A bicycle odometer (which measures distowy/c 9:oj1 fdance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle withowyj/d9 :o1fc 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point onpuy,gc:3f5fx( bb 0(qlvhkw / the rim have radial and/or tangential acceleration? If the disk’s angular veloc/xhu3k bc(q,fy gf (:p l5v0wbity 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 single value of the angular ve4x* qqwz vpi-p n;3pmux6xd-v,ae( t4locity $\omega$ Explain.

Can a small force evepn z+)2p cti3vm,6 h90c kpevbr exert a greater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behinuwkz-sp(d z;*d your head than when your arms a*pu- w(sd zz;kre stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has ske : k4tro ae6v1b22gxeven 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 small front sprocket or a lae61rgkbax2e4 : kov2trge front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with . pyw0k6+r4s movhd4h flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dyna hkp6+.whys0omv 4d4rmics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, e5 byz,im)kl8.r.y txdg2y(h narrow beam?

If the net force on auz)pcqvsr5y vp f1njx 58:t79 system is zero, is the net torque also zero? If the net torque on a system is zert) 5u 1 :x5 z8rs7yp9cvnjqvfpo, is the net force zero?

Two inclines have the same height but make different angles with t vsleaoz)1 0epi/2z m+ qd5yp s6y-m0the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be py/e0sq0ma ds oey1)p vm5l z+6zi-t2greater? Explain.

Two solid spheres simultaneously start rolling (frm.,khcof *qw:*dmw 3e om 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 greater total kinetic e kwmdh3qf,oce m*.w*:nergy at the bottom?

A sphere and a cylinder have the same radius and the same mawm-dl6v lj:. gdg uf5.ss. They start from rest at the top of an incline. Which reach .: jll. 6fgvuwgmd-5des 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 conservedu) i3xzzm :5j pgwm/;rbq xm;z.fd /49cq -khm. Yet most moving or rotating objects evx/ 4z)u krmmh jz;x :9b/piq3c dfg5w-mm;. zqentually slow down and stop. Explain.

If there were a great migration of people tt pzih 2aah://nv( ht to.qn+5mp3d;noward the Earth’s equator, how would this affect the length ofnn (tmza/t :vhidtpq/+ h a2n. o53p;h the day?

Can the diver of Fig. 8–29 do a somersau,ft7jr 4knv/ 8o.drfylt without having any initial rotation when she leaves th/o8 ff7ntyv4, d. kjrre board?

The moment of inertia of a rotating solid disk about an axjtk: zfrg0 .*u67xj 9qwti9;;lfu. cue6lu ri is through its center of mass r tfwqt.l i9 f9i;ljuuz erj67 gkc 0:.x*6uu;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 mas,qlea+xgo s w; c0f6r4s in each outstretched hand. If you suddenly drop the masses, will your angular veloci ,oa 46gf rqcxw0es;+lty increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow as*j+sr l0o3rjtd/in(nd the other is solid. Describe an experiment to determidl +sti3r0j(j/*sornne which is which.

The angular velocity of a wheel rotating on a horizontal axle points w r)hhwa.5rh;hest. 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 poinr5h ;w.r)hhha t 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 e(ci dc mw(j2n m3t6pl8(zxa w3v m;udchi4;)turntable. What happens if you walk toward the ccn8a lmvm(3 uwddzp) ( ;xemh3ctj;42cii w6(enter?

A shortstop may leap into8 n+j*4 4)jkvem* j yccxy2drw the air to catch a ball and throw it quickly. As he throws the r4 *xj4kcw)+8c ey *jn vmdyj2ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular mome7gn1gbcaem y(zv6a,v g (24hsntum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propelle6esb27zggm(, cay4g nvv(ha1r can operate to keep the helicopter stable.

  Express the following angles in r -(r2jpbetamh 5r4tr 6-x;tdqh1 ww.n. *qgx nadians: (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,-4b u7tf:gy go using the information inside the Front Cover, the tf:ug-74y ob gangular 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 kmpf 2gljngu3 ;b4*eb(b from Earth. The beam diverges a 4gg3ub* b2(fp nbj;let an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm bp/27jezh)l vsaqj 99. When the motor is turned of2s jz9ja 7/evq)hbpl 9f during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.fh 5 al; )36he(oyox9ahxcl( ftd5 /ho5 m to another child. If the ball makes 15.0 revolutions, what is its dihfoo/l) h;5 9( la(65ahth3xodcey xfameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions ,m0) nqs3y17sp eu lyddo the wheels ma)3sqysnde01 ulp7my, ke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates nfo-zl1; i ff8g;f/ f 1ygcwy;at 2500 rpm. Calculate its angular velocity in ; /;f cnfl;yffgy1ow1gf -8iz$rad/s$ $\omega$ =    $rad/sec$
(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 sjy7zxi3ds 4b7 zoy1m, (Fig. 8–38). (a) What is the linos i7xm,j 37z1zby 4ydear 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) in its orbit around the Supy gvl2 k1u2 0s8khw8hn    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed o)x i*0lc o5qmof a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from :1ifrkxnqi*8tj/ 4* dc1i khj the axis of rotation is toiiqt* 1 jxni:d f4khrj/c*81k experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly aboutll l6j)s- n.gn/a xr,t its center from 130 rpm to 280 r rgnl/).lnaljtsx, 6 -pm 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 radius ji+7w ss; 2so87fs3 vkd1 cuv epmp9(e$R_1$ 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 Apollo spacecraft put themselvesobekm1 /)g: q4t3u xae into a slow rotation to distribute the Sun’s energy evenly. At the startxk mob3e:1/ag4q )uet 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 fr, i.bdc :j2jzxom rest to 15,000 rpm in 220 s. Through how many revolutions didcj :jzb,xdi.2 it turn in this time?    $rev$

  An automobile enginep64r munvskh .ps5* 7b slows 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 stresses of flying highspeed jevt0cd 09nwv4l ts in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachin cwvn4vl 0td09g 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 diametn2zt.49 gp c.hx sztf-c4 iv)h*x:gnber accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of t9)4ngcg2fz-xh4thpnb* vc. itz . sx:he wheel have traveled in this time?    m

  A cooling fan is turned off when it is a2b*-7 )dd2qvenrj,cp o z:blrunning at 850rev/min It turns 1500 revolutions b cj*oebdq2- a7pnvb):,z dr2lefore 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 rd. zlw 5s(b7dcth/ :zvfu1ds y0f8jr(educes its speed uniformly from 95km/hdu7v (zhs50cj1dw yf r./sfzdl(:b 8t 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 uniformly fd4o**xd-kl ny rom 95km/h to 45km/h The tiresn* dx4o-l* dky 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 sb5b;f (2sdr7 juboztz)2)k iputs all her weight on each pedal when climbing a hill. The pedals rotate in a circle of ruf)(d 2;bbszk72btsz5o )jri adius 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 cm wide. What is tcx4:5,iz abj)-vdt:07x eaa6tlen nihe magnitude of the torqix ei7 : nzj- ,etc45taav lnda0x)b6:ue 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 wheel shown in Fig.y,f ui;t(;5 fcnllr h( 8–39. Assume that a fricti ;f rf(,(uintc;5yllhon 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 masshii 0/98c2z sps z pa:yp0lv8dless rod which pivots as shown in Fiad ziz/vi sc8p8lhpy0s9 p 2:0g. 8–40. Initially the rod is held in the horizontal 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 req0 shuh 0+;t ;lzpmi6etuire tightening to a torque of 38 lt;tm06pzuih 0 +e;sh $m \cdot N$ 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 inerr;3(xc1y1/ aiv x)z+jf0 2v qis*bpurood d /ntia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is throud/ xizvjn;pasdq / 0oc+i1(xu 1v3*o r2yf)brgh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diap+o6u ek 3vzx :.bp5pfmeter. The rim and tire have a combined mass of 1.25 kg. The mass of t53o z u:.ppp+v e6bxkfhe hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, edx a cio kmv*85xe,4y(p/wh, light rod is rotated in a horizontal circle of radius, vehwm c /x4e8koi(a xdpy5*, 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 rooyn 8g*tn.pzn jk9-) f- 9ckzltating at constant angular speed (Fig. 8–z - 9k9l*kztnynof-) 8jpn.gc42). The 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 inertiaib9,j m)vqs3 g3m7sla of the array of point objects shown in Fig. 8–43 a,bs793amv q )mg3si jlbout
(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 ,e0.+4+vcydbgmn5mwzxq / 4ppa 9 n ccoxygen 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 wo8(h4a38y n (osbh .b:a9kr on-kuay satellite spinning at 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 f-:(a n4ak bo3b.k n wuyyohsar8(9h o8orce 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 witoxt6 sz:,(3ds4tinokt kef1 : h a radius of 8.50 cm and a mass of 0.580 kg. Calcutste6oi(:: fs3kzknotx, d 41 late
(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 swingsbss-iadd kb6v/vib:3ul- l4km30 bvir . 2+ia 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 small hand-drivq h* wjxwk.9-* w j6w+zhmv6xqen merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assuxw*-jh *+q z q6v69mwkxwjhw .me 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, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,uu s6w s8.afil8un55 x300 rpm is shut off and is eventually brought uniformly to rest by a frisu586 8s5 un.fwixlauctional 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 accelerateptl*tha7 v6s*d0 ,;fz 6 lnyves 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 ba)v 3**mm bofzf wz,xc:x*r)jz x,u.yn ll is thrown solely by the action of the forearm, which rotates about the elbow joinmj)y,ou:fz,v .*w3bfzxxz r mx) n** ct under 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 blade r dupk 7r-r -:kfi .ccxug8.6dcan be considered a long thin rod, as shown in Fig. 8–46.u-dx..ku:fr dr8 r- i67g ccpk
(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 tw bufgmi a4 wx;;6w)v,xo 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 fr,ed --uq ub fg6rxe7.vom rest within four full turns (revolutions) and releasesue 7-rg, xevdb-u6qf . 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 i( 3 x (hexgsd280xtucnnertia 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 devel2 i bhvs;b43qgops a torque 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 x4+xgkrds;m5(1gle kyn,z 1x radius 9.0 cm rolls without slipping down a lane at 3.3 nl(1; zekxrm ,yk d5xx g4+g1s$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of t9kg.c ke5 ldf6pe*;iz(4x cbghe Earth with respect to the Sun as the sum of two c e. eg*zcbl45kfpk ;(6ixg9 dterms,
(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 radrm g395s( (pkqm4 qgvdius of 7.50 m. How much net work is required to accelerate it from rest to a rotr4mgq(59sqk dpvgm( 3ation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20 0krg2 usm8zy2.0 cm and mass 1.80 kg starts from rest and rolls without slipping down a 3z2gk rs20m8y u0.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall a4ia zpv/.a r(/ezx*pond 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 c p*p z.(i /ax4vzaor/eonservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on thc(ij av0k1k sef4;4pme end of a thin string in a circli k4mps(4 ;1 ef0kvjace of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindricalr7hqjzy ln)vxr3v. 9a(o j .d- grinding wheel of radius 18 cm when rotating j q- )3v.rxh9.ya(jr z7lno vdat 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,b/gr+)94jy vx+l4zvyo )ti tv on a platform that is rotating at a rate of 1.3rev/s /oy) ztt9b+4gj )vr4 v+lyi vxIf he raises 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 cbob,z8m-:p lFig. 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. If she makes 2.0 rotations in 1.5 s when in the tuck poslpcb-o z,mb: 8ition, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from ancrk +pu,8vp6 f initial rate of 1.0 rev every 2.0 s to a final rate of8pc+6pf, ukrv 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 roq5u0 er7ivv pma fi0eep)y*- 8tating around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be consideredvfi* e0)qp07em 5 p ey8iuav-r 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 center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure hvp1-nr5chd4) qdzn3e:/h c j 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 mos0(nzy;3g 2-)x n 5x;msgcl7 opbaj yhmentum 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 moment of inerndofqzls 50u 9 4+q/gn) p2wewtia I is dropped onto an identicgo5/nuwdfqn 42sw9) 0pzql+eal 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 at 2.4lwh6r s2 9h2s,pr yjrto (df) 2wjc44y $rev/s$ 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 rotating4 ;r6b/k7 g:ugzwcc 6lbazr c3 merry-go-round platform of radius 3.0 m and b;wg rrlzbgaz/7c:c46u 63ck 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-round is rotating freely with anh,a cty: jfg0fe288vy angular velocity of 0:yyc0,8hff8a t2evjg .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 c:izp.f qtui3(p un:x, ollapses 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 Sun’s new rotation rate be?(round to the nearest ini,tq 3p :u(i: f.xzunpteger)$\approx$    $rad/s$ (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 :fdznvq6c+z(k c ox/wmu w;61 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 p ,esah y+g7,* fepa8i$ 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 uw-y p55yns96gh2;9t iupvyy can rotate freely without friction. The moment of inertia of t9pus5yup;6 -n yyhvit5yw g2 9he 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 diametw )k95h7se dxfer merry-go-round turntable that is mounted o79dkfes )xwh5 n 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 rope rolls on the/t e*tol8b80bu)pvzd ground with the end of the rope lying on the top edge of the l80tb 8 vzb e/*o)tpduspool. 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 sqs:b9a eny eeum ekii.**/, 8iame side always faces the Earth. Determine the ratio of the Moon’kq*: 9ee/ei. bi msn8euy* i,as spin angular momentum (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 restb13 vnp 65pxgxv:d,a d 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 shw we3k1dnz): dape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calkw)3ne1 wz:ddculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of .91mo nvclww,4h1daz 3m wj5qmass 0.050 kg and diameter 0.075 m, joined by 34hwaoc.jqvmw19n , 51dm wl za (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 angular speed of the reag,g 6hd ye;t -bj. /*zksv/eoar 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 mass 8.0 t /pzcg-49m/fie (ci ygw8d/-nz (isbgimes 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 three-quarters of its mass in the process, what would its rotation speed be? Assume that the / (fiwp4gg9d-eicm(n z8-sgicz by / /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 fo mnr) vw8457vfjei e na4uv(x)tbyu75r 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 without needing a flywheel “sp 8 7 fmrn(7)vveabuyn)4v5wej 5tuix4inup.”
(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 a t zcnmtq+k i:;aj/dn8jp2 )/tn $H_2O$ 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)v95pftre y6 )ofnj+v2 ibp h+3xfns94 is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can piv5usgc+9 fwqb 7ot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the c9s cgwq7fb +u5enter of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertical1e: ez2k* kwbdly on the floor, and we want to exert a horizontal force F at itkb1d2 ze: *ekws 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 is making a turtxv34o1z rp ua:6j2ozza *o )fn with a radius The forces acting4foz:2x t 6por*zu1)a jazo v3 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 be*ww7 -k8eqy :hkr* rrypgz/1;y*scs tgins 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 achckr zrp /* qrseyk *7y-w1 t*;gwy:s8hieve 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 thm8q 2dm 2pmwfd6j2lx+ in rods, making reasonable estimates for the dimensions. Then calcu26qm+fmd wlp8mx 22 djlate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch au;vn:b jsb (s7ssembly which consists of two cylindrical plates, of s sjb: (nv;7ubmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alon3spq +jd**zc yg the 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 highest point of the loop wi c*dz3p*ysjq +thout leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do nyiqt / x.3)2weasr)m; 5osbbtot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as 9c 0euy jh; y1lj18dqkwi-8acf 2txx;the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleratd 9xx -;;h2tjy8jklwcucfy8110qiea ion 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