friction. The moment of inertia of the person bl.d+mupy i0*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-:5 z;16k4wypzrg pnrgm diameter merry-go-round turntable 4gp 1g6r kn zrpw5;yz:that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope roll hmhc)3w6 w d(9xm4jvpo6n6 lrs on the ground with the end of the rope lying on the th mo(j4dhx )3 9w vclpw6n66mrop edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Eard ;wx 2smmleivh)f:g2l 2 zas(e -36vvth such that the 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 the Moon as a particle orllv) zmde:fhv a(i2mw3;2xv2 -6ges sbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest 3 s/8n ;ukjsscat 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 mwe):p,uxcph7 uaig m64j3i o4 acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculatep: 7g,xhuiwi4oea6j)m 3 4cpu the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of bth:6+ nrq9nz two solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo b:r 6z+9 ntnhqwhen 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 5mcqj ,/zsm.mrear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as grx54semgb/n e 9 2 6do6emgk(wpeat, were rotating at a speed of 1.0 revolution every 12 days. If it weredgwpmee6(k 9 5e2mgo x 46/nsb 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.    $\times10^{9 }$ $rev/day$

  One possibility for a lows uc4ump*es p4yr0 ,4u-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, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needrps4upum0s*ue,4 4 yc ing 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 illustrat wp9 .i-* dqoywtx;w7tes 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 surface at speeegpjf(;tzl tqmd9( .:;0d 9sn c6k bsgu5.tto d 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 freel ljri3hn-6j/ q 0d6zyey (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is her/j edl6yq3j6- hizn0ld 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 verticqib.u;16s7 k;xry.s5c ov 8kmygfhb 5ally on the floor, and we want to exert a horizontal force F at its axle so that it will climb ro x6bkc vgq58yu;5m71k by shif;.s.a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2ax wt8m478)v 7/*cxigct frd4y1ewpx k2cgp8m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal for g8mtpc v1 4c8gxecpf a)wr7xd t/872iwy *kx4ce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m*t1c/1 o h5 iu/jguze 26xvcvd 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. What is the torque required t u1dzj vg5ei 2*hv/xot/cc16u o achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinderq8(2njjc(eg l and her arms as thin rods, making reasonabg 2n8jqec(j(lle estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plfi o8tf kph9,8ates, of maphf ko88 ft,9iss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 jzw4w6 2 i;ci+h-g bccrough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the iwcw-; jh iz6c gc4b+2loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do notzprj)fr g u87: /m( .0kn8 ldujujn.uk:fw)vj assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spee t)v9qr5ku ,zsd uniformly from 90km/h to 60km/h The tires have a diameter9vzt)q uk,r5 s of 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