A bicycle odometer (which measures distance travelzvx9de /a6qa k+)2s c;b/xg jded) is attached near the wheel hub and is designed for 27-inch;exxg/v/6azs2a)bk dq9+cjd wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a pointz +rl5jh,9babrl) -h z 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 accelj 9 rh zbzla5-rhb+,l)eration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be (l6 qrx 6dfsiz* /5mra0r:iq0zig3kt described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greate): j/e +wssm5wtru)srr 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 withlseipo/s0 f*32/.th:wko z n q your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to p:e3/.z*tiflnswh2/k 0 qso o answer this.

A 21-speed bicycle has seven spro4g- ze(* tkmelcd 7d,vckets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a largecvdt-z g (dm kl,e47*e 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 r0 9klj 3et0bxnun 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 distribution oe0b3xj9k ntl0f mass is advantageous.

Why do tightrope walkers (Fig. 8e yky7l,q tqvlz5. 93y–35) carry a long, narrow beam?

If the net force on a system is zero, is the)-5t ;h*zpf mqzuv b)c net torque also zero? If the net torqu thbv5pc )mq;* f)z-zue on a system is zero, is the net force zero?

Two inclines have the same height but make different f loap765led4angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the b65e l lad4o7fpottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. Oidqxn36 j dg:fpt+d+-87rtdone sphere has twice the radius and twice the mass of tdtqrd f37pj:o+td6dxi +g8n- he 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 rst ezxjri2 z6,9uc6 a:adius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which tjia c rzu:9e662zsx, 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 momentumexa z 3w/bhg+4 and angular momentum are conserved. Yet most moving or rotating objects eventually slze+b h x43g/awow down and stop. Explain.

If there were a great migration qsrlom/7-*ej fd e3j..q,r cbof people toward the Earth’s equator, how would this affect the length beesrqmjr*oql.j,./fdc 7-3 of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotatio.es*bfmh2;aqnr;zv:8a37d mg t2 mx qn when she leaves the board?qa;8d27v qahr s:tm.*mfn ;gm 2z3xbe

The moment of inertia tp7: *qf,icdpof a rotating solid disk about an axis through its center of mass is:*d tqp pc7if, $\frac{1}{2}WR^2$ (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 stool3qem-6ym pyzz0a yhu/(-cx. y holding a 2-kg mass in each outstretched hand. If you suddenly myae06 z-c y(xmhyypu/- 3q.zdrop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hdrahp 2-s*w 1oollow and the other is solid. Describe an experiment tdah r-o*2 1pswo determine which is which.

The angular velocity of a wheel rotating on a :4*qy4l3lif6hx ehxkw;w0z5n kx cs4horizontal 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 43ki yw464:l*xs 5f hx0cqzn x hekl;wpoint at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standi 4;zab. s50(i-jq: exz+eaxkkj xqxb7ng on the edge of a large freely rotating turntable. What happens if you walk toward the cente7qze b+k .q ei0xbx5a4xa xsj:( ;-zkjr?

A shortstop may leap into the air to catch a ball and throw itokxn *j 37)kuli(-h op quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the oppoxlh)n- k pkj 3(*7iouosite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why;c /hy6qw5g5,u(r yyyc ojha1 a helicoy 5ur,1y;wco/(j6y a gc hqhy5pter 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: (a)3 l-,w lg+pkxu 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 amaz6y d1k hf46igry8;u aying coincidence. Calculate, using the information inside the g y1fyuh8;i6r 4kyd6a 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 beam b/w qyn:5) p6p6b kaws-ckdszq4w 1 m0diverges at an aq6bw1qzss )p mkw:banpw-c 6 /y0k4 5dngle $\theta$ (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 motor isl *o4m( p*uw.cmyo6z*mfs7f7 zm-i br turned off during operation, the blades slow to rest in 3.0 s *.omy64l-fpczimb(zuo *m wf7*s 7 mr. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level fl :9jifdd2b4 ln- uzfunln8g +v7dah:7 oor 3.5 m to another child. If the ball makes 15.0 revolutions, what is9navg+u2u 7j:n8i7 4h-z ndlbffd:dl its diameter?    m

  A bicycle with tires 68 cm in diam9,blq1/ qde7q1 98 x dvc6szqwa2ucaueter travels 8.0 km. How many revolutions do the wh/q, 8auq 6 ab11uveqqcz9d2s l9dc7xweels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its uufx3 fsob*+ 0nzr*b. angular ve* x3*rfbo0 n+ uzuf.sblocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. zg8 d6y26zcop* 8f gwl0xn -yl8–38). (a) What is 6glpx*yzd0 g-n fy6 8czw8 2olthe linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity zrln )yyv:;c mi)rzsg j:cl((u1, hx(of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poih3n4l9u(qkop (4b*zhhn; no hnt
(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 aqd.i.zl3 6kft lp7 ncl*j q41 etg.c:v centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an accelenect1jdtp lif.z g.4 3. l:q7k*v6 lcqration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly aby8j88poto0ozwf0fjzym ; 9j5out its center from 130 rpm to 280 ; zyjpjyo0o88fow tm0 jf8z95rpm in 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 radiusex p/4sgdod w4:qkld w47u.5r $R_1$ 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 abs2:j6 8nerkggj: o rq6 dcdc7+oard 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 minu2 je6jn8 g:q gdrocs6r:+kdc7te during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 158 - i;wbagtxg0 b(emtwb(m:*w,000 rpm in 220 s. Through how many revolutions did it turn in this time? wbw(:*teb;g8t magb0i xmw(-    $rev$

  An automobile engine slow (teydk0*d+bd4bes: j s down 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 stremsvyrhe,pl f 3a.(q/71t p+ so cua5(wsses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn throu +w1cev r3p (a/(mus,o.psl5yhq7a tfgh 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 diamersf/9c a0(oim ter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the whee0 /i9sa(cmfor l have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 r+x, hr*bp g;r(;fpwr revolutions (r*; rr; p,frgbpx+hwbefore 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 reduces ig7ctz7yc8:f(: hu iggts speed uniformly from 9:ch:u7 z8cggg fy(i7t5km/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 reduces its speed unissyx3t o 5,k; 5kiywld( e:zm8formly from 95k( z5ie;t,y5do lmsk: yw8sx3km/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

  A 55-kg person riding a bike puts all her weight on each peda -k-bo z-;qpggl when climbing a hill. The pedals rotate in a cgo-bg ;qpzk- -ircle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 c)wglyts.e( 8;z9 w dorm wide. What is the magnitude of the )(rwoldw y8g ;9z.e sttorque 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 wh14 kf4) tuiit87 thwbeeel shown in Fig. 8–39. Assume that a fr4) eii 8ktuh 7btw1tf4iction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod whi)f7azwm ovhp*:l -f;pch pivots as shown in Fig. 8–40. Initially the rod is held in the horizon7am: - )pzlfv hpow;*ftal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque of .l sc1usa *d)uifvw0938 9.sav * lu)1siwfc0 ud$m \cdot N$ 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/qw* i(-vv o3)rkj3:doq zsxynz r/g8 -kg sphere of radius 0.648 m when the axis of rotation is thro /)*o3wd:yqk8(ioxr-nq grzv/v zj3s ugh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle whee:ti xs/;da9tti ,2/j g*sluh bl 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of s2u,ail:b/ *h gidt9jx st t;/the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, lightz ift 1- immt zzw4;ox:0df(m wm/h)p3 rod is rotated in a horizontal mo(;f -pmw0/fd: m)w zzmxh 4i3zti1tcircle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotate6vow:8 x,0 kl.0+md(tvu q o othut(ping at constant angular speed (Fig. 8–42). The fup0qvuhm0., tt(oo w x:6v 8ko+(ltedriction force between 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 point objects shown in Fig. 8–43a., a7id2uv wj aboa,w .2 da7jivuut
(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 3a.eagn eg2ff vn1t sl f,;5:stotal 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 spinni l0njas cs1m2)ng at the correct rate, engineers fire four tangen)m1n0c as ljs2tial 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 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 w7 xo.,nax-+4 xyzq)sn p vcf;dith a radius of 8.50 cm and a mass of 0.580 kg. Calculaaonx-csx;n fxz,q +d7 p.y)4vte
(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 swing-na:xqf h8ijkml ;5: iv/) ucfs 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-xc9gic/ qg 0/r3wuqz 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 radius 2.5 m and has a mass of 760 ccx 3 g/w-0 q/zur9giqkg, 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 ofrjc1rb yl8z v9b5.3,y6 tay qtf and is eventually brought uniformly to rest by a frictioltj5b6tc zqvy y3a1yb8r,r.9 nal 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 accelerateq2/n3a 0d1ge owwk,ens a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, whichm7oh v+ 7wcn*w rotates about the elbow joint w+ *ncw77vomhunder the action of the 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 blad1 , 2wieka c73rw-fzzxe can be considered a long thin rod, as shown in Fig. 8–467cfz1r- e,2 wkzi3w ax.
(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, hudgm 3 iuk81xgh5v.5m)pj llq qq*) ;yj6ap* $m_1$ 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 f42,mls rue yf,rom rest within four full turns (revolutions) andey rs2mul, ,4f 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 inerti6:fl2 s3bd bgr+thz8 ca 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 torque of 28h q17 6sqrkpj95t ) s92yyfgeg0 $m \cdot N$ 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 crhs.q;. bw: vae1wn;fm rolls without slipping down a lane at 3n sv:h;bwr1. .w aeq;f.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect ty a78qupz1fy/7 p98 qsclz tz-o the Sun as the sum of two te8ytz1p/z-ufaz yq7 c s q79pl8rms,
(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 kt-lg:i1 a;tzog and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 rev;:otg z1ai- ltolution 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 andnu 0u09ni wrza d41n,p rolls without slipping down a 30.0 i, u0azn9n4pndr1 0wu$^{\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 bxg-- v3p/p2u ojqgwewr0 ;:fnalanced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of thpu30j -pgvfw/2:qxgrw ;one-e pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating onm0u z8:-qbyeb the end of a thin string in a circle of radiume b8q z0b-uy:s 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.4o ai 3bg9);k n5etya/puoh:4ujdg d38-kg uniform cylindrical grinding wheel og/ 3udit;5:j4ykpo9 g4d 3bae h aon)uf 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 9)mn: af:5pv ef8j 1cbbbdqy+at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, F+1 :p b vjy)m:a8ne c9bf5fbqdig. 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 one shown in Fig. 8–29) can reduce her moment of inev,de 0 1ukc+04zjho pprtia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular so 4ch u+j,pze0vpd0k1peed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rathzx)la58no 1 z(9 dvlre of 1.0 rev every 2.0 s to a fz 9)n5v o(8ldlz xhra1inal rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axap 0rz 02k6xsppm 0z6xis 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 centea2xz6mk 0pxz0rp 6 ps0r 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 fihbuw ci* qo0)q (b;ljtn.-f6 cw*i8wdgure 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 theg*) b9w /zrwaz Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment 65 ur5cxx v-1oytx8zcof inertia I is dropped onto an identica xovu-tc6 y5rxz18c 5xl disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns hqmb42k.f * aoat 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,/ fazmu1y (ys rotating merry-go-round platform of radius 3.0 m andf1ys( m/au ,zy 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-r.le68 ,60oq1kt fywutwv-tlz ound is rotating freely with an angular velocity of 0.e .l- t qzyww6tlvt ,k1ouf6088 $rad/s$ 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 colz5sx0ci 3 a-.v.bil ex e*s-zylapses into a white dwarf, losing about half its mass in the provl0a. -es-xsy z3 bii5x*z e.ccess, and winding up with 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 inzlsyw1ey,gqzm4p : r2 (+mkpj)(t7jo 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 4g hoat y7u,dv-ha* y5$ 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 wgi3idok- :zw /ih q.3nithout friction z3d3oi/: gh-w .niikq. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a6 ess61 sqnh k, t;h2goy)uor( 6.5-m diameter merry-go-round turntable that is mounted on fe,u ohgns 6;s r6)q(tksyo12 hrictionless 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 b08*jd b2ti0h dwm)nws on the ground with the end of the rope lying on the top edge of the s )0*8itb0db wnj2hdmw pool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Ea hrsb3o,:tte72ef8vm rth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat 3,o t2tr8m: fb7eevh sthe Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerate,rzz5z8)pat rgc(3b es from rest at 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 radiuskg5ke b5 cb v:arvb5:-sr:z(l 0.20 m acquires ab5-ba: rv5c(ers5:blz kgv:k rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 gtfb 0 m- r*5)rstt3doh;+sqh 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 when it reaches the end t o)*5rh 0tfhdr3+g-;s tb qsmof 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/jqd bo xg 8f,zbs,ca164al 0k0bms)8 na;vut 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 wi 2d5k r *u4wnt5uj1 h:yxvdg/kth mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12*2w:u4k x5k5vh1jd ryt /dgnu days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it 1 mrp /y9;i9 neqzp4xrk 5v6yz3qfh0o to use energy stored in a heavy rotating flywheel. Suppose y9n0pxoz63qp f/4 hke rr9iv5;qy1 zmsuch a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\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- iiv l+sl1.a5a;bbaw 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 on8sim9 t(,g ira a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., 714zlnjgnfu: o8 .mih 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, deter.ugzoif84nml1 7njh: mine (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 l1.xe 9s/u3jh 2w 3kjb*zn(ltn4d eji5w8p revertically on the floor, and we wane3e5 z(isbwj3hnd84 wlr 2tl/ejkux *1 n .p9jt to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road i-myn a 4+ld8ahs making a turn with a radius Thn-d amay8hl+4e 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 beginsba, a9d5yom-: aadfpgu8 z.n 2 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 to achieve this fnp5dama- dzb,f2:ua89oyga.eat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin oz 4c g;8bivweagu75 8rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with ou7ui gcaw5zv8b;eg84 otstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two ;7dhv r70 wnoqcylindrical plates, of ma07w;nrh vd7oqss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 roug-h 0avc0gi ut/h track of Fig. 8–58. What is the minimum value of the vertical heig/ cguv -0a0thiht 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 assume zh* txioh:5 s*1z1 wrj$r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly trr(h m*fmb4v4oyi 7u5aurixf4en sg 7818 )y from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of eag857()vuir4 sirf4 *e8ufomy 1thxnb7a rm 4ych 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