A bicycle odometer (which mea* 3gz .wuc2to9s:o.g 4 zfthcfsures 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-t4f ozu .92fzs3gc . cwgot*:hinch wheels?

Suppose a disk rotates at constant an+ xg1 b3ygesg/i, *:cb8p mugfgular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular veloci/bem b gx pc ,1g+usgy:i3*8gfty 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 sinfir 0wc3 4ssg9gle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explag7v21:i pk oiain.

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 your head than wh- 2npe-p4cj/9c tpwygen your arms are strp cw92 pep--jyt/cn4 getched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle hasqa0- ueea,p x/ seven 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 sp /- 0eaxuape,qrocket or a large front sprocket? Why?

Mammals that depend on being abuh 50 xrluf1 52(.w4,kaim lsqqa2dof le to run fast have slender lower legs with flesh and mus kdh21 m.s(0x lu, qu5q fafiw42ar5locle 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. -ee y4 bf3bg;/nul2ko 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque al 5p*jbb*ua r,g mj5:q8h6q tniso zero? If the net torque on a system is zero, is thejg5j5 rtia6u 8bnq: qbm,h*p * net force zero?

Two inclines have the same height but make di*h.h-p/vhfi1 /)qajf aj3y qhfferent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the saqhf.f -)ijq3ja1hhh yv p/*/peed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incle iup7 q 5jigdnan*c j*7o 9a4jm7+r.aine. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? +p9n77d54u mqo a*i ei.jj 7rnjca ag*Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radn*ach.jd e *q3y(+pvd .ouzb)ius and the same mass. They start from rest at 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 rotatio (3 *ybqncda*j)..oud+ h zepvnal KE?

We claim that momentum and angular momentum are conserve3li1g /; mtdvad. Yet most moving or rotating objetig la;m1 d/v3cts eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wt1 rqn1v/m i8qswo*vv gr* 0d*ould this affect the length of the day?8qnds0vo /tmvwr** qr11*gv i

Can the diver of Fig. 8–29 do a somersa3f o;c 5.jovvmv.l6 kb:q b7h)tmg+oz ult without having any initial rotation when she leaves o.g5c37;.6kz bbtm m:qo+ lo )vv fjvhthe board?

The moment of inertia of a rotating solid diseq zd.k2+og/7o6yj + z p*cioqk about an axis through its center of j qe*2yoq+7+/g zk6o.di oczp mass 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 s ;xh*y 9me xg.7cmlp1v2 uc(j2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the s ;1 sxpj2gcu hv7 m(ly*xe9.mcame? Explain.

Two spheres look identical and have the same mass. Howev2d4kw j wxk8,x- zxmp3+cdbo9er, one is hollow and the othercob3d9 dpxx +k4 8,kwmzj2 w-x is solid. Describe an experiment to determine which is which.

The angular velocity of at, h692h)ufivs s 9; lftk1 t/ypu8cqa wheel rotating on a horizontal 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 angular speed increasing or decreq, )k 1/a8f9lthscst vyt;u6fpi29uhasing?

Suppose you are standinj lfmlc9) sx8kjz v 2wivg4(/3g on the edge of a large freely rotating turntable. What happens if you wv4g/wzi fskj2)l (3vclxj 98malk toward the center?

A shortstop may leap into the air to catch a ufsvkk l9 t(b0 (rcf8+ball and throw it quickly. As he throws th( +(kf9vfk8l0urct sb e ball, 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 o13 zhdwd+p /)vtonu9n .xp x/lf angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.pud hxp+o 1xt/w)lz./d nn9v3

  Express the following angles in ruxiarj(t fl);+ vzkt; j0+*xyadians: (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, using they5d vz2 za/5lhw5wl:q information inside the Front Cover, the angular diameters (in radians) of the Sun azwlvwqz55l 52y: a /dhnd the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam dive4rou* xi5 +y6evws fa.rges at an w5fv6+ ai4o sryu e*.xangle $\theta$ (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 aqc*7;;fn2mklizb :qno ri+5 h t a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the;+qi: klr2 h*noqc;bm zfi n75 angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level d,96 bio 16)ylb tf3ebcb:u0wjziz:wfloor 3.5 m to another child. If the ball makes 15.fb)z1zb: d,couw3it b0:b j6li y6w 9e0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revoil;2 dpa4l 8qslutions do the wheels 2d4lq pa8si;lmake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates atimb24;b to ez2wn61y n01nopt 2500 rpm. Calculate its angular2ty w onz11e pnbn6tibm2o; 40 velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makedlqkhef8l:b,or 5 qw .i ylamme/- 1.6s one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of am eb,dhy.flrel k.68-iq:/ a5q 1 wmlo 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 v1f)s; 5scqa9(w gjb chelocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speedk9.ko 5u2icld rmv h5( of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the oiv vb8o2kxg01 in/u0axis of rotation is to experience 0vg 1i0k 2xoinubv o/8an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its ceawh,rcf kz c8iy240k3 nter from 130 rpm to 280 rpm in 4.0 s 02hkz,wc8ca3r y4ikf. 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 radius3bg0p5ci t 5qok1j* oz $R_1$ 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 thyzha;v88 h()1zmq/zi dogc7n emselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft caz18/oq v7y;cdhhg)(n8mia zzn 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 res .carhw-apr*.2gc 1i,gyv)ict to 15,000 rpm in 220 s. Through how many revolutions did it turn in this timyvgi r-ar2c.). ,p1icc* g hwae?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Cal7:zs-b5zgogzl vc ; 4rculate
(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 higlkoq;s 5;o:lh hspeed jets in a whirling “human centrifuge,” which takes 1.0 min to tu; lko:lohsq5 ;rn 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 3wofxa y1nq/ h5p0 m(b*60 rpm in 6.5 s. How far will a point on the e0* on( mhq5p1waybx/ fdge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 15i u7iyqn; :bi800 revolutions befoiy:b8iu q;7nire 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 suy7 8wq6g07 sbuoyg/b peed uniformly from 07gug6qwsy7yb u b /o895km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its sp6 qg-ms*3s m iovtb;z(vn u04veed uniformly from 95km/h to 45km/h The tires have a diamev ;-mn vqbvm46stu*igos 30z(ter 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 h kp8ztug(hz4r7 ;yv o/er weight on each pedal when climbing a hill. The pedals rotate in a ctz4yugk( 7zp8r vh/o ;ircle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What tio: .rk ,:okofq *b(cis the magnitude of the torque if the fo (:ckq. fook *tb,:riorce 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 o i02wu -vcy(ah-(vb.spm5ypkf the wheel shown in Fig. 8–39. Assume that a friction torque o-.ksuvmi- hyb0y5 va2(wp p(cf 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of masm:c) fyy 5spt.s m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–f5pctm y y.):s40. 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 reqpzc+zxn1t u 1k(-r8 ,mb g)puxuire tightening to a torque of 38 z+xbpuxk8 c,t(gur 1-pzm 1n) $m \cdot N$ 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 4wpxca bo 0bis.7dz- )of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through i-)70zb owd.i4acsb xpts center.    $kg \cdot m^2$

  Calculate the moment of i/m3k3wtddu40rak*:85++ (c dtki go xf nyxcdnertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).+ m3n5 kd c*uk/a4 fdw38cxdyri+x(t o0dgk t:    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light r tovz -) 3w6w8y(8zlpyulde+ 0) m;q glow)knrod is rotated in a horizontal circle of rnl( t8rv yum)z 8ky3z+)06 wwl;lgqeo d)o-wpadius 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 py 8db: g(+i3qkhk 4lwxotter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the cla yxbg+4q (w8:hdl ikk3y 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 tnc j3q*,9txgv he array of point objects shown in Fig. 8–43 ab,jc9nq3tg * vxout
(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 consi0dju7i mr7yp0 sts 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 satellite1hmg hgryu 0x/n57 2 2ohhsn -wmhi*x2 spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. hi 1xy02*oumnh gn ws-x r25gm/h72hhIf the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm w 3eax 43hjwaa :dpy6*and a mass of 0.580 kg. 43 3: jhy6pwewaxa*daCalculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest *hex5*1l q5 of.lqp gvto 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 onzk:l )o*t: pj:hkv -hh 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 thk)hpz *jtk-ol:hv:h:e acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and m. 1as ,dvacz6is eventually brought uniformly to rest by a frm6daz.1,a cs victional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball (f,rn tuztd-.ttbz: ;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 thv*r uq+ ug/acaa-uylb90p am+.n0hi +e forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly frm +.i0 r0qpaan+gcb+auauvyu/l h-9 *om 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 shownzg/wj 53xuxq0 in Fig. 8–46w /qx5xz jug30.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masses,h )kxo*gd44xr $m_1$ 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 (;c8nlw- m-pkw ip 3ffthe hammer from rest within four full turns (revolutions) and releases it at a spw;3- miw knp8lcfp-f(eed 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 inerti+cm y4-moiwltdv/8 14 rwvn y4a 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 gstetfha9ii lksn .j3,082x g) 8qb7va 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 ram*pycstkkr)7(tf;dq5 b 4o0: sr n+yzdius 9.0 cm rolls without slipping down a lane at 3.3 oybrnmqts+y(*kr sp;: 54 kz0t7)dfc$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with resn3-sl88wfo 3u f0i quckus(y1 pect to the Sun as the sum of two terfoc8-fyiwsuns( 3 q l830 uku1ms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How mbxg lbms(0 n xs*m9ci, kcu6/1uch net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Ass l1kc su6xim */sn0gb, cm9xb(ume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rollq6yd(b d 2dooq/c.r,os without slipping down a 30.0yq.do / dcq oob(2dr6, $^{\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. I crt d(m3jp/5st starts to fall and its lower end does not slip. What will be the speed of the upper endps (t3r 5/mjdc 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 balaerbnd.5bh(6as:u *z .e,2 t dg/rbkx l rotating on the end of a thin string in a circle of radius 1.:x*sde./ t25nb6b edz.gu(rra bk ha,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 unifornr6daa;- s gy9m cylindrical grinding wheel of radius 19;-6n asyd rag8 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 aib7 c6*a y1s,d,tdavs tx2 ;34j- qt/dwbzziht a rate of 1.3rev/s If he raises his arms to a horizontal p st q,*jdh -a,ai;izdwb1/6 7vdxyc2z t 4stb3osition, 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 reduce her moment of inertia zapm7g-3n pc2w/3i6i * ohtma 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 positipn6a tgopz2 7/ iw3ha-3mc* mion, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin ntpb(xubn6j; i9. da/rotation rate from an initial rate of 1.0 rev every 2x/j6 u(n nabp .9bt;id.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 through its center9q/zo aw go5;g 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, approximately5ooza gw9g ;q/ 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 skater spinning at*qemscsjam b3u* - v s2a0,ti1 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Earth 7/ :7v+ ky9(mgm9gjbaj 6p exdo0cgjf
(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 I is ru+p g7ff2w8w dropped onto an identical disk rotating at angular speed7gf2u wwrp8+f $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns az6 79ld,ffw7e mkdo 7gt 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 kgx+jh. )kmtdxx. q26 ee stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inerq.. m6kext x2d xjh+)etia 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:kyqsw.e64(4gihmbn1 ziz-c a 1z.re-go-round is rotating freely with an angular velocity of 0.8iezbm1csy 4 i -wgk ezqra4:.6.zh(1n $rad/s$ 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 collapse1vs8sz:8qdisn26:k/kyt w0ro ) jr bhs into a white dwarf, losing about half its mass in the process, and winding up with 8 v )i hb/:80:ysdzqtwrks6sr 2nko1ja radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in ew o5k*,zu ojs7xcess 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 vsxwwgu*j/ + cj yq6+0$ 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, inig knh7 4v fyy6gr.u36itially at rest, that can rotate freely without fricti.hriykn4vgyf 36 u g67on. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands+ (ttncikidg 6 9ac.,v at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inet (nci6adckv,i9.g +t rtia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying o:(e2y970tdz(n0rkgnw ob ph in the top edge of the spool. A person0dbr7it2(k0yenn gh( 9op: zw grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same sixwg dc42 egza *cjueb9)n- j*.de always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moocd axgj4nwe-2jz*9 .g)ucb* en as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ratihr:m,mb tq2 (e 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 cylindenkcu1/d /vv1jpz c/brea90 s0 r of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor. ak1pvsjdc0r/cne0/9 v1 z/bu   $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg fj.qh0lc / lw9 wm g-d5e-f8nkand diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of masswlc .mq e5j-dgfl-8h/ w9nfk0 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 qj+3ku w1 p vz3+zzai7is the angular 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 v;b1 ;yv20 uafnorg b:Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolut2uobn;y b 1a0 ;gf:rvvion 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 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 automobiled3s1n+fb: opjud kwwn (; 77uq 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 undnuwu:;b 1kdns( 7 q7opf+j3 wiform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustratxd 8qwjrswf r1m hn.24bn1c((es 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 horizontah 0jjp: l9a.kgze6 e9,;atkjll 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 ignore frictief9vk9*c1/cur0 p9i -j gnf5 0gtiition) 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. Assumef-gk * t pi/igc9if19tjnvr95i 0 0uec 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 of *qal;1ts pn7epve 05n the floor, and we want to exert a horizontal force F at its axlep 0nq stp1e; a*f57vel 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.ahvsz:t 3 :c8ec:r i;k: 2hncnvkobpk2 d+) a*2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal )aet sakn *::db 8kh23pnk hcz c+v ;:ri:cv2oforce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 yp0z kk4zf12 arock into a sling of length 1.5 m and begins whirling04z2f ayz k1pk the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this 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 u/n.xcwj62 ehrods, making reasonablenju2x 6w. ceh/ estimates for the dimensions. Then calculate 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 assembly which consiso (l-mcv (it.uts of two cylindrical plates, ofo(u(vmt -lci. mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 trac-( el x/g) qbsy-ezu(hk of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is tsey-uq h(x(l -b/ez)go reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not )t x0:yu/j,ug,je ilktc8 +ybassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly fm a2.d( 0pah1jyf:iverom 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular1i ym:aahpf2 vj0.de( 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