A bicycle odometer (which measures distance traveled) is attached near+yybh 9*juif fq3/y5x the wheel hub and is designed for 27-in 9hfyy3jufiy*q + 5bx/ch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a po m-/uvvh1gl4ww(n 3tjint on the rim have radial and/or tangential acceleration? If the disk’s a w/3n(4u1mh ltjwvgv- ngular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value mv c24huaoqh49l r2mr+0l;dg of the angular velocity $\omega$ Explain.

Can a small force ever9-roxtr fl258 jo gu*k(z5h ca exert a greater torque than 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 1ra ,k f)dsd +rurm7m uyl rn,32dbd5+to do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may hel5mrd2r 1 runusd)m,d flabd++y 73r k,p you to answer this.

A 21-speed bicycle has seven sprockets at thx)miecvv 6.(r e rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear xmevr(.)vc6 i sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slee 9o:lwkn0tc0h j-r )lnder lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On thkc 09enhl-:j)0worl te basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig.4b7 x- t)sol si ov5+e+vlp+in 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net3nq:j )y a2qib torque also zero? If the net torque on a system is zero, is the net force zero?nyi:qq2)j3a b

Two inclines have the same height but make differenlm6v4v*qsa4hq.f p1 zdw5 p(ht angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the shf5(l6vp*4whd z1 p.vmq a4qbottom be greater? Explain.

Two solid spheres simultaneously start ro/c8wsd4wulw 2 lling (from rest) down an incline. One sphere has twice the radius and twice the mw/w8swl c du24ass of the other. Which reaches the bottom 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.pzb5pm p*uqvt08 y- w radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has t 5ypp8tp zmbqw.*u 0v-he 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.u 7n114b;eh9:kflfwzw i or g6 Yet most moving or rotating objects eventually slow downkf49f7g6 n 11uihwl ;owez:b r and stop. Explain.

If there were a great migration of people toward the Earth’nbkt 1jkn0 v*b cpxi 2-o9gk92s equator, how would tk 1xiv * c-0jo 9kbtnngbpk292his affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without havi*7jz(mqd) h* 9hjektnng any initial rotation when )mtj kne hhj* q*z7d(9she leaves the board?

The moment of inertia of a rotating solid disk about an a )wriz5uy+0h,khh cu qw;f cw /dtp1*(xis through its center of mass5)pcrh(w;i0z*h w1quwky/ f t+u h, cd 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 on a rotating stool holding a 2-kg mass in each outtj wgs ue;r(qc/vc,:-stretched hand. If you suddenly d qt;e-s(wjgcvur: c /,rop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look ident)*c4s 2t iqrnhical and have the same mass. However, one is hollow and the other is solid. Describe an experiment tqsti)2*n4 h cro determine which is which.

The angular velocity of a wheel r2 kxri*wt pil4jrt 5k50mt: *ootating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If thtx4li5wj2p:r*o*tkrkim t5 0e 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 *mhhyhz r:p t. ,na8olabh o01p8)1pqfreely rotating turntable. What happens if you walk toward the centern:tp prp.h oya1q,z*1 hh) 8lomb 0ha8?

A shortstop may leap into the air to catch a ball and throw it quicklg1new oxi n l+t9x4 d*)rft8qo:v7;yw y. As he throws the ball, the upper part of his body rotates. I yi; )wwqodf8:g 719vxt lxr+*onnt4ef 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 of angular momentum, discuss whl,l zpxx/)f 6jy a helicopter must have more than one rotor (or propeller). Discuss one or l)/l pjxf6z,xmore ways the second propeller can operate to keep the helicopter stable.

  Express the following anglestvi58 zqii3 k; 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 Ea-cbt q1fr ksp ec7x . wc5n*j8y-1ogt7rth because of an amazing coincidence. Calculate, using the information inside the Front Cover, 7 sc fxo-ye .p gtnj1c7-rb 1wt5qc*k8the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed a o gv. )f72ws ifg;42smxdfxn1t the Moon, 380,000 km from Earth. The beam diverges at an anmxog ;1wx2 g.f s4s 2)dvfi7nfgle $\theta$ (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 then +z;)rp7s *2robfh9* od tpek;mxiqgh/j0h 6 motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades s26/fb h+rp hdr mt9*kgo*z; qi n7sxj;)hpe0olow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball makesw-j3v -7:joslaa :i oyv/o pc0 15.0 revolutivvocy jaal 3ip::sw0o /-jo-7ons, what is its diameter?    m

  A bicycle with tires 68 cm i (wzu1x9c hyf+n diameter travels 8.0 km. How many revolutions do the wheels make? u(+hz1ycf x9w    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at vhgs g-0b rrok5z9i4 b 7g94jx2500 rpm. Calculate its angularb4 7 b5kixr0vh9gg4j9r-s zog 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 makes one complete revolution in 4.0 s (Fig. l s4nfk)nk7 +l8–38). (a) What is the linear speed of a child lk)sl+k4nfn7seated 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 thskq5041ath 9 7tpm pp xeec8-re Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pointb .pp4xz0 n5xi
(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 7zewm kmy95 +ub3jnl -7.0 cm from the axis of rotatiowb m+3 7ljzmk-n9u y5en is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly ab w2shhpz:u3 xecp8/4vout its center from 130 rpm to 280 rpm in 4.0 s. D w2p8sx p4/:czehvh 3uetermine
(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 76ijxsmkdg geb w7-30 $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft puu:7posyl:2g8 juwpj 6aj rl3/t 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 o 2 w:p: /7aju3go6ursj l8lpjyf 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. Througr dr)jjlvmb5+ uf8qv3 j 7j31mfd23hjh how many revolutions did it turn in t 3j)b +qdjm2jd1 5rmvflr3h8 jv7fju3his time?    $rev$

  An automobile engine slows d1ct .3akq5/q0u ge pncown from 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 highspeed jets in a whirlingc.j+: (n/ ct+ziqes*w v,wfpg 6esp-d “human centrifuge,” which takes 1.0 min to turn through 20 complef:s qjgi +stp wcc e( .wpv*end/+z-6,te 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 t w8 /qhenj l1ao,t*m6vsv/ 6bro 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled ivqwme/s/,h6obt la*j 68rvn1n this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revol1 w6qlbpvl+5 sdrvt(0jg (m7lutions before it comes to a (lvv 0swj (6q5 mglt1d7r+pb lstop.
(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 +qyvy,qav apu9z e )1.i.lcf0 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The ti)qvfev 0pi,9 .q u+z l1aa.cyyres 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 4m ljw.rnq,zb 2 lzd-/uniformly from 95km/h to 45k,j/.z2m4 wd rblz-nlqm/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 oph vc+ff22-cxa9 edu7 n each pedal when climbing a hill. The pedals rotate in a 9 hxfp7 f-2vc2e+uacd circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the;yedp:dd.u,w qa*g ::ph jhv, end of a door 74 cm wide. What is the magnitude of thedyph gw:,,q *d;pj a:deu. vh: 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 whhi2t*5nqyz-vjp( a6 7o 5 lri1h/y rdjeel shown in Fig. 8–39. Assume that a fn2pyjv7itih j o r*/1yl-6z5ahrd5 q(riction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of massw4rys iwsb(r)oku6. 1q5q 8ay m, 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 andaqw rbu6w 4ik1oys.s rq58y() direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a t afuw/kb:sh ie oxo v;694f6h+orque of 38 :f4hw6k/h6 io+bux ;f o9saev$m \cdot N$ 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 ;(4,xtk,vdp7r pt+go : c:w- cagdowe axis of rotation , cr k::;ogxpd(a7 d,vt-wtcope4wg+ is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. Thevzcs;l b65,xaqdtl / . rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?)q ;v/c ,t blz6da.sl5x.    $kg \cdot m^2$

  A small 650-gram ball on thp a;. 7b gq,jate4wq9ce end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculate jc9w ba7pq;et ,g.q 4a
(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 ang jd1n;/p w4yb6r aea2 .d1ygdrular speed (Fig. 8–42). The frictiond4;adj.2r penyg/arb w1y16d force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of 6 5wp1oz;mazvpoint objects shown in Fig. 8–43ma516;owp zvz about
(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 total mass i 9yqsjq76y8-nm 1c o:puqdps0s $5.3 \times10^{ -26}$ 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 spinninmr7dhk /y6;: m9vz 3vwwnx 4pug at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the xvy7zrum;4kwm3n6ph 9:/wv d satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniforo7n ;g944ttn(h 4lbqaa;tup tm cylinder with a radius of 8.50 cm and a mass of 0.580 kg. ;7a4(t t gnb a;topuq44th9lnCalculate
(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 uq5,zevh sy,. a bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small 0b;5 fqk4z fougs;ssaoj8u(rob ,0+of*vei 4 hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposito4abo(k u05* izs+g8b0ffe ru; so;vs o4 fqj,e 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 broumebx s(okvm1hw; .3l 4rrbh6o/uwpa:d* wo /.ght uniformly to resm3wxwu.owmrdkav/6ob*s;ho h .14e ( plb r/:t 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 accel42f daz/t tg0kerates 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 /oied:as tub/-m9s9q thrown solely by the action of the forearm, which rotates about the elbow joint under the action of thoatue: -idms/9 9s/qbe triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig. kf -61pk6w2 utlnvc1 x8–46.1 k 21- 6vtwn6lcupkxf
(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 (e yn5j 7eou1ukx1 4+quhehb *consists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within fo azh, dv:fn h-arti 2 xx77gp/ia0fd(3ur full turns (revolutions) and releases it at a sx:0-/gva2 frdhpd7 itxi3n a(z,fa7hpeed 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 mofhul,awhtnyy e,65 .9ms.1 uavum 67+ -a siyement of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of.irpizd ja9yo 291oj 5 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and rad hgktj1,)6 e:tjuc -voius 9.0 cm rolls without slipping down a lane at 3.3 g6k cuvtjotj,h:1-e)$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth withgt+x8 :chods. respect to the Sun as the sum of two .t8sh:x+god c 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 /etcju-a97) fdf,y-rut *v7 okl-m z hradius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 zuoj- du/*7atk- -cm fy7t,rfev)9h ls? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls wit+/x;ues6mii 4. qooc rhout slipping down a 30.0 im sq/4xo+ e;ci.rou6$^{\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 8mc5nokb fk3q4uz,q3o :s wq 3z7ii8sits tip. It starts to 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 gri3b3k4o m8qn: sis uwfoz3 q, c8q7kz5ound? [Hint: Use conservation of energy.]    $m/s$

  What is the angular mo,afqb)lr j920guv c vxocj,0+mentum of a 0.210-kg ball rotating on the end of a thin string in a ,c0ga vfjc 29xuq+r) 0l ,vbojcircle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2. 9rp)8vrbgx3c8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500)g b 8r3rpxcv9 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his si :4 fq-i6-t4vgey advgde, on a platform that is rotating at a rate of 1.3rev/s If he raises his armsfig-4adg-q6 ty vv4 :e to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shownla ; l5hvdh(a20rxoz.j/ b4dv in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing fr0vl.4;dh ol5daba v(j/ xz2 hrom 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 rot oebmf(,a21 sffga4*o 1qoma a5kp;*mation rate from an initial rate of 1.0 rev every 2.0 s to a final rate ofp qmsgfk5ao f4a; mm(2,*aa 1eof*1bo 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 vert)4 f/3/w tnbv. y 4xdvsdf9t-gkdj a9bical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, 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/3jwfvasd4db /-)ttf9d g.bn4 k v9y x the clay sticks to it?    $rev/s$

  (a) What is the angular momentum oqj3t(v3uz 2 jou8f1dlf a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum j-isn t(t zqaa 4t(d(.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 dis yohj1vn3u k 0qli-z-8k of moment of inertia I is dropped onto an identicyiq-nj 1 k0h8zolu- v3al 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 2.4 ponk()pi1 si-e op* b+$rev/s$ 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 m0k0 lqpqp/-yse rd;zi86 .y qserry-go-round platform of radius 3.0 m and moment of /s z qq0plrp0ky86s; i-dqye. inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity5)+ue9 lnlsh:heqax 9 .ymbv; of 0.8 xhulq l n .9hm9y5+sv;:ee )ab$rad/s$ 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 l r5l/:dhck*w/yol5 -m+ltjk about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what wo+l5d m *l: w-klj/rhy/okt 5lculd 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 excesszbxukf 7(bwm5b t:+s 7 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 j:qw ::qic)z x$ 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, 4,ae6t)im wwkw 3dq n2:bsyi5that can rotate freely without friction. The moment of inertia of the person plus thiwybt5):23ew46 m,q iawnkds e platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-rou qyh*ccb( jz5(kt46ig vpo4-hnd turntable that is mounted on frictionless h( q 4zpyt-*kv 4c(g iohjc56bbearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the gzuq- /3jk2v 1suo z5sfround with 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 rope unwinds from the spool? How far does the spool’s centers5 2q3uz-/sv kz 1ofuj of mass move?

  The Moon orbits the Earth such that the same side always faces t1e)srw s d(mi+he Earth. Determine the ratio of the Moon’s spin angular momenemridsws1)( + tum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from r/y1ihrbu1hk i. k ap0zgdv3 zq,/5h1 6rkt (ulest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in t57f6/mg q:qmo)uaem 0totmf 4he shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval m6: oet0)5q/7f fomagmt uqm4at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.qvt+upuxu: x3/8mwu3n da17c050 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 speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it ux18 ux/ t+3cwuaum np7q3dv: is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed od9aj4:7r8j 54llf gzts gs 8sif 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 with mass 8.0 times as gref:22 bknmh +0*bw u 4wm,wtxfrat, were 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 los2 wn*mbrhmtbwk+ 2 f4 ,:fwx0ut mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy storexz eon71w l68plf kpzn95;np8d in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical fly n 1 e 68npfpz5;wx9lpn8k7zlowheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an yp+g 16jj az cb(bw2m1$H_2O$ 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 sqlh+iro0l2pq mxre3noln;u(tp) 6f 2 -6 ify )peed 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 ignt:i3t )im hh6sore 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 ros)t6hi: t3 ihmd. 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 kra5 a(m ./befvertically 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 .kf/ar (b5ema(Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speedt8k.o7hi( ;jrr* sb pl v=4.2m/s on a flat road is making a turn with a radiprjkt87b;o h (r. *slius 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 into a sling of length 1.5 m and begin (oc2. d q:8fyfrac6yhs whirling the rock in a nearly horizontal circle above cyrf.aqc: 6yo82h ( dfhis head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms 7bm (kmmn:n:8b: fkdp 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 wpdmkbnmbk8nm7f :: (: ith arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, of+zy6h*z7(rgij lhiu2 mass +7 hhrj6( zui2i*lyzg$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of. hzeq:8sko h6k9thu9 ,hf h;o Fig. 8–58. What is the minimum value of the vertical height h that the marble mustzo68,9oh skfhh eh9 u :.tq;hk 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 assumetrk bja)k* .t/ $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed w+e4luh5uzffjyx b1 w ;z7w4+ uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration w4+w7z+f4uf whl;ujye z1x5bof 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