A bicycle odometer (which measures disk 8gw05na3hr : st,bgj7enul)tance traveled) is attached near the wheel hub and hruwat5g n)b s,l03ne g:kj78 is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a p;(be kc4;9x9bx5(shjlil( zxwe wrf 1-1 ip akoint on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/zx(( bwl1ki 4jblcxsa -19ehxf9;k 5w(;p eiror tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of th:*wa h91swd9re/ oe kw-mri z7e angular velocity $\omega$ Explain.

Can a small force evebk4uq 1keh*u kumd1 )(r exert a greater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behgdmv pm , :y8*mbu.su o7eey0wi: hf++ind your head than when your arms are stretched out in front of youh: fy.gw+*eu7d p meb y,o8mv0u+sim:? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three athdgjpt5 /8kg6 the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedalg/gdkt6 8hj 5p, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to ru tx( i y7aiwmvp+a3 ypf6k(x:8n 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 distrw:xi8p 3y7m6(pafi kt ( y+vxaibution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bem u/*,oqtwyd+ am?

If the net force on a syste v-4pg o(zn(n rig,bn*m is zero, is the net torque also zero? If the net torque on a system is zpbg- (,n*nv(ino4gzr ero, is the net force zero?

Two inclines have the same heighl1z 8hj/q+mq2l6ohj8ldx ;bvy i72ut t but make different angles with the horizontal. The same steel ball is rojl8vjbt 8ody /m+;722hx1 iq6uzl hqllled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously stl ;u t9d(inc kjb)0kn6art rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bokdci ;lut(n0j6k9 n)b ttom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius annfprsgi8j* 4ao97tt - d the same mass. They 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 kinets4 8fnj*t97ar- pgi otic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momenmkd n,r7 4ra(afaum ey3 b//1ttum are conserved. Yet most moving or rotating objects eventt ufbe/rnka7 aa3mdmyr(41 /,ually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, h0q s3fl**w dvtow would this affect thd*wql3 sf0 tv*e length of the day?

Can the diver of Fig. 8–:qv jcxp gol8xv7g-k284o2vq29 do a somersault without having any initial rotation when she leaves the boc8ojov k7xvvg p:lgx2qq28-4 ard?

The moment of inertia of a rotating solid disk about an axis through ifjmd0z9i48w 4 mwu d6ats center of m0ddumiz48 faw964j wmass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating eyd j cwe.f7wbnosi-v4c :c5i;ps 1ua; :p22zstool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same?cvzp.yisb:ae5p uo jc22s7n:icf - ; ;1dwew4 Explain.

Two spheres look identical and havh mi5zfjw 18m9e the same mass. However, one is hollow and the other is sohmw9i15zmj 8f lid. Describe an experiment to determine which is which.

The angular velocity onwh:v2v4 y trhy7s 1r(f a wheel 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 increasr 2r hvynwst4h y17(:ving or decreasing?

Suppose you are standing on the edge of a large freely rotating 7a45m m pyp4qpo3 nur5kid; (tturntable. What happens if you walk toward the centerm 5a4 5r3 ydp4 n;m(koitqp7pu?

A shortstop may leap into the air to catch a ball and throw it quickly. As hm3z+mj y o q7.x/ql;fxe throws the ball, the uppex zyq.+mf73 mxq/loj; r part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why 8yp8hmg;k 0-g 8hf,dt hrnwl0a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stabghy008,wt8 fhlmnph;r d8g k-le.

  Express the following an2c;e 8oc)a8j l*wdj hg 7t-ydvh58 tgmgles 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 am jg 3kqgxrf1t7a)/x1l azing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in flr 7/k1t)g3jx1xqga radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moocwb-5y:hdr ,j 6gnvr)ai x*1fn, 380,000 km from Earth. The beam diverges at ixf,1j gh*v5dwb) nar cr:- y6an 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. Whenptu:0)oa5 w yi the motor is turned off during opera0w5it p :y)uoation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anothezh: nqni/+3- daz*bnxr child. If the ball makes 15.0 revolutions, what is its in-z3dz b x: nqn*ah+/diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. Hqn2xo/ fvk7aa6 ccu,wt g)q)5akyj;6 ow many revolutions do the wheels 6kv2)), t7agc qaoq6j x5/fykcwau n ;make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angux:y; ;gwrzu6(5mtqt4tg y*8qsm j7h i lar veloci4;umytrm q t6i5j twhq xzgs;7*(g8y:ty 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-g vj/:u. j+hovround makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from jjug/:.vv o+h 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 orbrapq55+oa ib(1us1 dx.s ya; yit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a 2bbnchf *hx-n+ryjcx 4 (r a..tmso:* 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 centrifkv; ,03oiqjoui1j zp:uge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100u3q:k vo1j ; o,i0jipz,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accef-1a:y.p r(lo *hxp4wgm ,dwclerates uniformly about its center from 130 rpm to 280 rpm inar.wyg:1 lphd(4f x w o*mp-c, 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiu u(u(uf6qsugp i788;a qyc)wis $R_1$ 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 mel7btn2y,g( lcg7* i 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 tyglnlim2 7*b,7gt ec(ime 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 accelerat wk6j;cu5esl456 m )e 4ufpql nfq(0wies uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in thk)4f;0 lp6 lwmsuifqn65 wc5qee4 u (jis time?    $rev$

  An automobile engine slows d t fag09i4s2qvown from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets :;6 *v qivfdgqe :3rrn7t8asbin a whirling “human centrifuge,” which takes 1.0 min to turn throg;vi7* :qbeq tv3 dasr:rf6n8ugh 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 3-:zl4x( /m)awh odfqb 60 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in t:xmohbfd 4 w z()ql/a-his time?    m

  A cooling fan is turned off when it is runnineg,y9 , xis:aq-t8dpig at 850rev/min It turns 1500 revol i,9qt g8,sxp a:iyde-utions 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 make 65 revolutions as the car reducpti1u90q9q kww/g9g res its speed uniformly frw kgwu0p 9g91itqr /9qom 95km/h 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 as the car ( o,cy8dtrdgp0 h5mv-1f3zecfpt; , greduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 058tpzfe0fc rh dt md ,yg,;c3-pg1ov(.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 eacrn:lr b/z*w4 ce-yw t/h pedal when climbing a hill. The pedals rotate in a circle of radius wy/ l4e:zrw tcr-n/b*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 74m:lie 3 od+p1r cm wide. What is the magnitude of the torque if the force is exert:o pei1ld3rm+ed
(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 aboq7:s xkpz7;gpie/+ sz ut the axle of the wheel shown in Fig. 8–39. Assume th sp/7k+izep7zq ;g: sxat a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are a k4;k9n-+e-m th gcj4z7lvpvottached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and thenn-9gvkjh 4;tzl+ po7k4 cme-v released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylin nd+,3:r, ppx lzmdwe9der head of an engine require tightening to a torque of 38 pln,dw+m9x,zp :d3 er$m \cdot N$ 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 gljt/z7fhe:a:ad7n3wa xj 7x.f0,slof inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotatioe dxwthn73ajla0 /gsa7:.z 7:jfxf , ln is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diam8o qja /krm*b;eter. The rim and tire have a combined mass ofao8 q;krb* j/m 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 rotated in a horizontalx1ykz 8sz1*e*gn2hd x circle of ranzex s g8*y1* x21hdzkdius 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 rotatisn(+ vu,e g ilyah:-z9ng at constant angular speed (Fig. 8–42). The friction force between her hands a9z,:eiyvl+-a ( unhsg nd the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects g4lhv ( hb+wb+ajbioou3s(( knqi 93.shown in Fig. 8–43 abqsonabijv(g i.( uh43 +lo+3khwb9 (bout
(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 m)fw wmn p2m8mfj4 mj 61x:ieu1ass 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,d:cmf*co6 7 o.wtxvt3 engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if thxc oc:3w6 mvtot7.f*de 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 mass of *jibteqjm071af8)s7bgh8v xsv .i *u 0.fj* .sb0h1q si7ve*)a v8i7ubtmx jg8580 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 rest tow1vf9y93eutn5v g 3ng 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 apgi 9zz x ;+,y; z9ooc6cvwi:z small 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 disk of radii+,oxc z6gv:izo zy;9;wc p 9zus 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 rotarnly(7ai *0rs6i )ln gting at 10,300 rpm is shut off and is eventually brought uniformly *l)an7isi l6grr(yn 0 to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelera3uvp8 iw; ,2nykvf) cp1hb 2mzvx s83mtes 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 baly6v2 z g2fwj pedzz x(yc5s6))l is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest 5s)6(y f)wjzpz6y2vx ge 2cdz 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 conji v 45g ou6*d3hzf7spsidered a long thin rod, as shown in Fig. 8–46i z*6dpg57su4hfjv3o.
(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 c7lzh.t hx2mrj2tmw- fr*x2 8s2/f r gconsists 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 rest within four full turns (jk5/n r d0;mqu d6ft+yh9i3wcrevolutions) and releases it at ytdm;d0 j5 r9n q6+3icw kuhf/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 mom+ v3mf6ecl s 5rrxp2l/ent of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torqsz-i 2++eg+lgh9 a3z/4ry sy.fknn ay ue 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 i*:qf:c1schr kg and radius 9.0 cm rolls without slipping down a lane at 3.3 if*qh:src 1:c$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the s*h(a7f dom kx1yl r.q2um of two ham kxy1fq(.*2 drol7terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and s9( q:c27secbmnape . a radius of 7.50 m. How much net work is required to accelercmea s9qe7pc :(b .n2sate 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 and rolls without7hx:2n + 8i iobeyu*3 mm1bymfwcj 02v slippiixmwj 31fy+in7b2mhv: mo2ebuy8 *c0 ng 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 tips/ agj:orr/+y. It starts to fall and its lower end does not slip. What will be the speed of/ago+sr/jy: r the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a xnc x-9*p2 8u(uwwcxq r3a5zq0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angxc(- wu93cq52xzxr n p w8*aquular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum ugl qc38 lk)g;6 9vufgof a 2.8-kg uniform cylindrical grinding wheel ugc6u; 3qvg8)9fklgl of radius 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 pl *wo3v ,xv1phlatform that is rotating at a rate of 1.3rev/s If he rais v *wp,oxvhl31es his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the -a:wiwr 5k nlray75vm g-rd3eu i,:z,one shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changirr7dar wv35eylum :gia k w,--,5in:zng 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 j th81q d3j *1gi 5ulskeir03gan initial rate of 1.0 rev every 2.0 s to a fin ge1tkdi *8h3q3i5s1lr0 juj gal 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 rotatin +l.;pozx n 9m(gmsr9pg around 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 chppl 9z+9 mnr(o.xsgm;unk 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 sppaj+ehi8j o7t 8v a87einning 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 tt7s6tjox wbq0ig)p5 c k)hj86tqz1t: he 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 momeg/5usgg.-6x-us+ g azv*z hm ent of inertia I is dropped onto an identical disk rota-au5s gmzs6v g.zgu-h+g*x e/ting at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ago,wo o kin7*nczj:bs7)*+jof pft5 +t 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 stands at the center of a rotating bewdww))p7.-( rfwi amerry-go-round platform of radius 3.0 m and m b-fa. (r7pi)ewwd)wwoment 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 mera z-tmfza1 it,r1::airy-go-round is rotating freely with an angular velocity of 0.8:rtz1iaa-itz 1 :,fma $rad/s$ 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,,x5d ,aajizw6 losing about half its mass in the process, and winding up with a radius 1.0% o za5wdajx,i,6 f its existing 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 wine* onit gpr(f(akldgg.5*9c9 ds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass um nm16u/t.xy $ 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 wlzw(sq; m3: jsbqm8aez ry;0 :ithout friction. The moment of inertia of the person plus the platform iwzz:lmm 3 q(r ; sqyejsb:;a08s $I_P$ 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-go-round tukksm6qt8 4e72lk1 g3xcavrj5rntable that is mounted on frictionless bearings and has a moment of inergk71c6 q3 8xv2rmk4tla5eksjtia 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 ro06 6;exc iwopells on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding 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 cen;ewi xpoe06c6 ter of mass move?

  The Moon orbits the Earth such that tg1jso7mb2im+vu +v+m .wj8 r-ar0qc nhe 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 gqmr+wb-rm u0+i.8+ mv21nvs ja7jc oMoon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at ad0dh7jzq e;smn9wy:o sqy-0) 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 uniformdfyalt07yzk7c5j98 qew vuw(d/ 2u)e cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration.u 8cd(yadvt ) j/l0wqfky7z95uwe27e Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solidz3ak j6x52gbki)e1 mr cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mabmz )j2 56gxeri 1kk3ass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angu /.cl uh8nv.cllar speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but witvkjd s03jp5q0d4+u tmh mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If k0dsjjutd 3q p0m+54vit 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.    $\times10^{9 }$ $rev/day$

  One possibility for a lowy35 ll 453tl1hqt i. ygcvo7nk5y9gvb-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1 .lolqy5954ygvt 53tvig l ky317bcnh400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an h80cvvs6 bl28q8 vf ip$H_2O$ 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 horizb0ty6urnpso5 q5uo :* ontal 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 cz aj8fh/kme3;an pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linzja; /hmke38f ear 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 vertically on the floor, and we wh/6rt, :gej* kh y3hyoant to exert a horizontal force F at its axle so that it will climb a rk:,eh/t 63h yg*oyjhstep against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling witcb,wu eajb;,nu)5 )5w6raf fth speed v=4.2m/s on a flat road is making a turn with a radius The fo ;nb,5e 5 )rwauwc6f ufb)tja,rces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of le /5tldp **,om ou3pzsdngth 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. What is the torque reup*d td/3l5, mps oz*oquired to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solidylr: 47qj -k5 hzcmlpl8z10 t ic9hec. cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstre 508q9lhc4:tr-lzlp1icj e yh.mzk c7 tched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cyli ryqrzjux)802o +blyhl01, al 1/m xwbndrical plates, of massl yyl/awqm+r 1)hbj8x 0lo0rz, xub12 $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fig. j0 a(5n5zbwq dq ;cvdcwd0 g7ou81w (v8–58. What is (u1ncw0(qbd c ; davqz575wowd 0jvg8the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not asel7;*zx(sp4s nwg g;oi: n9uow/l f*gsume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car.wc u)p yj4j*2c6paby reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter opy c4j2b ajw.ucy *)6pf 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