A bicycle odometer (which measures distance traveled) is attached near the whprirzg-. 6/mo9q o,kolc x8nhvy*r.3 eel hu9r*.p on,lmy.q8hvi3 g or orc/z-kx6b and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constaglkf lg 88s;7ent angular velocity. Does a point on the rim have r88sg7fl elkg ;adial and/or tangential acceleration? If the disk’s angular 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 single value of the angular vk,pawlqmc -(9 w9su (nelocity $\omega$ Explain.

Can a small force ever exert a greater torque tbzn .au23 p )f,txdi ua)np20ahan 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 behind your head than wa2h5a4 uxe(g lhen your arms are stretched ou45ehxag( l2a ut in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at :p/gwhb,,vxzdi+hdt* y -c7 q the pedal cranks. In which gear is it harder to p/ i yz 7cdbxh +vqt-:d,*hp,gwedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lowe3ozt, u*6 mffkr legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotazm t,3fko fu*6tional dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walke i:epq- r/d;vrrs (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net ttgk)p zn-*;s *xtd;0 5nrjg ororque on a system is j5rz n ;stdrkn;og0 gt*p*) -xzero, is the net force zero?

Two inclines have the same height but make different angles with iid1 q )j5w)qythe horizontal. The same steel ball is rolled down each incline. On which inclinq)i)jy1dqiw 5e will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously sy o wqw1o9sgp8)xxcu.wwmr s 13bc ;2dfp1+ n3tart rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline fd9o + mfn 1;)oqr.3w3pxwbscw8 21xwyp1scugirst? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and snm,fmc2 xz ( tq qj1ik93mc+1the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has ths(k1inmmz2c1,9x fqjt3c qm+ e 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 and7iq. sdwq6nt 7 angular momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Expla7 tns dqqi.w76in.

If there were a great migration of people towardwq2qfms ln/4/,sawb4k 9rk 5 ni-+gne the Earth’s equator, how would this as/ qn-i a9qw 4w n/r24mklgnb+5kfe ,sffect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having anoorvh u9 q((+yy initial rotation when she leaves the buv((qr 9+oh oyoard?

The moment of inertia of a rotating solid disk about an axis through oys5rq6l-gw( its center of mass is (ywrs-q5lg 6o $\frac{1}{2}WR^2$ (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 + lcri45i6c wzon a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity 4+ icclw 6z5irincrease, decrease, or stay the same? Explain.

Two spheres look identical and have the *v0d+pe hds-gpse c5,z )8bk oe,gg*esame mass. However, one is hollow and the other is solid. De becp,k*g*)gos, dvz-8 e+ds5 0h eepgscribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. gwobj *d1;gl. 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.wl1 ; *bojggd the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntab4w0 6n:ywp skele. What happens if 4 ewspwnky6:0you walk toward the center?

A shortstop may leap into the air to catch a ball and o8n*vln8 cnd8*ba12b kcu 0ei throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hincn*1o e0vc8*ailb 28d nkbu8 ps and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a heo p552x nylwp1ig3g c8 mhq4;dlicopter must have more than one rotor (orgx3 igq;5dmw ocp452yhp81nl propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30/xqp9 wt-961ub e. yulu( vkfr $^{\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 x1z zb ,v2(8o+mlw daqthe information insideolzb xm,2dq1 ( vz+aw8 the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Ear+tl) 1mf jq7)rg .ohumvi*) jnth. The beam diverges at an arf*t mgq)n1jh u7)vi.jl)o+mngle $\theta$ (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. e72a* hh8hvt8cq5v-eokmk8p d4r r 2wWhen the motor is turned off during operation, the blades slow to rest in 3.0 hrtvha7wke8 vhd e*mpr4 8528-koq2c s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3. qhpyx (97ubwgt2*k0z5 m to another child. If the ball makes 15.0 revolutions, what is its(20khpw *z ybt9ugx 7q diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many 4bglvqrd0 7* hlm9,mrx7 oqy1 revolutions do the whedbqxmyv*r1h,9m0 rqlol77 4 gels make?    $rev$

  (a) A grinding wheel p4mdreuq,g+, * p2m4q6 tsvyv0.35 m in diameter rotates at 2500 rpm. Calculate its angular veloc gs t*mq,,v4dyr+p 642vuqpme ity 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-r(;m2v)l:dp vj0yj agk ound makes one complete revolution in 4.0 s (Fig. 8–38). (a)2amy;)d0 g plvk: (jjv What is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a)y13 w-tlm2zm5 mr r b:8)v ovbnh;ey9nz92yhr in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of i4d2nymfn+g lmn)w k,wg1-1b hh /qb; 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 centrifugenc 3:zwlr 9p8ew+gee9ct1ac)d-di o 3 rotate if a particle 7.0 cm from the axis of rotationrwt1 ad+-9zwldcieec gnec893 ) 3o:p is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its centern(- un* 1vmxny from 130 rpm to 280 rpm in 4.0 s.n 1*(nm nyxvu- 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 eye/rj-m) ;cf$R_1$ 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 themsequ26ka zj8r6fokr, ; e:duy9 vlves 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 revolutkk;8:fyr 6j dr uqa2u6v,9zoe ion 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 uni2om7z bp+elp-a,1 z enformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this time?enzo1 am-eppz7 +,2lb    $rev$

  An automobile engine slows down from 45b y1zlb.c g+(v00 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 jets in a whirlib60xlv0cw :oe ng “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reach0x6 b:oel0cvw ing 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 f-ni)x m- sm9 :ewyhi;rrom 240 rpm to 360 rpm in 6.5 s. How far will a w) em;i9h- yism- :rxnpoint on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revo-3j y2(ybo8zi)wsebs0 xoj(i luti)i o0y(eyxwj(bo js3b z2s-8ions before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformlm *6wso;o.k2eui 4thytf l* p2y from 95km/h to 45phklo.us46*ey*;fw22tm o it km/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 revolutionth ua(yp1ioyp14c-k1b )6ag ns as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diamet np)bypa 1y(a4og1 iuh t1-6kcer 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 puuqy ajz5 ;x0bdib8. 3uts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 c5u0 3u8ab zdb y.;jiqxm.
(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 4mqau)hq, y 7ethe magnitude of the torque if the force isqu7ay eh),m q4 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 sh7 b5zqtgk)b0+pu* q6htqp *lh own in Fig. 8–39. Assume that a friction torque ofu7gt+ *pt zl6) *bq5b0qqhpkh 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to thjy;1y/ jr ko5ke ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position an1yj/r5k j;ko yd then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque of 387gr*k y k8n;k 3xcy a;*bqlam0 *g8ak;a krmcl0x 7 k q;bny*3y$m \cdot N$ 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 gn yi8pc77si7of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through i gynci p8777ists center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rim mo f5(i3-uof+ kpr4 vh(xq:fband tire fm- xrfhio+b(:53f4ou p(v qkhave a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball20oiye. (ll3b xhk: xf on the end of a thin, light rod is rotated in a horizontal circ:(y h32 fx.oxile0 lkble of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angular pn 7rca8g 7:v ay:g(acspeed (Fig. 8–42). The friction for p c r:7(y8g:vacgaa7nce 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 array9icgd:f17c74 ggviybo i+l .g of point objects shown in Fig. 8–43 about 7 ggy1gvcfgd :coii. b+94l7i
(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 os9lepg* 21/uqw phvj21g0t1, phjifoxygen 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 correct rate, enginhak1(lc41 xqu9ph u55nys g4seers 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 325huyk1x slc4hpsgnu41a59q ( rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniuf dn:a+r+v-lform cylinder with a radius of 8.50 cm and a mass of 0.580 fdrul+na -v+:kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swingic 39hzj pq(2fs 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 amke o(/m 7qe foc5f0 5*hyxluyy3*qf: 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 0q*yf eqy 3 u7loox5 :mcyk*5fem /h(f25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and0s if20 55,dl44reaoktr 1 at+dtzrg n is eventually brought uniformly to rest by rr02a4i5e, 54 kdn+ frgt0d a1tlzotsa 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 accepdn-.(/w z5dt w4fyqmlerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, whi-bdy ywn ;ttkl,n6 5g)ch rotates about t)wk lybdy n;,- 6nt5tghe elbow joint 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 can be considered a long thin rod, as shown in Fignd3yp :2pkv y(. 8–42dkp:(vyp y3n6.
(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 6fwp0 lx w8ay-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 fu wdlodnyd8 x c.1c k043qso0:dll turns (revolutions) and releases it at a speed of 28 08yo dx .cdkqwn1c lds403d:o$m/s$ 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 olst::9tpp*6 l+cykmqel/ (kmoment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torquem u 071ghk: at6mr bjk6i7:jvfzl f5,a of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slippin( 0/amr2/cpbpmu4 ribg down a lanempmp/ (0b c r4bi/2aur at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect tai, 6t:4wwxp kb0t7prb ;/re zo the Sun as the sum of two t0, x4rwe p/i6z:bpkar;7bwtterms,
(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 g0 mxy+e20qh jliz4t *radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 2q+m z 00e4lxgjy* ithrevolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls with :9dhvbxsq bthp*4v3p5b hle;r5j b1,out slipping down *1lb hb exphbjqpd,5t;5bh v4: 9r3vs 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 to 19fs)d):y cu976f fw gkbsqay fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits1ffb96k)79w sqc f asd)uyyg: the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum o5)iduir1czjhq6y(q+ r: uvgm tn:* *ef a 0.210-kg ball rotating on the end of a thin string in*:m+ ur:1*uvq 6(5hz)idq ercn tjigy a circle 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 2zzwo.y,;t cp9t 9p2i x.8-kg uniform cylindrical grinding wheel of radius 18 czz y9pt x.coi2 ,t;w9pm 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 platformx/v;udb ysni5kvn / *b97;xxw that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, they / ;bbuwxv;dx9v7nn*ix5k /s 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 4oxc9,gweq 92az4 (jfc e0uabher moment of inertia by a factor of about 3.5 when changing from the straightxf2ec a 4(, 4c0jb9z9oagwque position to the tuck position. If 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 increase her spin rotation rate from an initial rate of 1.0 k.nu4k 4(b6 zw tlg;imrev every 2.0 s to a final rategim4l(;bun 46 kk. ztw 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 aroun b8piwqzf 6s3(zme42wd a vertical axis through its center at a frequency of 1.5rev/s2b8p3w (wzm zfies6q 4 The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the 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 momens4 *-q da0pizvtum 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 )gj.th(qo y s h3r)u,cthe 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 inertia I is dropped on xixj73qi f-i: 5kvtv4to an identical disk rotating at angular sik t54vq7-xi3jx :ivfpeed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4d u,xv.6*cb+vsk b7e k $rev/s$ 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 t8r-qkqni9 ci-mwx tgx9 ,,4wkg stands at the center of a rotating merry-go-round platform of radius 3k- 8rnwxc qti i-t 4x9mgq,w9,.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round isvj 3y +,3qrxbjpm0c3*a* thw6f 3sb cx rotating freely with an angular velocity of 0b03ty* jwqxp3,jf3s*bc hrm+x 36acv.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 collapses into a white dwag8ob:)t) g j mgllas)0e2x e0krf, 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 )slg):omg0)0tgeb8 l xke a2jrotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess yq,he:q7-tgp 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 lt-ux 3pq-3 l qhefy96$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate bn*9p lz .wt.ybf 3lv;z* l3i5smm.)duek d:a freely without friction. The moment of inertia of the person p 3p*mlbm9a :..3y ;bfz . ls*)5vndkdlut wezilus 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 g1tnq; ; borxewf bo.99+2hxka 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has ob9+fo1xk r2t ;eqx;b9 hwn. ga 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 gr/pv c v8i7n dcv03zt-bound with the end of the rope lying on the top edge of the spool. A person grabs the end 8vvi7tbc vn0 zdc -3/pof the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Eaadqb3w/w )cqq (chx2 4;2c uqwrth. Determine the rat2x3/ ;aq cqqu4w2 wd) h(bcqcwio of the Moon’s 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 acceleratetvw/fqn5* 4b1v dcjb6,ih+g shkkq+2 s from rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of 8b 5cix rfr37uradius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the u xc7r3f8i5rbtorque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass x+z6dq:yf zkl7* ze0a0.050 kg and diameter 0.075 m, joine xz+ y7qaz0fk led:6z*d 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 angular speed of the reaf coievu sw3, jnb0a/ 25qjc3tm l h.,5(wpk0hr 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 times as great, were rz/z( r.-rkgq -3)obtav zxtx1otating at a speed or( oxagzttz-)v /31rqkb.x -z f 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 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 p xb8;sa 2zu)nfor it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindricx2ab8) pzsun ;al flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an ij.;ph2x9isyc4 l*eu $H_2O$ 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 speed v=3.3 eojcsv02rw b4y 68n*z $m/s$ 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 freel:uf*xln zk1 -ny (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,*nlz fk-x :u1n determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing v11g 5g jgbor/dertically on the floor, and we want to exert a horizontal force F at itr 15/jd1 gobggs 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 o,ks fw2oa8 v8znj 06lcfes:6 gn a flat road is making a turn with a radius The forces z 2c:lasekngf8,s 08j6wof6v acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and qr6jgq.bq, k9qlu -t(. +hvpx; cs8xdbegins whirling the rock in a nearly horizontal circle abov+x6qkqhb j td. -s(qq xp9r;8vgc.,ule 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 r (vw3 56jlg amafb. 8ea:lm8, bmf.rltods, making reasonable estimates fm(ma:gamrafl vw3 l5t8b6 .,b. je8 lfor 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+dk5bry 6x ;yxl9p-gt consists of two cylindrical plates, ofy+yrtp x9 6;lx-k5dgb 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 track of ; :oybmu*u me5sa0okg/80lsty m l)m1Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the hi yo/ l0:*msmy g0t)obmmu; 1ulase85kghest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, butqesoa5:6znc 2 7;bs of do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolu/ ,ku/fp cpsx*tions as 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 acce*/kp,f xu sp/cleration 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