A bicycle odometer (whixz7 /an5ycvrar,)n6 fch measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch w/,rcvf6)az 5nya 7rnx heels?

Suppose a disk rotates at constant angular vel fvc 3*+o siwdt37pze0ocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, d fi3pvcsdz0*3oet7w + oes the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described1yj un .*-wjh6 nobua5 by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque tha;acdlqo9hrao0-7 oi3 n 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 diffic/qg/f;x l-4 u+oz +n;qt t-mpxlivfmk 2l(xr7ult to do a sit-up with your hands behind your head than when your armvtkf2/ f /xpti qq-(m7 ml++nzrg;;x-lulx4os 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 m5 m8n4omj 4yswheel and three at the pedal cranks. In which gear is it harder 4mms mo 5n84jyto pedal, a small rear sprocket 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 beinee/2vbo)va 1kl q) i.jg able to run fast have slender lower legs with flesh and muscleo)./ )ikejqe1vva b2l concentrated 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, narrow beams ;pbj7:ug9b h?

If the net force on a system is zero, is the net torque also zx o 99b8d 8c,zqi7k6nsf0qzda ero? If the net torque on a system is zero, is the ne 80bq9zkq s,df7d o8xz6cnia9t force zero?

Two inclines have the same height but make different angk(7t6yit )4* muvgxw nles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? xym g)ut( kitvn6w*74Explain.

Two solid spheres simultanez(0 vh(0 h7pt,r puy-dubn(cnously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the y(nu(t7c h0n dru -pz(0bh,pv greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They startc1d kt 9;83z iok*tiod from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has3t dk;io1ck8 o*tid9z the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum b c ,dl90mm9l ;viny)tare conserved. Yet most moving or rotanicml90tl y ;v9)d b,mting objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equa;z7crdg 3x2z rueu-y0wx8 9 xvtor, how would this affect tv0 - dxyrgz7;x2ucx e3u8wz9 rhe length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial roa0y-j uinzi(t7 vw+z7tation when she leaves th7 zai(tw n0yi+v7ju- ze board?

The moment of inertia of a rotating solid disk about : y*z qqm,qx-x cw12cwan axis through its center of mass w:yq c2* wmcq x1z,qx-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 in each outstukbqu65x- p-u retched hand. If you suddenly drop the masses, will your angular velubquk 56 -p-uxocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However,kwc1/hae 04y0 z9zbael g5l .y one is hollow and the other is solid. Describe an experiment to determine which is 5094ae bh ag0wkll 1zz./cyey which.

The angular velocity of a wheel rotating on a h wzz(ud0;k4m gorizontal 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 ;dkmz(4g0wu zangular speed increasing or decreasing?

Suppose you are standing on the edge of ff:wv8/ n/q;ry fbx+ ia large freely rotating turntable. What happen/w +b8x:fn; fq/fviyrs if you walk toward the center?

A shortstop may leap into the air tm /xom4raw k5z883 7 geqf4y)pcyof7 jo catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips andz) 4/7mejpfoomyafr 53 4 7q cxg8ky8w legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why -d w npf;o)eufq;m: 8ra helic-;n 8 ;mwoerpquff: )dopter 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) 3czhkgr5- f 6hark 1*1j0 $^{\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. Calculate,8d )gjd.bb :astpnp.0 using the infot.ppn :)as .8j0dbdb grmation inside 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. Thedba46i j lvwsd+8u;e+ht 5,gh beam diverges at an anglu+wgtbl a4ehh+j ;d6d s ,vi58e $\theta$ (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 bihkrjid0*5z: 0 0xhn rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accelerat:jk*0dxi ni r 50bhh0zion as the blades slow down?    $rad/s^2$

  A child rolls a ball yb3nz7.zb( uo*kx +vxon a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, whb3zy+u (x7zk*.nvob xat is its diameter?    m

  A bicycle with tires 68 cm in diameter travels74 ti5or/+aa +ty5u5qvlqpvv5 d zpy, 8.0 km. How many revolutions do the wheels makep5dvpyvy7az u4 /5qqla o+i tt5r+5,v?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its ac7wx4ym/ n9 hbngular velocity inxc hw m/n749by $rad/s$ $\omega$ =    $rad/sec$
(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 rev eck 4;oypg0cqk0 y0.bolution in 4.0 s (Fig. 8–38). (a) Whatpckcy04g;yqk. 0 0beo is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a):njs 9ik zd vv5eur2-8 in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed +li ii0ff :-w;em (forytn,c:j7sj6n 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 93uj bu w4zvlg)je1-ma particle 7.0 cm from the axis of rotation is to experience an acceleration4wjvm-lg9u3zb u e1 )j of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its cente9dhx-osi 75slza ) 6d/ fuv:j3mfe 0wer from 130 rpm to 280 sof6)iv dm3xla: js h 79u5ee0 f-dz/wrpm 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 radiusq/jm-g3+fxk 5s qxfs : $R_1$ 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 Ap(qht re2oem1q x o:v p-l79pl3ollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of :qo1 pr2xm-9 lpq37e(lehtv otheir trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Th.wpqaw-zf d0oj l x,91rough howow1fqd0wzx.lj 9p -a, many revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpe 2l gbuwu*6;em 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 vs4w (g v6uhv dms2f3qog(:q 4rk; kj1stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed;v vv hr4swjko (q: muf1(ggks32 6dq4.
(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 acceler x9k(:kyp 1yhqates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this timeq91kk ( y:hpyx?    m

  A cooling fan is turned off when it is runnidj xe+m,w2 qh:ng at 850rev/min It turns 1500 revoludmj 2,+whexq: tions 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 reduces its speed uniw2 7 hewi7 g72tbc;qfqgzl;e/formly from 95km/h to 45km/h The tires have a diameter of 0.80 w7g7teefih q2;qcgz7 ;2/lbw 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 rexh2b c 3dzj+m ne(*m*wqi p6r,duces its speed uniformly from 95km/h to 45km/h Thzx3+p62 cwm, ij*re *n(bdqmhe 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 hsi)n2jykh2 g+er weight on each pedal when climbing a hill. The pedals r+) nkjs2iyg2h otate in a circle 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 fsm:b.j4rjpr -;zpjt3uy,a6the end of a door 74 cm wide. What is the magnitude of the torque if the p;. as6 zmjj y:f-,u3rpbtr 4jforce 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 wh(9atwvzle0ttxp/v () eel shown in Fig. 8–39. Assume that a friction torque of 0.4 twt lv09/v()(aet xpz$m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a masslessc vqkn797 b)crc ou3vb)alc*. rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate t clc3)av7uocbc*b.)k 9r vn7qhe magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tighteni9vr vvg-gx q.;fed6 f2ng to a torque of 38q.vg6fe -grx2 9 vd;vf $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0 wcly37 anxwb.ebj1 jz8l6:z0.648 m when the axis of rotation is through its center..1xlwj6a8 w7 ben3zj yl z:c0b    $kg \cdot m^2$

  Calculate the moment of inertia of a bicyc t+: 6 jlzji2kj)ix(hmle wheel 66.7 cm in diameter. The rim and tire have a +zx mk)ij:lijj2t h6(combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the m odq arfa+l59+*mf (pend of a thin, light rod is rotated in a horizontal circle of radius ffr m+*5aapq+ldm9 o (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 poul e0 3 +j syq*mkw7efa.*0fzotter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clayel0k3+ *m f. 0jq7uoa sywe*fz 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 pointd6lcm-zkl-q.q/m q4 e objects shown in Fig. 8–43 al -mq-kmldq4/6qez . cbout
(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 whodf)wsn lo.n(f 6foc(d g2uk/x;+cw m( se 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 at1xmkintoj 58. the correct rate, 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 the satellite.jtx58nkmio 1 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 of4 3o/xnk2kgd j2 y jtw7-v1 sorrpa*f; 8.50 cm and a mass of 0.5x 21n2- jr4krv *gpkyao;dotf/jw7 s380 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 v)3tl 4,wil+x0yd g ukfrom 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 tangen 6c j6+gugg o8(p(bgyxtially on a 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 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 accelero+gbu xj6(p(g y cg68gation, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm ox 2jm;x4ph52xt/mcxis shut off and is eventually brought ;p2tmo5hc/m2 j xxx4xuniformly 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 acc-o h+s b*oy0yaelerates 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, which yw g;z 9s8owjgdly) 9)rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is 9d osglg89y zj; w))ywaccelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in +k3-/o sbs gb+d,xc 5erbvdo-)tr +wsFig. 8–46.s+o-+,/ bgbdbtc+) kx vr-o5 seswr3d
(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 consi(l-ipw0v 8xekl h92pu 4x (hcists 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 ft0p, 4,oy 6+ actpquzeour full turns (revolutions) and releases o+pttyza,p eqc460 u ,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 abvyk ah,n5 8uzm0y 6dzpf yqpj7)3ula( 2,ot0 moment 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 .7y+s:a/rij9od mphw)* z jubtorque 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 witf :7xj4 al-ok;vhcrz4:kuc/ ohout slipping down a lane at 3.3kujo/4:k- olx avzhcf:r74; c $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with-e57ur b53ff0q g)lk t.tfcxo respect to the Sun as the sum of two term3 5t 7ob.exf uf)-f kr05lcqgts,
(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 *l)uucmk t ) 1hlnla :jhx(.7mradius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolutionak(7h1uml xhu)mncj ll ).:*t per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kdcp kn-c+ -y 6w4q2tiig starts from rest and rolls without sli-6i 4ni-wd2cc yp qkt+pping 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 lqx p9qz05 qr9tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.9pq95l0qqxr z ]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on t53b,lc mfw :llr7c)h+s(hd urhe end of a thin string in a circle of radius 1.10 m at an angular spee5r7 ( )h3,+lscdrm: fwlclhbud of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2+veh0qes3m4 v.8-kg uniform cylindrical grinding wheel of radius m3 qhv0s4eve+18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating bp/ouw7d.7cbat a rate of 1.3rev/s If he rais 7c.ob/u bdw7pes 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 one shown in Fig. 8–29) can reduqo ),m105oufn4hy. eewujbx/ ce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what .mqhef4u )o05buw,yx/e n1 ojis her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial ra8 he8. hp3co j+ -loj9bz)j)gww qy+amte of 1.0 rev eve)8 .8mbj)-g pc+ yh3jjew+a z oohql9wry 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 vertical axis tna(1w)xz4 jc 2ohfue3 hrough 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, onexa13h o2c nz( 4)jfwuto 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 angul69pl6b mxgebw/*csw nip 01l 2ar momentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momec5bq(7r v5dt3cv i ll;-s; ewlwjxy,3ntum of the 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 momentsozpe+56n5xrlm f; f: of inertia I is dropped onto an identical disk rotating at angusfen or;px5z5m: f l6+lar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.odbmfs .xk3f;)p o3y-4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round platfortf04v/usvo k; m of rv k0tuf/sv ;o4adius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-ryz96s)n/hldl4k.e 3q x) ,t ,rcem vdqound is rotating freely with an angular velocity of 0.8 6) nct., 3zs 9qlrlv/)e4kedyd,qhmx $rad/s$ 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 nl(calr0-ezl8 i f *b8white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away0zea8icf -ln (b*8 rll no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 12m)v:ldss1w06v ofs)1 w4btoq0 $km/h$ 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 fe.dosxhz7 /kaf5b1 cbn 00-y.fga ;q$ 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, iniyieb6hxmf )f 271bt6l tially at rest, that can rotate freely without friction. The moment of 6t6lmb 7fi b 1ey2)xhfinertia 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 a 6.5-m diameter merry-go-roun2ef0)0t,ll fncnlfw.b t m y51d turntable that is mounted on fffce. n ly 0tfm)tll w25b,01nrictionless 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 rolls on the ground with the end of the rope ly2; wwzh(3qc)va s-plying on the top edge of the spool. A(l w2v-a q)yc3;hwspz 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 r7))3o x 7x kl(likvnethat the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentu ix773l )xrvkl(n )koem. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of wwcxr.3 mzdppfy*) *0 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 shapbn * -dqfhd *0enk7d7te of a uniform cylinder of radius 0.20 m acquires a rotati e7 ftnd-d7d *nhqbk0*onal 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 kg :qrqb h/ 7o/ 84py zfsq9*hsetand 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 ib* q/hp8sq:so/ry h9t zq e7f4t reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear whee/9kzqg- 1wzg il ($\omega_R$) 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 Sntv1 /f;ms*u eun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing thftv*mu n es1/;ree-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 to0d(u4ef11s yu gvha 8- dvdeo* use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel * dyvh11egs(dev80 -u4 uofad“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 illustrate j/6h xu:u/qexs an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a hsr8j-en +nn pv ana5.-orizontal 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., we igno5t05qel; 4q:htk ny ao2c ts)mre friction) about a h)4q clt0nt y5mk2a qhto es5;:inge 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 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 radpsnj3kr (2thny2 j ;(lius R. It is standing vertically on the floor, and we want to exert a horlk(n (2jnhr ;s2yt 3pjizontal 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 wi64urnt * yf3gz+0 t micymt/r1th speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and 3zt+ r0in *m6t/yg f1umyrtc 4cycle 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 beginlk-lv91 7j 0 gd2q1kos+kmneps whirling the rock in a near 1 ke1 9l70kpd+n vk2mlqsjo-gly 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 feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid bzv6v8j t tll9;9 zx:ncylinder 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 outstretched arms, and with arms held tiz8b 99v;vl: xtn lj6ztghtly against her body.   

  You are designing a clutchk-e7cd08bvs+l djzi7zdch v*ou-9t2 assembly which consists of two cylindrical plates, of mas- o8d+b9tzd ek07vcszlvu jid-2 ch 7*s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 m9ffy 6twrolc; 01z(;4bm dlr z5z1juthe looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highes5wmfl;o0z1(6 mctubdr zlyf;41 j 9zrt point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not (/kxri50d lb tassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 bmi 8+u sph8*x08s.ruwzv: zgcc;x+g revolutions as the car reduces its speed uniformly from 90km/h to 60km/h cgu;xzw.+b*mp8s8v0 u:z8xgc h i+s rThe tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s