A bicycle odometer (which measures d.k*up 6tf orsyy 0.-sfistance traveled) is attached near the wheel hub and is desiy.0y *k.us tof6rs- fpgned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim 3kglkxvg01fww wa l*)3hntkn- 65k3 thave radial and/or tangential acceleration? If the disk’s- 3kgx)3 awltln0 *g61 5h vktww3kfnk 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 de upw0,nk*yj (1kqvn:kscribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque tha7al:tg.k j:l;jg2vwt n9:dae3v 5il yn 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 yourc i2xm 6pd:x mew607ru head than when your arms are st6 upd7ei0x6r :xcm wm2retched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wj2gf dnce4ya7jc 73y ,heel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front spr,en77 4cd a3fgycy2jjocket or a large front sprocket? Why?

Mammals that depend qrp.-y d z-d,bon being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational .pb--, qdyrdzdynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a lk;1* i,1uy76vwpu:tj lu utbck3(lm bong, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the n i, xxk;-um/.r0 kmhbup pm)s9y,,gsmet torque on a system is ze mh;iuxbkmxr0.u )k mps/gp 9y-,,,smro, is the net force zero?

Two inclines have the same height but make different angles with the horizo 13vjcfj ;,mjph )fbv;ntal. The vj;j,m f3v; )jhf b1pcsame steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneous t083w xxtehr)ly start 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 first? Which has the greater speed there? Which has the greater total kinetic energrx)8 ehw03xt ty at the bottom?

A sphere and a cylinderu9 dra ti;,bp8 have the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotatidtp a,br;i 8u9onal KE?

We claim that momentum and angular m+y jp4a d6aoz6omentum are conserved. Yet most moving or rotating objects eventually slow dow 6j zo+pda6ya4n and stop. Explain.

If there were a greatk2m*sgpqaqn)i /+k+i migration of people toward the Earth’s equator, how would this+ msqipq* ) /ki+nka2g affect the length of the day?

Can the diver of Fig. 8–263 dxvrlkw d8o+ -xz 7g:h8sgf9 do a somersault without having any initial rotation when she lea: krv3d gox7 -8wsdg+hzx68l fves the board?

The moment of inertia 5mzb(sm/-iocu: *xvk4x wd:oof a rotating solid disk about an axis through its center of mass is ic( dm4/zx*: 5ox msb:k- owuv$\frac{1}{2}WR^2$ (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-:b6otqg x.u 0st*c yk5huvmji1+a h 1 a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the sat 5mov. i0axyq*ukc 6:sjuhb+1hgt1- me? Explain.

Two spheres look identicqt rqk-8-mm.v/d-0 wyo+ b/hkfd-zj hal and have the same mass. However, one is hollow and the other is solid. Describe an experiment to--zjqrw0h/hmy+q-o-tbkv.md 8dfk/ determine which is which.

The angular velocity of a wheel rotat6 g0s rfj0;,glzc,on ming on a horizontal axle points west. In what direction is the linear velocity of a point on the jfgmcn; ,0lg0sz6,r otop of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. What ybkx ; c71bfeft,sfajq+.7j0 happens if you walk toward the ,;s1fja jkb0x+fe.7c7fqb tycenter?

A shortstop may leap into th(pitx:s9*fir e air to catch a ball and throw it quickly. As he throws the ball, the upper i(spr9xtf*i:part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the 4 q+fo; 4-tv curgfjy.)a+g9 lhab5w rlaw of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to b)jl+aru;g4g whq v +tc5o- r4y9 faf.keep the helicopter stable.

  Express the following angles in ra -t:5fb9zvvbbdians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an aq bwe,x7t *mv2mazing coincidence. Calculate, using the information inside the xv*7q2me bwt, 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 Earth. The bh .+tz-wn*iou eam diverges at an ai*h utn+w-z o.ngle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate43k;a6q-m-ff4 mhtvtbgr0n07 uv qpzw w)9 dz at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades s;4amr 4g hk06zvw0qf-p3wuf nqt vdb )7tzm- 9low down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball makes cqv0o1oo 5j/2pp+mhy8 z)h wz 15.0 revo w zj2h8hq /vz o1p05o+p)ymoclutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels o1*g x+a.;hn w9ymp1y 6vqnvy8.0 km. How many revolutions do the wh oyhv6ap1 xn1 yy+g*;qwv9m .neels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Cv t*olbryze676kk vppz ,k9p63f )xp6 alculate its angular velocityfr79p)bop*k6xpz,6vyekkpt z63l6 v 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 ab:;.j ec8vyp revolution in 4.0 s (Fig. 8–38). (a) What is the linear8p;: vbcja.ey 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 tu3 2ayeluzb005m7 mmf he Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spe8 ycmhin1m7/(qm. gpmed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a p vx+-zxa ou;z 4wxff,.f onp 8d7+4rfmarticle 7.0 cm from the axis of rotation is to experience an accel + xp.uvmxo4fda+ 7;-nffzrx8fzo ,4weration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly:fc )p:dqgda9po d o.8 about its center from 130 rpm to 280 rpm in pgd:a8c:o. dqfdp 9o)4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius ym 8qe+yw xriqb+2p8rp *e7 3y$R_1$ 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 spacecr1qif 9 h3 nid)y ai5r8wf n.6 hwjmt8lsc6rq,9aft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 .fl)8ci9mji8rn di 5w 6hf 9n ,atqhws63yq1rm. 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 frkdnvi8 j-qg4 cf2whxx4, g2u2om rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in82 g2vk xf2gx ,4c4-n dqjhwui this time?    $rev$

  An automobile engine slows down from 4500 ao 2y-n0gl4vs 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 highsp pgf u-59nv6p-iqlgj ok96 p/leed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 nk9g66u/ -q jp5o9 gvli-pflp complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm tp7pe/5r n-tn iu. 5rr5d wz6zso 360 rpm in 6.5 s. How far will a point on the edge of t7/p6t5 z 5 irrnwe5un. r-pdszhe wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850req( qgs*vmj+y;ex z7+ lv/min It turns 1500 revolutions before it comes mz;eq j+g7x(q*ylv +s 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 scl+fw k+kl9p y)u ol14g mz1*npeed uniformly fromkg*+4w+cl)lfy9lpo 1mukn1z 95km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly frl.5*fol,gj t 2l3nya3,a eidavbl5 b( om 95km/h to 45km/h The tires hav2il(l doa ab nv ,3laj3*,lyfbte5g5. e 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 whetj )mjpr l79u*n climbing a hill. The pedals rotate in a circle of radius *ulr jj7p)tm917 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is ui3kccla 5x)04/l cxhthe magnitudexl0 3i ckh)/ 5alu4cxc of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–3 kc-rf3ai7 qh-9. Assume that a friction tokq7- -a ricf3hrque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attache4y 9zvnco 84pc4fe+o yd to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal p 9 +4czevpfocy4n o48yosition and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightvkxlz3k8)2xq7 ay 0iyening to a torque of 38yqaylxvki3 8)7 20kzx $m \cdot N$ 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 o,raa9vprppz /:8:zd y *swd1t f radius 0.648 m when the axis of rotation is through its pv s9*/8za dzdyt rpw1,: ar:pcenter.    $kg \cdot m^2$

  Calculate the moment of inertia of 1i5b2 ./cp lhtzsymz 6fd/ oi/a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can yf ch/p l/m5s.boi i2/d6t1 zzbe ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a h.m05nr9 ub wk6g9* wyjld8ztc)znk*3qwxb d0 orizontal9brj.w c0tk9wy6 dzugw8k 5ndm)l*nxq03 b*z circle 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 2 dn8y o8hnl2twpow5 (at constant angular speed (Fig. 8–42). The friction force between her han2dl28t5w 8nhnwyp (o ods 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)/ rgx tk4ztt0 of inertia of the array of point objects shown in Fig. 8–43 t4 k0z xr)tg/tabout
(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 t+jdd 9l dy/o0r +0)t p/vh(azmok c5bfwo 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 spinning at the corruvc+8gu2 e r 5bcmwl47ect rate, engineers fire four tangential rockets as shown+l wb7 5muc8e2ruv 4gc 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 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with ))f(rtfase-e a radius of 8.50 cm and a mass of 0.580 kg. Calcee)r-ast()f fulate
(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 advuj61 -rddajuyq ( (n)1r 3in 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 x, 8vm/pnu1kk9n5ht )mwj q h6is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the8m h9q1/v5tm knpn h w6)ujx,k merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off go e w.zv v--x* r*sku5+t:nfvand is eventually brought unif n-5-t evx*vfrzkv:s g.*+uwoormly to rest by a 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 accelerates a 3.6-kg ball a369 cmjemhzk/ .z5 ttht 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 bonx8 2q q+os;sy the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. Tqqx o+s8n s;o2he 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 ofs0 4ulj8h ,yneui6,z. e 6uflong thin rod, as shown in Fig. 8–46.48.fhu ufjeu6o 6i l,nsz 0,ey
(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 -1vq er4k4lyl 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 foy+ype 0 g2mz;b0q i1xhnll b*7ur full turns (revolutions) and releases it at a speed of 7*lb1q hi el2bpym0 y+;ng0x z28 $m/s$ 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 inertia of-sc gu kt2;we5 $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a 34g3q*ka23cysmaqn ltorque 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 andsz h1 --sjl*aj radius 9.0 cm rolls without slipping down a lane at -h-j* a1j zssl3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum ofc(bq0o:kj-o4)ia bo. o)a (wj+ mxujh two termw )xk +i(aoj-oqcj0 .a4hbbm( u j:oo)s,
(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 kgxbji: 7 yu1zw1fe+pk6 and a radius of 7.50 m. How much net work is requiredkybw1fui 17j:+z6xpe to accelerate it from rest to a 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 0t(3)ldssjqua d:j0u mass 1.80 kg starts from rest and rolls without slipping down a 30su jd tu:300 jqsa)dl(.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 ly*nyk6;q ed)m529 yx,no4x- y0oa z2la z ppcto fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use co0q okx-p2 y2emx6n9n; ca)lo ,zz*dyla y5p4ynservation of energy.]    $m/s$

  What is the angular momentum of a 0.21r06rk:pn kyc9y.f y8vp8ei)w0-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular spernpkfp.80r cy869kye y iv:)w ed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular myyppnayt6+f d 5pbk *0,h y+e w:e5d6zomentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 15d e0yyeyt n+fp k5:pbz5a6w+*,dp h6y00 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 him*d/z pu6ip:6:yg2 diqlt*zl s side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, thediy :/* qmp t2dpzi6uz*: g6ll 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 h9: d6r hj0p4 orj(u u ,72wrj*aqtqvvreduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when vr0ju4qqwjp9, *h6( du2at:7hro vr jin the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can 8h8lmw s0 vxzs:lzzx*n-hl ;+increase her spin rotation rate from an initial rate of 1.0 re- l8:nxhsv*+xz;0llz 8ws zhmv every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its cen3ur:aj so2*mtz ht (-qter at a frequency of 1.5rev/s The wheel can be considered a uniform di(jqtuho* z-r2am :st3sk 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 mome5j ps82ysysv/ ntum 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 momenq *o7ovawp h88tum 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 dropped onto an ident htzrojox( 9u 3-q,g-oical disk rotajro -ou3x gohz9(t -,qting at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4k 3pz:/ff4 csv $rev/s$ 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 st-/bz7ry)c3otd w n jb1ands at the center of a rotating merry-go-round platform of radius 3.0 m31bt ndbc/y)wz- roj7 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-grw4v,qym u bct(f-9k1o-round is rotating freely with an angular velocity of 0mvcr-u1yqf 4b t9wk(,.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 copt;a r3hxf :;bllapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assum ;: haptxfr;b3ing 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 78puogyn-vc + 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 e+s7.sbw7t z b$ 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 r cir/3x:uaxsi*zc.e7otate freely without frictionic u/ ex3r*scaz:i.7 x. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the e3a9ibp)c39o q4dhqo5 nfru:-hpm0 r cdge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a momen5 um34np bfq: o)i0hprch-orcq9a 3d9t 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 witm nxxce8f3 r4fu31bi)h the end 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 rof3xn4 1mi8xr) u fce3bpe 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 facesi8trtfzn )tn+fb1a/cl1 0 jttcb820p the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angulart8jlc1/1 +tnc00abzftnfpr t 8)2i tb momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m +clh q0di2ak)ltw0y./$s^2$ 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 0sa g:)t)cej3w:q (hec.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the mototw:e shg)c ceaj):(q 3r.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disi)g dc d:yend)m:-znf4 ,ked,ks, each 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 cm - n)kcye)zdednd,4:fgd,:ionservation 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 f2d md*43 -pdudo;cmospeed 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, but hz0 ay z- +qx9doit9rs.z :fu6with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitaty i9zd+u9xf:ozs r.6tzha0- q ional 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 ib04ji 0t2wnsuh+y) lj s for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should bn+)ytj 04i 0wshb luj2e 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 4 3j 0pkil yy9vkkm)b+$H_2O$ 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 d 7yx fg..f9sh$m/s$ 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 lengthi x5b rqd* ti-lt,m(2b L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as show2i5bdrlt(mx-*iq , bt n. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing veb zl6gvf eg (90b1o2aoa+yph y55l 3qirtically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step aga yp5eblv +(3z0aygl1bh6oqa9 2o fgi5inst which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/ r16;qcmnuq (l-)k/r)mbr ejks on a flat road is making a turn with a radius The er;) j n)lkqkbrr/qm( m-6u1c 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 into a sling of length 1.5 m and beggas;;v/xvr3 j,zj gp* ins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What i3;jx*gr ,;j sapvv z/gs 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 sobx/dr1quyyl 5g *p/+9joz(al lid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly 9ajz/y5o/ q( dubxp+lrgyl* 1against her body.   

  You are designing a u5ghbq.:-sgxuw+, ,p( bwh v rclutch assembly which consists of two cylindrical plates, of gpbw:r.u ,suh,v5 +h-( xqwgbmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 thb )zbv01* er *dcze0irm rw)r5e looped rough track of Fig. 8–58. What is the minimum value o* m) e1zzb0e0rvrcrib dw)5r* f the 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 dokvgnxi*+fd6+p+-y qu not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces 8;dl.mk9qz83e ojpohb svq)0 its speed uniformly from 90km/h to 60km/h The tires have o0j9k qo b)z8h; .pl3v dem8sqa 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