A bicycle odometer (which measures distance traveled/s-fn4el c 7,i ox+ rnu,jw y.qt()tsg) is attached near the wheel hub and is designed for 27-inch wsuer,cltw . ynx+)o/g( , -q4 7isntfjheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at cre;fl g**)q++c ka elxo+kvgip b6+s.onstant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular ve i+)glao rk e6+ex vkc*;+p+* l.fgqbslocity 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 siwd5*7s2feoy x ngle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forc* 938+yjeii2zwi1 f 92.fp o yzhwzxpie? 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 tw 3pvhc3a)* fbehind your head than when your arms are stretched out in front of you? A diagram may help you to fvt a*c 3hw)3panswer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at1 hf,ijfn /vl 3 )h;/h;yubwsu the pedal cranks. In which gear is it harder to pedhiy husvnh;b1/j)/;f uw 3 f,lal, 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 sleeki) af 53 ,e6ebgf9jbnder lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of ma6ie 3) jffe9eb,akg5bss is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bea-ob2 uy .l6z*z- ljifcm?

If the net force on a system is zero, is the net t2 rsntwuwi0 w+ax920torque also zero? If the net torque on a syw0 wwru0+ 2 xat2ti9snstem is zero, is the net force zero?

Two inclines have the same height but make different angles with the hub ay/chtvsd: ))4x2oorizontal. The same steel ball is rolled down each incline. On wcxo ) :4y a2sd/)hubvthich incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incl a b9h3z05jyjgine. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline fir 0ghb5 3za9jjyst? 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 the same mass. T)fd45;6ualg ui t5 s91 smlnelhey start from rest asad5lg4e)u m5ul1if t; 6s9lnt the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or cfa )(3hfr y30 l3*6nb crubfofz7 lz:rotati0azblc rrhlu)b c(3 ff3ozn*3ff:67y ng objects eventually slow down and stop. Explain.

If there were a great mehp44*g*da a eigration of people toward the Earth’s equator, how would thiaha44**pdg e es affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without nlcsb 2 o(cioc z 4+qt)q4q8+whaving any initial rotation whe (tz4i8o wlcnq++sco) 2bqq4cn she leaves the board?

The moment of inertia of a rotating so 8/kef:gc4) cahu 3clflid disk about an axis through its center of mass euc3f g)fa:c khl 4c/8is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstre z;c( rd9cmkkt ty7 0cnl0ahb) gk(m;(-9q nsetched hand. If you suddenly drop the masses, will your angular velocity increase, decrea7(kn9m (q;kld mky c0 cn;)zh0est9ar(gc-btse, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow a ;6d)dghnw7dr(b;f roxl.: fdnd the other is solid. Describe an experiment to f(xr n ;w7)bfgrd.;hd lod d:6determine which is which.

The angular velocity of a wheel rotatf7c2 4dx46f n gr7nxgling 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 lin7xdn4 gfx4cr 6n lg72fear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large frh;8;xe xngf,1wa72 ldkkc ;zu eely rotating turntable. What happens if , 7d1z;u kc e;h 2gfxwnak;l8xyou walk toward the center?

A shortstop may leap into the air349rrv6f) ss7j4bsaey:-dddn m(kxs to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36).e dna kd 7v9ss f4mrr4s)ydj3 s-6:(bx Explain.

On the basis of the law of conservation of angular momentum, disp -7)kzjj4 pl4 gmg0apcuss why a helicopter must have more than ozjlkapgp70-4 mg4p ) jne rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: ( n*4a w8wzo*ui: *mplna) 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, umynq6 6/ 0cxzqsing the information inside the Front Cover, the angular diameters (in radiansx zncq m6y0q6/) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. Tno v vk:pwlp6e0c8pww h/v:6; he beam diverges at an angpwnw0eph6 pv :cvl;v k6w/o 8:le $\theta$ (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. rn-yh,pydad(p hr703 5kns ioqj6ro1/-b kn; When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is t dk rs k-0/6nphoy on,bna5j;(3p r7-1y hdiqrhe angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If d awzx( aqcc876a)fr3the ball makes 15.0 revolutions, what is6wqr) (a xcdz38a c7fa its diameter?    m

  A bicycle with tires 68 cm in diameter tra:j (rwe+l4z guy)9x 9*lvbqj tvels 8.0 km. How many revolutions do the wz(9l q4x gw+):t*j9rue yvj lbheels make?    $rev$

  (a) A grinding wheel 0.35y k-b-)kwe(ick6tk4s m in diameter rotates at 2500 rpm. Calculate its angular velocity ikek kwkby-s)t4c- (6 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 makes one complete revolution in 4.0 s (Fig. 8–3 v6jqzfn 0.qr;f 7zdd68). (a) What is the linear speed of a chil.d r q6d;6z7fzfqjv0 nd 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 v9w5 wlfa(u 9jyelocity 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 speed of a pointd.wgh 3l-+bf5tgrm : n
(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 afole rn9;(0* gtd7r xj centrifuge rotate if a particle 7.0 cm from the axis of rrtrl (e 7dgon *;09fjxotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accel7xiz/c+g y0 mi kauw9k3omc )0erates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determin ioic)g0mxk7ucm/ 03zya9kw+e
(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 qfe;u bupzi.*j 2)ge6 m9*1*uapl r nv$R_1$ 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 th*wzof3qh*ikom ) 3s-c e Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotatiofo*sh) kqocm-3z 3i w*n 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 fronr3 ziotm53su* k(z) xm rest to 15,000 rpm in 220 s. Through how many revolutions did it z xk(ts3iz5)o*rmnu 3 turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Ca ;x9 a1ojrio8*u*zs ullculate
(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 whirling “huq1 2l(aslk pbfg5 +fk 4c/bgb,man centrifuge,” which takes q lklck4,b+2 fg/p5(sgabb 1f 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 ,906cp d:)kzumgx rdz n2smul2rfl64 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have travc:m ldr,d29z2l6f u znx)u4k0sgp6 r meled in this time?    m

  A cooling fan is turned off wnfq2 f) p 9yfjm5im2z0hmi/( vhen it is running at 850rev/min It turns 1500 revolutions before it comezi /9n(my qf mjmv)pf22h05fis 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 ps: gx/ahy l q dklbn 5b3(jlvh5/26e+65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h k+hq36(bl5lse2p ygl:/ dv/abhjxn5 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;uhtr:dcse5s l 8c*mvqad507 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter 80rd s*dhl :cc5vtmu7sa5;qe 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 b* o.(8qtv (nq jqo6dball her weight on each pedal when climbing a h tovdo*j.8q6n((bq b qill. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N)o3mt9 smi3 a:crn;fv on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exerted f atms mn933rvco)i;:
(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. 8–39. Assume i4pirafvkser5czrg090.6 j ;that a friction torq g.cs f0 jziv 90ae5riprkr;64ue of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached ( va6 gqmlah.bu1l 7m:to the ends of a massless rod which pivots as shown iamab g m(v7.6qllh:1u n Fig. 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 antr -h )o1v6gjd engine require tightening to a torque of 38 o6gvd )-h 1trj$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius k/tpe2n 8)aiu4 mobg7wl* r9o 0.648 m when the axis of rotation is koo/wlng4mi p 28 *r9eub7a t)through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in dil. d/u, l((pyzja,sqa ameter. The rim andj p(udll.q, ,aza/ys( tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end odv;agw*wd qs 1wo0v;3f a thin, light rod is rotated in a horizontal circle of radius ww*vwo d0q3;d ;ga1v s1.2 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 mwz,bkvwgy b f71tg q5,xc9/;wheel rotating at constant angular speed (Fig. 8–42). The frictiwbbxgfq v 7 9;,z,tm51c k/ywgon force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fig.b-yblprs42 z 3 8–43 2b lbypz4s3- rabout
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose :6; u 7nidh3igqzwm,o 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 tncnw3bll- cce*ez)/p q 6:l+spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass ofe l*be zc/t6l -)w3:pc+cnnlq 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 cyli.(wy w55m b61yi jmemrnju:d(nder with a radius of 8.50 cm and a mass of 0.580my56 w(r(dyun wej: j.15mimb 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 swinn -/y*re(wybggs 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-driven merry-go-round and li jz. sd:3b )y,c+ptgis 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 thesclyt ): bi+ dj.gp3,z torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotatihninh ejiwl*kb19-:, ng at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torh kh:li1n -n w*ib9,jeque 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 ba d9;kuw.q 9nxjll 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 throwj sb72 htra6-wn solely by the action of the forearm, which rotates abou-jat 62bh 7srwt the 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 lo+z9nsnqtq 5:zng thin rod, as shown in Fig. 8–46.z nqqnt+s 9z:5
(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 consist9j c(f6e 8vlyn.n6n ojgr .,o-fnh to4s 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 hammgny 9.tb*g1njdqwzu3 4k 4tr )er from rest within four full turns (revolutions) and releas.g3gd4zu1tny 9)rjtqkn*b w4 es 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 inx yfh0ax1x2)c0gr 3e6qe5qipertia 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 torq1 6*7-ud*v cunzzou5peuhu /sewf58 sue 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 raf ++ x fkaho3nr9 15mfh4d*gpydius 9.0 cm rolls without slipping down a lane at9pfk3r4xffnahm+d oy g 5 h*1+ 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum o vkip7 rns5sr39d;f2gf tw9k5sr2p 7sir;f3 vdngo terms,
(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 muc; 7sx:nw0 :ypfgb pd/nzm)2ogh net work is required to accelerate it from rest to a rotation xpb;ns pm):dwzf/g:7 2gny0o rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls withou3 n wwm(ms(6 2jdb3qfmj8ia bd e)f98ot slipping down a 3e38q foi8b69fw(j d(as3wmb nm)m2j d 0.0 $^{\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 ver mp9 rejv33 g) tn)(b8:smo xjsh0a-zktically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end re(9vn :)3z t3jmkhap80 s)mx-jgbo sof the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum opr v7 x)6rdzfn. cu3w0f a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed)c6p rx7d.vr nz0wu f3 of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrd+ ;1g7klty6 ;qgi5uf7ht okyical grinding wheel of radius 18 cm when rotating at 1500 rpty1l kqo6g;d+ k7y f;5igh7utm?    $kg \cdot m^2$
(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 rota+9llh k kff+qj yli/9.x,.sweting at a rate of 1.3rev/s If he raises his arms to a horizonew9xyfh k l/9+.,k+liql sjf .tal 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 Figuy s8qri +c4a7. 8–29) can reduce her moment of inertia by a factor of 7asruq+i c8y4about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can i:bz1 2zf ox:lc lztl7:qh9+ fqncrease her spin rotation rate from an initial rate of 1.0 rev every 2.0:l :h :o1l7+ qf9zctzx2lzf qb 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 a38tfj 1ltax/ qfv 15js vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approxi ltjx58 1qtjs3/va1 ffmately 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 a 2jeebj+/acw1 (n35ihg:yvyq;x 5gl 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 moj yn96hl+c m-,5htndm- wx.dcmentum 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 inertiaougjw adif;js)2 5aql 3/d ajdn6f8)2 I is dropped onto an identical disk rotatgd56dj3/lf; w jfn j uaqi)sa2da)o2 8ing at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4e/19mod6 q4y2xxr n ca $rev/s$ 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:yv. up . 6t; dof0owijvn.al vjw5+1a rotating merry-go-round platform of radius 3.0 m and1a :.v0f j.5 +o.upntd6 yowvj;l ivwa 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-roun7ajgey8ov0 )zd is rotating freely with an angular velocity of 0.8jy0g va 78)zoe $rad/s$ 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 dwarf, losi(stt) wf(g xqgkfz. o: s, zwro7-d-7ang about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carrz r(-xt7a(oosw- ,zd)w .7gtkff gqs:ies 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 tn9 xnn *plljr:3:.9fruvb v5winds in 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 .8fe m3tk i:nm$ 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, in t)tf ebx10 ( v1k0qkvaj3po1aitially at rest, that can rotate freely without friction. The moment of inertia of the person pl bkop(q1x3at )t0vf0k jeva11us 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 dia, /f 4pma3+ 9;c9guiew s cd3ysurppw-meter merry-go-round turntable that is mounted on frictionless bearin p;c e9w/cr-u4u33ips my9wf +apg,sd gs and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the evbrvb/)yj 9/g u/.xff nd of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwirxbfujvy//b v9g .f/ )nds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same sidea 7 s 6e*tj;bg6ieqwkvf8-tbmr2*zr; 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 Moon as a particle orbiti;rq*rwj k*i e s6g2vbeza6 f-8m; 7ttbng the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from redrm x 3/1hy(nast 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 un+)rszc37f l8zdp jeq+2a;f mkiform cylinder of radius 0.20 m acquires a rotational rate of from rcjz d2as q+l;7k3rzfmpe f)+8est over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solidd:r/g 3) bz/ a eb+;ghwlczcn0 cylindrical disks, each of mass 0.050 kg and diametezelg3cd+/z h0wb ; nca/)b:rgr 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when 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 th5l3pvgru,kj4, dhf:d e 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 kot d f5g7qo1:.yo )fsSun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to under gksdto o)5o 1.fy7fq:go 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 /5 nh ovbg;.jflow-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass/j5 bvoh.n fg; 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 “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 illustratita )k:/s mzu4pym:5oes 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) isn9cfst (u +t0z 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 pivot freely (i.e., fuhc5 1umyg31ny) h,mwe 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 center of masu51ucn 3ym)y mhfgh,1s of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the flooe+w)o-yvfonhf41ht+ r, and we want to exert a horizontal force F at its axle so that i1fo h4wo) te f-nhvy++t will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed bj1po8-a3r nv v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cycliprob-3v 81na jst 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 begins l:t,*wa :bacewhirling 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 bt:a,a w*c :lethis feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a hlk lyi li, ifq9 jkq+v32m8*/solid cylinder and her arms as thin rods, making reasonable estimates formjy /q hki*f38 +kl,vi iq9ll2 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 hk:u.w 9 yhz-u no9fl3co5j,rwhich consists of two cylindrical plates, ofon9fhcuuh:-ljzw5,9k.y 3 r o 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 rold)u (/2(efjbpa3s je1-z er agls along the looped rough track of Fig. 8–58. What is the minimum value of the 2eze)rsg (ajbe(j/ap- 3d 1uf vertical height h that the marble must drop if it is to 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 assu.-ut eacwy ,6 xo+ekq*me $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniforml1ti) /ju v;exylzd:8:w*a u2qwe cq ye9xe 71jy from 90km/h to 6czx7/q:ex12e at q 8el;iwdy *1ujwvj 9u:ey) 0km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s