A bicycle odometer (which measuresr3 r+q5nxq6j s 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-inrq36s q5 xrnj+ch wheels?

Suppose a disk rotates at constant angularooc,;aivv,ds-sj 9 ;l 1 iuyqxjy2 r5. velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angula;-va 5 ;l, .rsviuoy 1xiyc29odjq,j sr velocity increases uniformly, does 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 described by a singr;:y1ogpa uv6le value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explai mo3 siv+3r:rin.

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

Why is it more difficult to do a sit-up with your hands behind x6ke0o7m o, ht n -uk7gm,3lniyour head than when your arms are stretched out in front of yot0,7 gkmnn7xo-,oe6i mhlu3 ku? A diagram may help you to answer this.

A 21-speed bicycle has sev*+mh 809z8bxuepu h3bjzf n)g.mfcx0en sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a)*zn bfb0h mu 30f.e+ucmp9hg xxz8j8 small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have ;b yn8r0 -kyekslender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rota0ynyk e8b ;r-ktional dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig./s*kvoop 8xo (o:uq:u 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero?80brkj p h-glg7c 9ll; If the net torque on a system is zerlp;c0h9-lrklggj 87bo, is the net force zero?

Two inclines have the same height but make different anglet- dfu m2vui*+s with the horizontal. The same stee- 2*+udumvfitl ball 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 an inctr vwf h)uipj,;). /tfline. 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 greater total kinetic energy at the bp; ,fittv /wrh).uf)jottom?

A sphere and a cylinde z sm-/i7 sm73ssicxq6.uo s(rr have the same radius and the same mass. They start from rest aimu s(7sqsz63 s rcom.ix-/s 7t the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved.4x ttornp w3zq--1qpv *rj;-u Yet most moving or rotating objects eventually slow down anjw3 *pov1--r -prqq ;xt 4tzund stop. Explain.

If there were a great migration of people toward the Earth’s equator, hy- rf24h4; hv 5ol/wov)w ntjbow would thn-v; 5w t4 4/hwyohlbjo2f vr)is affect the length of the day?

Can the diver of Fig. 8–29 do a somersault withdy7 f2-w;y( jxu)iio zout having any initial rotation when s fo7idixy)u(w-;jyz 2he leaves the board?

The moment of inertia of a rotating solid di-mmvf..j 1xf8bdhcnn5 2t:b3lzpq+9 m0 dtflsk about an axis through its center of mph 3nlf5d-t:.9jdcvnz l0xt. f m281mmb f +qbass 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 onz hw6ml7) 8wwi a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or 687wmz )iw wlhstay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow and3h;g,zrqald- e+s.s6-,)j 9b tsvmrs j,u ukd the other is solid. Describe an experiment to s qsa dsh3uj,6-d-rg)v9+sj klt,e.;r um,bz determine which is which.

The angular velocity of a wheel rotating on a h0wp:g( o(ncldmgg 6-yorizontal 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 accelegd(m c: ygog-6n0 lw(pration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. Whb,b u ; b*ree;:gy;z wcv7,ic;b *cowwf t;;chat ha;;cw egc :bb7bzui,r,c twf;*;v;hbyc ; w*eoppens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it i tm3w4btd ;e0 p(7sxhhv(si: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 x7(hw htpms di3; bsti (:40veopposite direction (Fig. 8–36). Explain.

On the basis of the lawdkjos1b( *;v7 *kk) buv blj2j of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propellelb*( skvvo;)bj12jjkub* d 7kr can operate to keep the helicopter stable.

  Express the following angles i 3x1 )r:ugw6iyld )mp)nnp/ lpn 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. Calculate, usi ;jix dpg9,69cl*f vgfng the information inside the Front Cover, the angular diameterp6;c9*, 9xifggjfd l vs (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 i.2c3x( de eywxrr5t wbx;j-8 beam diverges at an ajx c2x5xywrde t. -eirb8;3w (ngle $\theta$ (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 tz+ x um.q5 mial3b t;ga/)ayo,he motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as th;,tm u5igzlbaa3 y mq/o+) ax.e blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball ) bkxs 6pw2mqs7j +8uamakes 15.0 revolutions, what is its dw7 u6bp)+ 2mqsaj8sxkiameter?    m

  A bicycle with tires 68 cm in diameter travf9 dmp3hap*:ewn 2ni, els 8.0 km. How many revolutions do the wheels mefdmni9 h *3p,2wnp:aake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its d0 : em r5gzo uu:2c/p;ql 1gckn1zud;angular velocity inod05:ecd:n z 2;g;q/mpuc rulz ku g11 $rad/s$ $\omega$ =    $rad/sec$
(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 complhm*f9f .(i sbhete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of *is mhh.f9bf(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) in iw(l ey+f h0,0qxg u5uats orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of xqk/o2 rk*hl2a 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-12rifrjes1c a particle 7.0 cm from the axis of rotation is to ex-ifc1 s21e rrjperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniforh0oys,n zk:9 jwi2cy1mly about its center from 130 rpm to 280 rpm in 4.0 s. Determinn ywso0:912,jhyki cze
(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 radiupw/dc ln03ch 7s $R_1$ 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 aboryd3cp5 :ie+py 3g)w6 es7p jjard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the 6ysje +ep37ip dcywj3p r5)g :start of their 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 15,0 8b1m0-czrtur8k+ c;r)ofl rp00 rpm in 220 s. Through how many revolutions did it turn in this )+rpl crz81 tfrrumck 0-o;b 8time?    $rev$

  An automobile engine slows dvo. ,ggn(u ad4own from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspee7/q c28 v/aa6pz o3y.mu midqdd jets in a whirling “human centrifuge,” which takv qymz/dqp/amcdi328a 7.6 ou es 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to i4w/u nb;hy*w360 rpm in 6.5 s. How far will a point on the edge of the wheel have travele/ihy;4wb u*w nd in this time?    m

  A cooling fan is turned off when it is running at 850rev6yub:7tdwt b49d cjd+/min It turns 1500 revolutions before it 6+c jwbydd:4t7 9bdtu 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 redcw;d)4:jngd z k/b0am:sk 4wsuces its speed uniformly from 95km/h to 45km/h The tires have a diame g4/c zmd;sk)w0sbd:j4na :kwter 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 spee1)usxf-s9vr pb7z8du d uniformly from 95km/h to 45km/h The tires have1bss7r9d zu) vp -fu8x 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 climbingzm/, d l2ortwp k2-t8g a hill. The pedals rotate in a wl/rg 2 pz-,tm8kotd2 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 the end of a door 74 ugbkb n,,ynb)n d1g1 :cm wide. What is the magnitude of the torque if the force is exert),b kdn g,bn1byu1n g:ed
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the- tnrz;og7 w 7:k,wtnj w.n(ih wheel shown in Fig. 8–39. Assume that a friction torque of ng:w,n;-wrtizw o7(7.kht nj0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless r+-s557r fxf: f/j nl tm6jrzfyod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direc m5nltx6zj/ +-rfj5f f:y7fs rtion of the net torque on this system.

  The bolts on the cylinder headl x*lga;fqhd8 o.b iaa:9: 1gg of an engine require tightening to a torque of 38 bgq8x1 :h.aal*:d9ogg aifl; $m \cdot N$ 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 in*ttl 2 u uvz, dj jr +6yooqxvhyb;:sc(11s.k3ertia of a 10.8-kg sphere of radius 0.648 m when the absk 1+,3r dlo(yyj:*stoc6 2zqxjh1tvuu; v.xis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm ,xvr4 gmw 9l0q;pkk3pin diameter. The rim and tire have alm, 9 0kqgrvkp; 3px4w 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 end of a thin, light rod is rotated ing-q r, i -xnytn2xvub3e:dy;. a horizontal circle ox-;ryeb23: gd yi- , un.txnqvf 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+dq q hx)sm e:c2,4och bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). 4hq+x,emohds:) 2 ccqThe friction 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. 8–4p1 p 9c9li4z ,oon;efd3 abo49leondpo 1fip;cz ,9 ut
(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 consi ocvad(7jan06 k)d q1 r-f1zovsts of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the corr2t jn4jlcqhz2t.sh ()ect 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 is to reach 32 rpm in 5.tqlh.j(22hsjn c4z t)0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder win,*fk hwp9 n i4d8akt8th a radius of 8.50 cm and a mass of 0.580 kf98dtpk8*h n4,nwaikg. 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 b/9y0hy 2qv )il5c7xen ukab0pat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry- m.+nn(v 5th4c-zxfnjgo-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 acceleration, negle vcn(nxm.45-nfjhtz+cting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotj+ytfkc+f+7mopxa * * ating at 10,300 rpm is shut off and is eventually brought uniformly to rest byc7*tp+ akxomy* +jf+f 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 accelerates a 3.uj :gig1q, zpe;2s:cu6-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 thrownxrw:9xortp(x 0ev4 : f solely by the action of the forearm, which rotates about the elbow joint under the acti 94 :pfe(xvo :rx0wxtron 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 blade can be cons(ngt2 rx 8tf1nidered a long thin rod, as shown in Fig. 8–4xr fn g8n21tt(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 fu5px8+vns2ipu( r a3 consists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turn50c/p o rk za92 t:sc;ymeiin7s (revolutions) and releases it at a spe iz a/tnr:c0cseki 9ymo2p;75 ed 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 kpn;6aairjajo0bm8lg mvpk 6 5k-6 *+ $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 280 /(xxxzyb05 dhp + sdd($m \cdot N$ 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 withmt.f*hjrd5 gep g z(u,jq -*n(out slipping down a lane at 3m qn** uhz-j5 g,jtge(r (fd.p.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as tbp*hoqyude v : :.t*,che sum of two te* dhe:pcub*.t v:oq,yrms,
(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 2t xu3y.-gy9 ddd7i wbradius of 7.50 m. How much net work is required dyg.29yu3 w xdt7-bid 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 start g vipxe6l uzln4y5/u;/(uq -gs from rest and rolls without slipping dowl/quneguux4v ;/- ( 65yp glzin a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts tn2um w) p*mh*rpo:ja/o fall and its lower end does :mhw n/*)urpo2m*j panot slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotati;fzag)6rwni.l ;l s3 lng on the end of a thin string in a circle of radius 1.10 m at an angular sg ;6l al.)zlfr3 ns;iwpeed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-ecg9p., zvjw)ml*msu6-5dm e( a 1ap fkg uniform cylindrical grinding wheel of radius 1aj5z*m .,ppg( 1se 6w9emc- vdmfu) al8 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 rotatino+x,3rg8ztw;u ly d *.ih2xwng at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.x+toy ur. ihwz 82x,lwng3d; *8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one show-x67qqq/li m:t1 zewhn in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. e7i6lq- q w1xh :tqz/mIf 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 iaax / y- k;7f-vbn*0k+c9apmr/ yew exncrease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a finvy9c 0r+nkayxea 7-;*ameb/-pf x/k wal 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 through its center at a frjitmr.fvk z*tb5 48onf **o4sequency 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, approxim8 * fo.z b5o4 m*f4*vrtstinkjately 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 momkfhgikq;-x) p79+hupentum 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 momentum of the 02unwxobr +p.+nf1 qtEarth
(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 of inertia Ikjdrasy;5m t:;f9gkk(:n kk3yq4s9 x is dropped onto an identical disk rottrjxkk;ad( kk9 :nfy 5: 3s4;gmqk9y sating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns hf xdw,aq v meolq0mu50w;gfv)z(e) 8l;7:rz at 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 rot 0uxwcnmp3: yf)++ wpiating merry-go-round platform of radius 3.0 m and mo :+3pwy xm fiwcnu+p)0ment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotatihg h eo1h2 dtgh- fwv.-1i,6,k,cuitjng freely with an angular velocity of 0.ihu -ftocke .,d2 h1h ,vj6tgw1ig,-h 8 $rad/s$ 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 colla50uu)/fc ;4;am-n wow emxqc opses into a white 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 away no angular momentum, what would the 4uwxmuf wm-aooqc)e5;c;0n / 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 3/pzk0 r;jwmnh z(zh6hpw( k ,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 6isct lrgo38 9$ 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 rono et0nsl9- q*1q+hbdt0)jujtate freely without friction. The moment of i) b1jqtt9husdn*q -0l+jon0enertia 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 a9b fyc;1tq-cthe edge of a 6.5-m diameter merry-go-round turntable thatcq91; ycafb -t is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rop(go y ,1ax9 ftr3oghchapvz2k1oq :/( e rolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds frot: h1(v(og xafz23g9 q pc,oak oy1hr/m the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side a bqo w-/ gr(p2qg4ws:ilways faces the Earth. Determine the ratio of the Moon’s spin angular mome: sqw-2qw/ o4gb(gi rpntum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from ixb53jslf(ki +o4,* lsju8sf 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 ch.-k+6qhh yz1k*d,v yly s,ncylinder of radius 0.20 m acquires a rotational rate of from rest over asy. 6hd,k+z*hvk ly1 -yqh ,cn 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 solid0la/9 tboq;1c ; wuont2/bwf c cylindrical disks, each of mass 0.050 kg and diameter 0.075 m,f ;ouba9c20 l/nt;q1wwc t/o b 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 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 angfy 6n*ftml n7)ular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with m;8t;wil, kz+gmu sbhd xp+ uu48 h1y5wytln81ass 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 111+pl1t m+uk ;w8xuduyw5;8slny z8 bht, g hi4 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 aua li,dsz:kk6 a3t0z) rtomobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km wikdia0a:lr tz3s6k),z thout 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 ay.f vg 310-hrdx8pe4cx,o. eml l r-nan $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at t 4 2qbi(lkq3.i k xr;l/3njnispeed 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 lengt+hybs m/hyg1 rall336h 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 (hl /hms6b3+3gyylr 1aa) 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 vertically on theh,,hqn 61 otxc floor, and we want to exert a horizontal force F at its axle so that it will climb a step against whicn,6h h1coqxt,h 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 is making a turn witnn1ns tt,7++x;wv j(tnl bg5 dh a radius The forces acting on the cyclist and cycle are the normtbdx t;n1 7s ,++twgn5 (vnlnjal 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 amz.evd9k8/3d) ti )+qz wtqou 0.50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque z)t/ iukov qtzw3d qd9+8).merequired to achieve this feat, 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 rouu,qsw9l )+ 7q1mpaqrds, making reasonable estimates for the dimensions. Then calculate the ratio of the angula7q,sul)wq umq r9+pa1r speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates,4 fnnv:eul* w1s. fz) jso-p.a of mass v n)1s n.:l weao4fp* -ufj.sz$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 -1)0q8wtwkx siqsia;2 (depb track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reache1x q (a;2s-btdk iiw)ws8p 0q the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, bsrf * f5;ul9tcut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spe+k nbc)9n kb+7jb4aqi6/j oezed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? +bz k9qjiknenc74b6 /+jabo) $\approx$    $rad/s^2$(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