A bicycle odometer (which measures distance traveled) is attached near the whh9h-pp l*ah r9 1)h73awnkdyfeel hub and is designed for 27-inch wheels. W f1ahdp)p7yn9kw9al* h 3rh-h hat 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 b3flji/mv z/y4he, d1 agkt)2 have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which jh4 i2a3)/kfvtdm,e/yb l1gz cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be dzc: 3rne7 wtv c51r+jcescribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? E7sp(2g0be:tw w- k ux8yi3g;mpx5w o ixplain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behind your head t 3q5rjv 7-b3aiq1 kskzhan when your arms are stretched out in front 53akbz s7-kjqv3 ri1qof you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and thr+s..7iaejq/ sm;ln vbee 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 sprocket or a lar7mbjv.+lss/e ni ;.a qge front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with flf 4o63eo9jbzc9 1he scesh and muscle concentrated high, cs3964o obe ec 1czj9hflose to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fi*iaj7 /oqezt.g. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net mb d d9o caz,vz2zrghozhw:2 n706x;,torque od,wbzzovmz76ch;h2r, z9x gon2 d a0:n a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontalpsx/ piw2 bl;2e3, z8jp7sy ga. The same steel ball is rolle3ipyp b8/a2 w gel7;sx,zspj2d down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rollig 1(l1l 6y/x8cwscyaong (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?8lx6oc/wc1y ( ysg1la Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start f- ghbxock:5cez1-eaf 4rgrtj;1rn1a ug01g4 rom rest at the tog5b4rrkc r uf gc- ajhg1nx4eoea;g11:z-t0 1p 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.n0(z :f x8uz3pqumte/ Yet most moving or rotating objects eventually slow down and stop. Ex 8(nezumuz/x t0 f:p3qplain.

If there were a great migration of people townx )fe.9qmewfg i55 *pard the Earth’s equator, how would this affecigf5xem.qw *) n 59fept the length of the day?

Can the diver of Fig. 8–29 do do mb4);x+8 j p dwohvbz:kbdw.04,b ta somersault without having any initial rotation when she leaves the mj 4p;bd0, h:ko b4w+ wb)dz8xvbtd o.board?

The moment of inertia of a rotating solid disk about a o+gtr7w a-*mbv e-:vit 8uy1qn axis through its center of mass is rv*8mou ig tave+:q1bw7--ty$\frac{1}{2}WR^2$ (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 outstrzv:o)ugja6t a/j9-v) +/occg ekw c(vetched hand. If you suddenly drop the u:)gv+ caz/j (kj/-vgov9otc)a w6 cemasses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identicxc jefstqbpg ,a pe0h;/04f /;al and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is whiah0;, ctg/fepxf ep0;bsqj/4ch.

The angular velocity of a wheel rotating on a horizontal axle ptr)ze d069yup oints west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at e dup9)rzty 06the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freep4we 57wy5e egp+;ouxly rotating turntable. What 7pp w wxy+5 4e;eo5ueghappens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it qzz+4u:t67 rbzhuuu f9 0odio-uickly. As he throws the ball, the upper -zu7t+ oi:zr69hz ufu b0du4o part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation oa 9*wjalkw9z7f angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discl zkww99aj 7*auss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a)qz)( i v/r2lzk)m/g se 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 a9x79 vwd3v sbxmazing coincidence. Calculate, using the information inside the Front Cover, thxs d9v9 vw73xbe 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, 380,0:0 puso8u onvoo:pvf :z4-ez2 00 km from Earth. The beam diverges at a:2n szopf o-vo v:: pe4zuo0u8n angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotar.vd7+m*s d ddte 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 angulad. d+d*svrm7 dr 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 the ball 2ewa)h izmt;* v1gl v+11kx8t mu7prjmakes 15.0 revolutions, what is ittvpm11ir)t 2aw;71jx 8hmg l* ue+z vks diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How 5,l po7 .o1u(7a k sts1hl:0 ,wapbb1kuaxvkr many revolutions do the wheol0.r7k(o , s:1x7pupvl1ku ak5tab s,1abwhels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate it ps63i/iwy e0pip;ea/s angular pi ;e pii0/sy3ewp6/a velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round 6 erh rj7ua;qm 8:.+neq kpkt3makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m ;6khrt3:k ua8 +p7rmnqqe. je 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 theg p,8gxf-d;jf Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed -p gj +a3r9qdoof a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axis mltmc. )qd a3vl7+mqvgh4m5 f1rh5b4of ro lhrtf m5a)m4m5c+ 3vb7vml4q1 .gqdhtation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates u9w94i4 l,wj:rhz yb cjniformly about its center from 130 rpm to 280 rpm incy99 l:h4r,zj 4jibww 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 h(6hs pea-fd 3mba41*gye1 7t uk 4mux$R_1$ 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 Moon5(r;3po:ug kxp ii6mq, astronauts aboard the 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 rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can bxupoq 5m(i k6:i3prg;e 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. Through how;l,bsdi,l 7g,nzg5zc*7 sj jrv u x00p man,7l0ci v 7 sgxb5j,s0ljpz,d ;nr* guzy revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm ss*wzk v: ymnub.4;p0 r0q9dlin 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 flytw k479ee6r2ahli if7ing highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachi 6 r 2tfieaw794kileh7ng 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 k4d5q)x:b3 h;dn tkvc240 rpm to 360 rpm in 6.5 s. How far will a point on the53b qndc) 4tkk;:xvd h edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revoldzamx5l rc. n4*-8 umnutions before izl .cr-84mnmu* d5xnat 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 reinnkw.ld*-*ip8xkw e z) s p3,duces its speed uniformly from 95km/h to 45km/h The tires have a diameter o) wlk-.kpd3*en8x i pzsw* n,if 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 ca)0t.p by)a x sw5lj*bg)+rbjkr reduces its speed uniformly from 95km/h tobsj rxwl0ay + jbb.)k)gp* 5)t 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

  A 55-kg person riding a bike puts all her weight on each pedal when climbing a h)wc*2as,fab1tt m4u/d+q rtyj e, f2bill. The pedals rotate in a circle of/yb)4r+,d atfte ,qm*c sa 2w1jtbu 2f radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. Whatu, 3wurioz0 tk1hgx70 is the magkuxi, 0r0hwz71 g o3tunitude 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. 8–39. Assuc xs.0xch44ku me that a friction torquesx x4 uck0.ch4 of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass mibsgz lcq,.9/ , are attached to the ends of 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 direc,bg9 i l.c/qsztion of the net torque on this system.

  The bolts on the cylinder head of an engine require tight9mm et95cdxb )ening to a torque of 38 tmbd9e5xc9)m $m \cdot N$ 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 when the ag6 vm)x6 x6jcgxis of rotation is throughjx6c x6mg) v6g its center.    $kg \cdot m^2$

  Calculate the moment ofl)ud9 myn qk(5qdwy4/ inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1q4/ (5nwk qldyudm9 )y.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the endep+flh l6n0a(7o1 ue zqd/o f8 of a thin, light rod is rotated in a horizontal circle of rad zdl7npe1(+ qfleu6/ oaoh0f 8ius 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 cons)i.st(noh w4cg(97 fjhi7cw co tz93v tant angular speed (Fig. 8–42). The friction force(iotiz3vh7o)tc ws h 9c9w4jc7gfn .( 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 th75 qokalw -c)jpb. eq6e array of point objects shown in Fig. 8–43 a.oqk) c j6a 7lp5-bwqebout
(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 to lw9ik0rvqgi.f5 /3fptal 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 td udg s+bvaez* t4nv*vb 5agq01 x4+oy./b, xbhe correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has an+a +vaus5dbe gy *q ,*/o04bx.x14tbdv vzbg mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0.bzn0 ;xqb; b)f38k 3emsdbwlr 2 ;ody3580 kg. kmw8brzefx; ;2yq03 dd;bos3 n) bl3bCalculate
(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, accep+h ,zg7ghrow5ipf ; y. rw.v5lerating 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 small2sb.cii32 zqm7it+ i c hand-driven merry-go-round and is able to accelerate i 2b2i3+mq.iti szcc7i t from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce 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 and is eventually brought **rn fb0odv 0yuniformly to rest by a frictional torque of 1.2*nf*0r vdo yb0 $m \cdot N$ 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-o6k;:wvg ,ca bxj;1 jwkg 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 throwx 7pp rhg;j,i,/i e pox;(n9btn solely by the action of the forearm, which rotates about the elbow joint under the actione /xh;b,j7i9x g;npp(itr, op 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 co i x2qrfo1pvx;j/2r2tnur+) rnsidered a long thin rod, as shown in Fig. 8–46.n ifr)+t2;rrur 1xqjx/ 2pvo2
(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 t:n218lrwt0fakgneh zh +a) 0rwo 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 accelerates2q 4hnzfd:ck: the hammer from rest within four full turns (revolutions) and releases it zdc:f kh qn:24at 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 inertia ofhrd eoh/7 ,m)qgm+qg 6 $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine d br8 jb*u1aqwgv0l j-:evelops a 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 k;jfo p4dak b4: xy/t0radius 9.0 cm rolls without slipping down a lane at f 4 oykd;0:/j4bxp kta3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum ofzmcb9eu4 9dhr5;)yf gl9i qc ) two t9qh icgfu ;bm lr)zcd e95)y49erms,
(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 5w xmcf ,wyq+2net work , wcm yfx5+2qwis required 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 maty4dm nemx)zbdym: n0:4jtq p564 yi,ss 1.80 kg starts from rest and rolls without slippid:4)eqyn4 ,04 mpmdj6ny:bzymt x5ting down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts to f2f6l ua 2u6fl 2 up2oxzzy,p(wall 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 f2(,6puz6 2y wxulol2af2pzuconservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotatinftqt oziy7 b*m:u/x0d/) uqo ,g on the end of a thin string in a circle of radius 1.10 m at an q0 uobmd *:,7/i/x )qttyoufz angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.5xpljc(k(2 ;wil jsj3 8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm?(;k j5(jxl jls3 ipc2w    $kg \cdot m^2$
(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 ta9hbvp9)wt +q8xpe ;lhat is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rol;9w b qvtp+x eh9)8aptation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of vgkk+tz mah4 a07y+zy)fj. p ,inertia by a factor of about 3 yfmzaj+,p 4g.at0k yv zk+h)7.5 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 increase her spin rotation rate from anvur8qij -wu.*gp;( wv ktl) 0vg) lha( initial rate of 1.0 rev every 2.0 s to a final ratetw08qv.))lhgu;aur v*pwivjg(- kl ( 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 verticam4nyh/ *wspb.l axis through its center at a frequency of 1.5rev/s The.pnysh4w b/m * wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentco k; m)v0p1bqum 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 mo(hg xv2 /btdg5mentum 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 droppo9 xl9v-xu +ised onto an identical disk rotatinoui v9x9l+-xsg at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns onn 2 x-l+ -ak)nbqdkvp6he,5at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotatingici(,gajmf7- ghh a; :.t0ua y merry-go-round platform of radius 3.0 m and moment of inerti(.a mih-ycgg0h,tuj a:i f;7aa 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating free :x/hqh :bbim0p6qyd8ly with an angular velocity of 0.8 6: qim0/q8bd hhxb:p y$rad/s$ 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 about half 5(7j(f lfh y2care(qxh,t xt( its mass in the process, and winding up with a radq7(hcae f, (r(j ttx2f xl5yh(ius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve *k ow72sj,ph t4q rbua,/0oxs winds 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 mwv o9im (i+p*3i arx/$ 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 fr5yv xlywi (jw*)+ sjpe /r)mfvq9+(kheely without friction. The moment of inertia of ))/r jwmk+*s95+ xf(viqjv(hy lwpeythe 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 edge of v, /6oulhp8pua 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a l up,op8hu /6vmoment 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 the8ccpc -r7 lx 7yt zhu3p6shb*( end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a d87 c3tcrxp l7z6bc(ph-hs*y u istance 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 Earse7cmh9w 8 6aqth such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbim76 w 8eas9hcqtal angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ratec wmn8-me 87( /xgelkw 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 shaaw8h*5q j couu4ci,vqx ()ec41px do (pe of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at consta8o4q)u c v (cadxi5w*(u1cqx4j,oephnt angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two so9 )y*esqio eu2lid cylindrical disks, 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 conservation of energy to calculate the linear speeye 2q9eusoi*) d of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the ren6gy(s g vf8ht7)g wu2ar wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, wer61-zuxycqj+ i:x2 sbk e rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost masc : jsb+xikq2 -1xu6yzs carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stor6 rzc-*d7v 4gg5+q .i-7sl ntlvbcnkled in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniformqibg rt v-l7 67* n-cn.vscllkgdz+5 4 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 illustrates lrgjda.ecs2po ,b3d+,al5 9uan $H_2O$ 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) .j ,b.:gzisznee ygrc q ;:5w+is 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 masoxy j t7or/.w .,wj+yps M and length 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).yjwoj 7.x/y+prwto , the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertica wakuck pdo7t1/ ,o8)wlly on the floor, and we want to exert a horizontal force F at its axle so that it will cli)ko/7 a8twopw ,1kcudmb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling w9h ns2/ bcd:5n,alkhox; ntv*ith speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are dh kcn *olns9a5/hb,v2tx n;: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 0.5umb.rx9z ,wakgo4 ze4 hc c0+20-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it fromx z +hzrkb.2a om,cc940 uwge4 rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylx3(nqgpnr( ;d inder and her arms as thin rods, making reasonable esti;rndq( (nx p3gmates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which j 3gps 4mwe 0fkt9c.1mconsists of two cylindrical plates, of.emcks9mfj0 p3g4 t 1w 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 rtgrd)bk eru2 r p- 0h ujm,p/r:ai*8;pvtp8i4adius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical heigh )88gd ,;puba2rjthi pm4k-rt0pv *rur:/pi et 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 assum,9jxnv mdn;;unc,bh bpt;w2 mr 4 p 3ijrp1f4;e $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces itqec c4ze s+r0h:rn;y2s speed uniformly from 90km/h to 60km/h Thc hq:s 4r0+nezy c;e2re 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