A bicycle odometer (which q8xc6i, wr4 hsmeasures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What hahc,6 ixs8 rq4wppens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on theskav 4z vg/6(z 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 compone vk/z s64gvaz(nt of linear acceleration change?

Could a nonrigid body be descriau 7x03bzl6t kbed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explain;t w)ayza -;x090egq 7t gup(,kvrkns.

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 sitqnylx55 m20f a-up with your hands behind your head than when a 5x 05lqfmn2yyour arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pedal a;-mx ;r6 bgpstq 1x4fcranks. In which gear is it harder to pedal, a small rear spro;- ag mq4ft6xs b1;rxpcket 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 withz0f--f*ygcjei /ob ,s )jx3ng flesh and muscle concent ,-cz3)gjx be/0 isg*o-fyjfn rated high, 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,6xegm4)2 jp on03qxb r b.mv0v narrow beam?

If the net force on a syste 2m)iy -l7 6nlykwf gh,qr0i(eof :dy;m is zero, is the net torque also zero? If the net torque on a system is zehi mrdy ewg6k2:n 7(ify,lq-0lfy;) o ro, is the net force zero?

Two inclines have the same height but make different angles with the horil2v dpn81lmt9*o (u o bgv08knzontal. The same steel bk1n0uvd*l(no gb9v 28tml po8all is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down 5mh(kwo ewag6 gv4vz/w+ y+vqieoixd0 5,0 h1an incline. One sphere has twice the radi,v/k604150oh 5 +e iq(v+weaixwm gwyzv ohgdus and twice the mass of the other. Which reaches the bottom 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 and the same mass.c7mwi*lk aw3 y 3*nu9t They start from rest at the top of an incline. Which reaches the bcwin km3t*aluw 7*y93ottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conybc/vc 75qyd 1.b xgs 6w87xobserved. Yet most moving or rotat6vgc/8cyxb byq s1.w b757x oding objects eventually slow down and stop. Explain.

If there were a greatkl6p -ip 4mvua+cr o27 migration of people toward the Earth’s equator, how would this affect the length of plu42o 7k-cvpr a6+im the day?

Can the diver of Fig. 8–29 do a somersault without havingoa3q za* h9h0q 7osk1g any initial rotation w ohszhg a1oakq973*0 qhen she leaves the board?

The moment of inertia of a rotating solid disk about an axis through iht3y56a5b :he rik**l1z rznx ts center of ma36k h zb*ryzn5ae*xlth5:1irss is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass+t/ 1rhlhw 9v in1za2b in each outstretched hand. If you suddenly drop the mar9/1 hlh+1 vwnit z2basses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look iden3b :m kayce1cet7il 0+tical and have the same mass. However, one is hollow and the other is so7 em0cy1l3te :i b+ckalid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horiz* rof/twf*n, xontal 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 fxnw r/**of ,tthe wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turnth 6mjxox)-zx rsul.zw49- +9suhtl h(able. What happens if yohx9t+r.) u(shxl6hojzz-s xmuw l 9 4-u walk toward the center?

A shortstop may leap into the air to catch a bawzj r ;piz9 amdh2t *nu;6*k,mll and throw it quickly. As he throws the ball, th2r hwnzpmdz mj;iua**tk96;, e upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation opaq 5faxm .g,gf0 l.-:gf6lccf 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 keep the helicopter st,lf a. mp0 .gc: c5glgf-fxq6aable.

  Express the following a4 3ezv z+abbl5ngles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence: cd+qv7 wkd3o. Calculate, using the information ins w7oddqk:+v3 cide the Front Cover, the 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 from Earth. The bewe4pv 5fi, vc,s ,b4bjam diverges at a4s,vb w,ji,45cfp bevn angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the mott ffz0h eilgi)d/(m r3i3.hp*or is turned off during operation, the bi* fh gmd ehl(.3t03iizrf/) plades 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 sch5.d.q0qrg .5 m to another child. If the ball makes 15.0 revolutions, what isrqqh05 .cs .gd its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutionsvic y+9e:w: jbsl2cg0 do the whey9cw:+ig clevb2s j 0:els make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 250nba: 4dot-1xf0 rpm. Calculate its angular velocity 1a: 4ftxond-b in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution inla)du q 0vpx4hwfi0 6. 4.0 s (Fig. 8–38). (a) What is the linear speed of a chu 60aqifv)hpx.0 4 dwlild seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around thv bm,jpk + yxu/jg26r,e Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spewzxof5sft.- r 4hn (9xed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from thevvt htlkt 22oik45 +g. axis of rotat42g 2ti. thtv ol5+vkkion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 9 sr2/gcg,rufw42fhd jtf 4o ;6uh6ewrpm to 280 rpm in 4.0 s. Determinturc oe4/hfw g; jru6,2d fw4692ghf se
(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 radiupp tw8l 7:jmd;s $R_1$ 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 therr1bzao a*. r1 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 time interval. The spacecraft.1 1roa* abzrr 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 s (/ectr (mzzwb160av uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it tur (cz(ev/zw1 t6smbra0 n in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1204b 0ts d l7u1y1hhni1l0 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 highsp at*bu .0nk(9p)mm exneed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 com.(* bmna) mu0ktx9pne plete 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 rplx 1rp56yd:s; c4 mos vk5,yckm to 360 rpm in 6.5 s.1coks6;x 5 r4,ysk5 lpcydm:v How far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 85 n a(c+yzje.,;bffrl60rev/min It turns 1500 revolu6lf necjrz y;b a+,.(ftions 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 m)3ix 23t qd rqc57zmkuake 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tqx uq325i kzr)37cd mtires 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 of3 3j8gdve*e u4e8mecar reduces its speed uniformly from 95km/h to 45km/h The tig oe33evu 4f8jm 8de*eres 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

  A 55-kg person riding a bike puts all her weight on each pedal when climbinh0) ,c5zvxi c1xnrjgpy.2q,:f -dcopg a hill. The pedals rotate in a circle of radius 1zq cdpfy5- g icxhr,2 )pcxv ,.:1nj0o7 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 cec-1c2qwk)/6z ko huq0lnf9f m wide. What is the magnitude of the torque if the fowf-ccq1 6f2ekn)qo h0 klzu /9rce 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 in Fig. 8–39. Assumev, ey(+lb:gp:.r(xvrh/*ua l 1 wx txq that w:lyhg xq rxa(*,pv/u+1 ve. x:(ltb ra 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 attached tox(mmnk so 0q8: x vf6apf4pl2( the ends 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 of the nx2kxl(0psvm :fp (8a qfm 46noet torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque otnw(rj+rn clh6 9iv). /0nom pf 38c+prm ()jt/oi6nrnn.w l h09v $m \cdot N$ 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 radiusgiax +wp. vy3 )-o,wss.x(nxb 0.648 m when the axis)s-v( b, oxnswyx.pi3w a.xg+ of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inerti+lc- hu by8q.*cj5 dzga of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The massuq5g-c +bjy* l 8hcd.z of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on th bc6,ewj5hr0rxc pc;0e end of a thin, light rod is rotated in a horizontal circle of radius 1.cp0r;hx0e5 ,b cwjr6c2 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 constant angu19nr*)yy ccqylar speed (Fig. 8–42). The friction force between her hands and thynry)q y19cc* e 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 shvx9* ob y3dk(dfr b 8-u6s6rz-/bvnm pown in Fig. 8–43 aboux ub6bpf8/s- (d-vrm nzdk 9o*b 6vyr3t
(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 whopk mihgjq1oby/ 41 2:gse 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, engi,hu, c.*iivv3y a(hc zn bz6z+neers 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 f, zz(iu.i6*bz ancvh+yhcv 3 ,orce 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 79r l*lh,5om w jf4houwith a radius of 8.50 cm and a mass of 0.580 kg. Calcula7hml*hljo,r54ow f 9u te
(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 r5a35rl zz2+yq1jl x7s phe3kmest 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-driv h81u wjmghin;1x(68 ddn pst9en 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 radius 2.5 m and hasnhu1ix p1(t w h9j8d;ds6ngm 8 a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually brought /*qbj d;czd5 euniformly to rest by a frie dq5;bjz*cd /ctional 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 accelerates a 3.6-kg ball atd.f(e6j fo-e( kbz 8di 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 actig7jp0vrx 8h 0lon of the forearm, which rotates about the elbow joint under the action of thel0r8px7hv 0jg triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considere+i1gc4t cecyf+;-) f/ hsmlki d a long thin rod, as shown in Fig. 8–4t4h +l ckcm+ fsy/f1i-g;ic e)6.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masse/yzhd 10x2 asf,46a p7zlf rjes, $m_1$ 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 hammeq:infh(q e lqga45 7kdnob1fn/* u0t0r from rest within four full turns (revolut ltfndk 7*qbaq4e(/0uo5i hgf:nn1 q0ions) 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 inertia of f8-)nfl0ou8x;,r h;tmcwvw w/va.l n$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a tpy4 .-sn9d1c)w pzkna 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 radius 9.0 cm rolls without slipy)l 6ui(xy 3amxsbpgm 7x 5o,.ping down a laneyyxo65.(gp sl)m ux,bx7 i 3ma at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the yll)nt:z,u3v sum of twoz vu3: nltl,y) 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 kg and a radius of 7.50 m. How mw p4:*rsy/- 7rtset9qtf 4w 6rpzq :asuch net work pa:t*qr 4:9t rry/wtq46swefp7z-ss is required 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 1.80 kg starts from restdxhqw*+8ec qw d;y/bv(( tf5 a and rolls without slipping down a h ;bd85qfqw/x(c+atyvw( *ed 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 an8r sabj/k6zs89mw7h jd its lower end does not sa96/8 rbhw7jk s8mszj lip. 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 of a 0.3:hldv5w o/ln. oeo f. br1uy4210-kg ball rotating on the end of a thin strindf:l1buvw.o./ r3loho ye5n4 g 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 momenirh*q0my 2 2,k,xf tautum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating af*, umt2,ri 0q 2yahkxt 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 h3rrq(ow ,ok5wis side, on a platform that is rotating at a rate of 1.3rev/s If he raiseo(o,wq35 k rwrs 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 onpd7xjc 8z(y /ne shown in Fig. 8–29) can reduce her moment of inertia by a factor of about yn/jzc(p78x d 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial ratep 4+g jxuo*h 7omh-lsn2*tmut5+ejc- of 1.0 ruu2xm go5 -t-* +hnjc*7omjhe4t p +lsev every 2.0 s to 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 v3ur*wa .vw3tgq0 gyczqh59( uji 5/hmertical 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 a*w 5hh/.3yt9m i5uc(gqu gvrw3j0q z 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 fa8wv+u x-4bnj igure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Earth;u8e,1 rtf uqx4 3tufw
(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 vmw6c8z3c:pg moment of inertia I is dropped onto an identical disk6g8zvcc:3p w m rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.-vczx ; johr1,4 $rev/s$ 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 t*k gj6os1y2m zw+a* gat the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 92tso*j2y *am1gg +6zwk0 $kg \cdot m^2$ 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 angulan5rk( 4:aj2j sc( usdor velocity of 0.8 s5 (jcrdsn2 a4j(uk:o $rad/s$ 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, l*hh9 hzc g5vjwm ; r /1/a9et;kkfsj1kosing about half its mass in the process, and winding up w gjvmf*/;/e9rw 5 hkzt 1hk;9hs1jka cith a radius 1.0% of 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 winds 3xrx4.oed /l+w3;cwofx2jk3o*- cy ,bigwa gin 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 *)j8-s z5t9vuan03mfxoxls a+ jpyk:71t ihb$ 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 platwady (6*:sszj xt sw50form, initially at rest, that can rotate freely without frict(ydw sxs*j: a0stwz56ion. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands k5 fdt*(mlnhl ssn 0).at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings andl(sh) mtf*5n0.ls nkd has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying on thetu9 yz8 ,mv6rm 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 wtm68 yvm,ur9z ithout slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same smm b6bihv 2(:mide always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own ax2m 6bibhm(v :mis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest aip xy 6d49qt,7d6tjvat 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 inyuz4h i6ab(.m p+6xnf the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculateyua+n.xifhp64 (bm 6 z the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of massdfvz05c4 5bs g 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.01 fbg405cs5 dvz0 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheelml /godh b4 8pjl2s/,f ($\omega_R$) 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 1g::6mv3pdifoiv8nlas great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational c gn:6l 81:ip3v vfdmioollapse 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 lobnp. pgxm/wvao6 *y8zr 3tro(+44uebz-g4e f w-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 350m8zfer -ap */ eoov4 gr36px tbz4w.y4ubng+( 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 illustrai a s)yvk9, jofbln(dfo9;,*luz*v8o tes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (h12t e)y 1steg;o t*vzdoop) is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and lengthngz1:zfpz. wf3yo648 tyw2 wn L can 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 linez .6 wf3:8w2nyw4z1zynftop gar 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 stan 0l zenqow74fjb :-fuu 2fgp4i-b2pv+ding vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The s4fu2:uqv f 7ibn0+ -eogbpplf2z j4-wtep has height h, where h

  A bicyclist traveling with speed v=4.2j;rb z8a,f:kym/s on a flat road is making a turn with a radi:ka8fy;j b,r zus The forces 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 length 1.5 m and begcbfks ).vkf5v57v 8 ecins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm aftck )cf5 vv5b8.vekfs 7er 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinddb+o6 ckx;ofc: yks-p b+5pr+ er 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 outstfob:cs; p 5d-x++6okpycrb k+retched arms, and with arms held tightly against her body.   

  You are designing a clutch asse1vuczbp( 0f/8m r ij:cmbly which consists of two cylindrical plates, of : cv8ib(rz/0 p jfm1ucmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fig. 8–5e0m83p3utdcg3 na mle) ;,kci8. What is the minimum value of the vertical height h tn ,i 33tdulec0;38pkgm ema )chat 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 nothpt-6 p.8l jr*dc7zgu assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformlyf apt v7h)x3w0z4wju 3 from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was t 3ft3vjwh4awp)z 70uxhe 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