A bicycle odometer (whica uz5tll x-1i2 ;-5qehu nk5hch measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it5h5kxau l1 c2;einu5 zl th-q- on a bicycle with 24-inch wheels?

Suppose a disk rotates at consta) q eksc.gs/w bj xcop;e8u.52nt angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does) s g 5jwpqocc .e.uke8/bxs;2 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 ufcn 8x4b0j 35vyyz w6value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque thang5d8r)xk/i;2fx f in p 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 j 0v;i( )x *2utp0xzl nrqst2fbehind your head than when your arms are stretched out in front of you? A diagram may help you toz qj2*lns0t p)0f2;vrxuxit( answer this.

A 21-speed bicycle has seven sprockets at the rear whe: krq mqi7t 2yixi*+y9el 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 sma y:iq29* qtkirm y7i+xll front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run ae2egg6 :q /i5th .uygd*z0nonaqi+ 6fast have slender lower legs with flesh and muscle cee52 q a+yt.*guq 6di:0ighg6o nz/n aoncentrated 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. 8–35) carry a long, narq7oe l(ti nvu-:p)z(m o 3zdn5row beam?

If the net force on a system is zero, is the net torque also zero? If the net tocy/tu1e-nae fg/0g r (rque on a system is zero,ert/g0f 1g/ec(ya-un is the net force zero?

Two inclines have the same height br/,o8o8a uge uut make different angles with the horizontal. The same steel ball8ru uoag, eo8/ is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest5 tzgeh2 :hqe0) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bothet:h z 5gqe20tom of the incline first? 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. Thmbm41b j2xb;x rsgr+*ey 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 th;xmb1j+ xrbs2r4 m* gbe bottom? Which has the greater rotational KE?

We claim that momentum and angular mo7bg bv p iay.immg6pz84r), 3bmentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Explain) iya38.gvbg m6,zm pirbb74 p.

If there were a great migration of people toward the Earthx) bfez rih- wz(r,du 0ut-5p)’s equator, how would this affect the lengt e(f0thuxdp)z w-,-5r u ib)zrh of the day?

Can the diver of Figz,75+2 h/ g tupjzp7s1e eqcqk. 8–29 do a somersault without having any initial rotation when she lea psqq51u 7,zjc+ thkze2p eg/7ves the board?

The moment of inertia of a rotating solid disk about k)wv:kcr3wd 2vu7t6yy+ 8 ghg an axis through its center okw 6) :7+chkdr3v v8tyywg g2uf 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)l(bz. yvo,cr 5*aeyp on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increasea)e pbvzylo5r,*c(y ., decrease, or stay the same? Explain.

Two spheres look identical and have*4cjn6 pt1f y9a i3mlx the same mass. However, one is hollow and the other is solid. Describe an experiment fy n39 ict4*a px1m6jlto determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west.2kk;o vl qpewucp;42j hhr1;h3yy (2u In what direction is the linear velocity of a point on the top of the wheel? If the angul22 ypkurc3yl(h;hvej 2 14pquokhw ;;ar acceleration points east, describe the tangential linear 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 af n9)hwav:lu5 large freely rotating turntable. What happens if you walk t59ahln)f wv :uoward the center?

A shortstop may leap into the ai sf(7/alckn i-r 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 oppossc /fa(il-k n7ite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, dis-3ea3(i m qjn7gcapj87,u wrjxxe37n cuss why a helicopter muste7j ,u8ixaq m wx jeajrc37-73g3( nnp have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the followingtdl a(gkw7h ). angles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth becp8t4 .dixgm 0:bf zm6cause of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in ripf0bmg :m4tdz x6 8c.adians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 47 q1mgeu* dg3ssz /sokm from Earth. The beam diverges at an anglezu*7s1o4sg/sq e 3mdg $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motok(sh ma-9vvg /lnx2b) r is turned off during hx9l() knv2/a gm sb-voperation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anl 9 z8 -jvisn(t;tw-ynother child. If the ball makes 15.0 revo ;n -zy s-tivt98nlw(jlutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revo3sm,3g talq dki5q+ ;slutions do the wheels ms km;dg5lqt3a3q i,+sake?    $rev$

  (a) A grinding wheel 0.35 m in fohu0 y;m0 frun3a 025dhfo, mx0yd+fdiameter rotates at 2500 rpm. Calculate its angular velocd hou;f230 f0u0no0yymxhm, 5f a+frdity 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 onf+ 4q) /elevfqe complete revolution in 4.0 s (Fig. 8–38). (a) What is the linele/fevqfq4+ ) ar speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around tw-nqu 4 fgeo,.he Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speml 2kq,u nl6b0w r5vm3ed 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 rotat/ihm*q4grx+ wi +ag/nym bh(4 e if a particle 7.0 cm from the axis of rotation is to experience an acc4bn4hi+/mg w(h rg/i+ym q*xaeleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accw/ew**2beo ,/qvdal0ek.wm t jh)w s(elerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Detl/w)kv*(dahw* q0wwe ejesb,.t/m2 o ermine
(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 radiusksfrxi : 4wk j,ql:f(6 $R_1$ 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 spaczj3e8u/b6vghm x oe*)ecraft put themselves into a slow rotation to distribute tj6ge* uo)mb3 8ev/z hxhe 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 can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Throu ijbd/9 9gtle4pfj* h*gh how many revolutions did it turn i4dj*gf /le*pi 9 hb9jtn this time?    $rev$

  An automobile engine slows down fr)(; pwvlg7v q.8fcdi lom 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspionf o:ah9125 t0k h g.0tl l*bhqnzg*eed jets in a whirling “human centrifuge,” whicg*95qi ghoknf02lnbt0z: o ta* 1h l.hh takes 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 ac-l ys( rdb,tc+n9mpk1 celerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in mt+ls- dy 9 r,kb1pn(cthis time?    m

  A cooling fan is turned off w v;/ivqdf -,r(mkn z:lhen it is running at 850rev/min It turns 1500 revolutions be:vqlkz v,n (m;r/dfi -fore 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 sph c gs,bakhn9j5-0 4zbeed uniformly from 95km/h to 45km/h The tires have a diameter of 4 ah-0hsbzn 5jcg,b k90.80 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 60(ub)x2 mljvda 6 /cc te:fll85 revolutions as the car reduces its speed uniformly from 95km/h to 4 cxlebac)t/jml(8l 6dfv2 u0: 5km/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

  A 55-kg person riding a bike puts all her weight on each pedal when climbing a h(f ylhw ,xn0tr-z2+j v mxf)d8ill. The pedals rotate in a circle of radius 17(rlfxn- ym 80+w )f hx,d2zvjt 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 ouno;3b7 uq;qc f a door 74 cm wide. What is the magnitude of the torque if the force is e ocuq;7bun3q;xerted
(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 md4+ 8ve5 a*edouhh2*booc .hthe axle of the wheel shown in Fig. 8–39. Assume that a fre*m ve 2hho4douhbc8o .da5+ *iction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of5 bs8+i a+psvu a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and directbi +sa+u v5s8pion of the net torque on this system.

  The bolts on the cylinder head of an engine requiro z-gc e2u/w5u7 cdg7se tightening to a torque of 38 dg 7w2e/scz-u7ogc5u $m \cdot N$ 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 0.648 m gt;wy35 f1ey*fkjizl1grc 9+when the axis g5z ;w1j +erig 1kyf *lf3yct9of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter.1o65jmav9s /h br.j0y0d xy gk The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignor xors 905.yg ay0b61vk/ jmjhded (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a tk u dr2-b,/ejjs/fd g,hin, light rod is rotated in a horizontal circle of radidjfjgk, s2/u db e,/r-us 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 angkxdh ;-)kxld. ular speed (Fig. 8–42). The friction force between her hanxdhx-;k.l)d kds 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 arrx7 dm-pav r v0a +mg1q;u*/yonay of point objects shown in Fig. 8–43 o pvgd1 qnxm*y0v/mraa-+;7 uabout
(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 ofy p uv+aq6/5-k*olhyf two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinubx/-hexbtn; .slt2 jyo6 )z 3 a;by9sning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass o6;ybxjb 9 ./ystnx-b e)ouhs2a3;lztf 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 a (p0bha oavmert(f5fy w-vh*k.q) p00nd a mass of 0.580 kg. Calb qkmhyf0. oh0v*05tp(fe)wa (-vpra culate
(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, acceleratin ut0hks9crh1am) ;bj6 g 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 ha+p1.no0c l;4uy5 u mtqvqxw )ond-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 r q+nwu.p54xo lyv)o t0;u qcm1adius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10bgt: v w t4c3h+hrt;j.,300 rpm is shut off and is eventually brought uniformly to rest by a frictional t; htgb+tc4v .3rwt:hj orque 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 4jk 5zc3zv-deytqy 2;vi22qu accelerates 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 actn -*qn4vepyj8sd 1g-rlf07bvion of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball r8 4jnnl -v7yg seq1fd0p-vb* 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 l 7xlrvfds5pr uiw1)r4o 0x3t *v.mk:*zi l8y yong thin rod, as shown in Fig. 8–48 xw41r*dmxkv:plsut )l05 *zf rvr y.3oyi i76.
(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 luf fw.i66p3+ as xo.pmasses, $m_1$ 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 wit ebo-wn u:s++qz2l7 mthin four full turns (revolutions) and releases it a-wt2n ouzqm :sb7+ +let 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 hasp5sfkv jdi +2w2;:5r- l(zmc3qlj h mg a moment 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 an ;mf c)pp-(l p,ws/tv 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 radius 9.0 cm rolls w2ik: op(km56 arrx,f yvad 6:tithout slipping down a lane at 3.3ak:im r,xfayt:o2dvp 66(5k r $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth withqrdw,g (m9wq ;70:pykift4 xhxi(. pc respect to the Sun as the sum of t,w (gkxfmc pxqpqy;90r i:7 w4dt h.i(wo 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 much net worxbn).y8rnffza0+x c,jrd4) wk is required to accelerate it from rest to az8 fybr,x0.w)nx +jf4 canr) d rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from res b-vs0v*yf4f bt and rolls without slipping down a 30.0-bvyvbfs4 *f 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 omj,iqk yafi+r0zye*7; 7+l zon its tip. It starts to fall and its lower eno ekm+yl;*0y7+azr fz ijq7i,d does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball ro+l2 2g r64hoodnrbq:(q)3s fxgbx2ec tating on the end of a thin string in a cidglorq(6b2hx :c2f+gbxq4o ) sr23n ercle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum o-wb7 d4it;aj ty j3vojiq3. 6nf a 2.8-kg uniform cylindrical grinding wheel oftjyq.6 4j7tj3ii 3aw o;bnvd- radius 18 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, handssrl7a8i96s5yweyhnm0i,5t6 au-c f h at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal positionmuyftl-w98 7 ,y5hs sera66hnii a50c , 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 hh f96nps5 .ecver moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the 65e. hnv p9scftuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation c2e slpmf3 wa3;3bn 8rh: *huwrate from an initial rate of 1.0 rev every 2.0 s to a final a e*un33w w8s2:hf3pm;lbcrh 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 +u xg 4rida0j8edq. g5vertical 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 .ur58 ji e0x4dagd gq+a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skatidb9z8)ujbxnmd 5i t3(5ib ;ger 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 momentu c2 gxm9fj 6z1*mgbmz/i/0bfb m 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 inertia I is drt845z sb:e;2 7ba6cwcrbxwb lopped onto an identica b6 xwc2els54;r8t7ba:cb w zbl disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 28 dn/ib-tsj; sy3ytd).4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round platfvx2u +re 0a0tyorm of radius 3.0 m and moment of inertia 920 utrv0yea+ x20$kg \cdot m^2$ 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-ro6vkic l lu2lp:1*cq q,dh3v+a und is rotating freely with an angular velocity of 0.8kvulq*dh+3c6 l,ai21l p: vcq $rad/s$ 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, losing acm vjc 4g;1yzwq 42gj,4fyyt7bout half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming4y g g2y4f4tc1j7qyc,jzm ;wv 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 excess 1iv uv(wav3y92i f1ig 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 u)rq axueq8-q+gub9j2ey5i1z 2::2w u h ztzy$ 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 1fe ve og/8o 0fd09iecfreely without friction. The moment of inert/ f 0o f1oeg0eiv9ecd8ia 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 stan vcv.weg6r p f6k4.pi /;ytf9ids at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on fp46r fk.v t ivy;e/w69i fc.gprictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope roll) npc qn*uz9-79m/d2ztfwatq s on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks-p dmw72/caz99* nq)zfut q nt 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 Earth.h6,n j/pe ozw, Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angzw,phojen 6,/ ular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate ofrvix6 -/hzjs2hx8uf8c +dow ti3oh7 2 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 radius 0.20 m acquirests+n: ;z.hbub1wegk5y3h,rwvc6; nn a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by vh.b;r ;k wgunnh5e:+1tbcw 3n,6zysthe motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, .uk9 2 u7cwzt:4qz;rd2edfeieach of mass 0.050 kg and diameter 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 w rqid2k4z:u 9 72euf. ezc;dtto 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 ape15:nca v 5 9p3dl9nlyaa yg5ngular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun,z)79i-u 0k,yy qkcxsj((nfmm but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 1ksq(ufy 7 c i,9n)0kjm (yz-mx2 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 for it to use energy sa1fv9yslt( ns geh3,0h+g 0yatored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical( 9asn vg0ehf3,ty1h s0layg+ 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 illustratej7a/cle2xn ;waf66e u s 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 od:4 -mrkmu0vfeml a -.n 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., we ignore friction) 1crl12 uoro+x b:s:ej about a hinge attached to a wall, as in Fig. 8–54. The roxl ob1 j2rr ce1:su+o:d 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 mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is sta+fl y itd()h6.z1kqs;ije c -gxmwgj**0cb:unding vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). Theyiiqz)1j+t- c:l(kc b 0d*w mjs ehgu6.gf;*x step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is ma-vr 9 (vvwy1 ,guube8cking a turn with a radiu,v-8rubvv1g9 (ycuwe s The forces 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 inton6s xr/y ph*60x*b9 *, g,qx5k ywcf/b nsknum a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it fr qb*swnxhs0x/6r5b6*p kxy ,9nn c*kfum, / gyom 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 a* xr/h.lt4m.nk ;kt ebody as a solid cylinder and her arms as thin rods, making reasonable estimates for the dim.k r *exh;mt4la./kntensions. 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 assemblexni p-hvf 2+* 5pusmm((i +dkxt6je8y which consists of two cylindrical plates, of mass(ut5jxn8 k6-+p( fmdsp +iimeevh* 2x $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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-9s( i+byx ihvpmt;9w the looped rough track of Fig. 8–58. What is the minimum value of the verticahw- i9y xs;tmi(b +p9vl 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 assume3ai2dz-g5f g65 vsiwm $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformliaxf v0b+3x 7fy from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of e7fa0xf +v i3bxach 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