A bicycle odometer (whi5t6ke km9 sc/rht,o.ech measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle w/ t ecm ,sr65et9o.khkith 24-inch wheels?

Suppose a disk rotater(.tpk+k-say4x*w/ ci- fenps at constant angular velocity. Does a point on the rim 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 cases would ta+pykiprt4e( .s* c/n-w xf-k he magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular velocity7,uvf9up;lb4geko7ujy8 r+ a) qyt c6 $\omega$ Explain.

Can a small force ever exert a greater torque than a larger f fz2f1,57j * aihjacpporce? 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 )4v tio:a8i9t q scp2xdo a sit-up with your hands behind your head than when you4t opq)9c:iix tv8a s2r arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel ane rzt:2(e6ysxu hicro, 1x,u 0d three at the pedal cranks. In which gear is it harder to pe0cue ih6,zos(e:ux,xty1 rr2dal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lowesw16 9bxx2m; w:.va ddjyu2fvr legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis o ddvm69;b :x2yjv. awxu 1f2swf rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fl 9wxs 0sumhj5q 99y*jig. 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 toir*q drg:( ,)pc/tjdn5faeb r 6ac* b1rque on a system is zero, rn/c)eb1q (6c*:ridrfdj a* p tg,ab5is the net force zero?

Two inclines have the same height but make differentk9tchy p2t(x-(spw f ( angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed ofw p(s 92tyt( cfp-h(kx the ball at the bottom be greater? Explain.

Two solid spheres simultaneously s9 ir +aaezdi:)tart rolling (from rest) down an incline. One sphere has twice the rad aadz e9r):+iiius 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 energy at the bottom?

A sphere and a cylinder have tqp(cy5v6jb(6mg z u8 yhe 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 greacjy q5v(gb86m(6y pz uter total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are co/9i g -o-dzkccnserved. Yet most moving or rotating objects eventually slow down andz-cd9 i gc-/ok stop. Explain.

If there were a great migration of pe h.zf9xg5a4f cople toward the Earth’s equator, how would this 4gxf9hfza5.c affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initialdq04;6ikoe7l*s yk kf rotation when she leaves tsko fyd7qk06e4k* li;he board?

The moment of inertia of a rotating solid disk about an axis oasq:mx 41t4 vthrough its center o:1m4vsxqt a4of mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstretx0-:alx b)c47z-cm ,i.vrbkmzcy ya/ched hand. If you suddenly drop the masse 7r4yiby-x-vma c)/zkmc,0c.bax l:zs, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollo3ws pwf (ud) ra3el):aw and the other is solid. Describe an experiment to rpaw3)uw df sa)le(:3determine which is which.

The angular velocity of a wheel rotating t8c9 skg4znp:0kv*jnon a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If thesg84tkp9n*nj0vk :cz 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 turntabl; u pqrrhen0o12ma+j 7e. What happens i; 1n+0 7m2jrqpuo ahref you walk toward the center?

A shortstop may leap into the air to catch a ball and d--ob2/je1jks0i8wx.x rj bn throw it quickly. As he throws the ball, the upper part of his body rotatenrx1-dbe. j8bwjs/j-o2 k0 xi s. 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 of angular momentum, d z;o9jpyp8 ;ukiscuss why a helicopter must have more than one rotor zjy ;;puo 98pk(or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a)xatdrgwup.p h n.ha3 ;(: v;7l 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 becaul9stj gd+k9w0se of an amazing coincidence. Calculate, using the information inside the Front Cover, kjwd9gl 9st+ 0the 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, 380,000t: q* jf)(gftl km from Earth. The beam diverges at an at )( ff:ltq*jgngle $\theta$ (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 rrvw ),v4,)qz9jr* mvyh u4zw;eik, fzpm. When the motor is turned off during operation, the blades slow4 *wz)qf4k r, uv rhjm9)vy;wzvez,,i to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another chiltpi4)t9)pppp.a, agt ann; b3d. If the ball makes 15.0 revolutions, whanapp 94tip gb)a p3);,pntta.t is its diameter?    m

  A bicycle with tires 68 cm in ,uiau /g0uf)ytxj*/-ech v j )diameter travels 8.0 km. How many revolutions do the wheels mak-je) v*u hi y), ux/jag/u0tcfe?    $rev$

  (a) A grinding wheel rz ,xlg2w4.iep 9l/ul0.35 m in diameter rotates at 2500 rpm. Calculate its angular velocity i4z,.l pl w9u ligr2ex/n $rad/s$ $\omega$ =    $rad/sec$
(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 revo:eepx m:f-u 7*(akdcq:z /z stlution in 4.0 s (Fig. 8–38). (a) What- 7 zqkp:x dm(sc:z: /uetefa* is the linear 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 angulabwm kbdb5f24 uw0c*ub+5 uc6 pr velocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of 4raxztf bca *mqt;r d7 ;/3a4ma 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 ax0 *0s pxe+t0qs1 pm zcfbl/hc :ni6p6vis of rotation es cc:6bq100*+vtp/ 0hppznsxlm 6i fis to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheelntv-ih+ 9z1re: hgx75 id+p7ebn n3eg accelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Detere37i 71en hggzv+ei+x5:rnnh9b- p t dmine
(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 radiuswh.-6 qc4lzdl, xte0a $R_1$ 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 szkfxsq (2 3eq2*i -vbhpacecraft put themselves into a slow rotation hbsfk2x*(v q3qz- i2 eto 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 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 h:8g .bpmxqcu4 6yzu5how many revolutions did it turn in this tim8:m 6buc pg.xqyz5 uh4e?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calc y5;zhh if45vvj;.edi ulate
(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 th8 dv62cgngk k2vn46 7 k :lf6nxdeufk*e stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn t*8dxuf6vc7 2 g:e6f24kv nnldknkgk6hrough 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly ,1e33h kg 3rrv ggvh2ifrom 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have trvv3g hhi33 rekgr 12g,aveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min Itkbxzu 0opdlk32+ w7.a euqoc)n t 3o+* turns 1500 revolutions beo.7t)xk+ld3z*on o 0kuuebw3 +a2 pqc fore it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly qu* -5)ntirk hfrom 95km/h to 45km/h The tires have a diameter of) q-rn *5thkiu 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 u0 mmx-2 ewo91kxc wfy w.7psb/niformly from 95km/h to 45pwf./1x m9-mkywo esc20 w7 bxkm/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 hh 0ku +zeqa*j3 3e5oqver weight on each pedal when climbing a hill. jqe * 3hoze vk3q5a+0uThe pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force 12 kww 98(zk6 nqguptmy hxer 0;.zr8sof 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the fouk9r h0tmkzy8g8 .rw;1xpzq2nw( s e6rce 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 or(;uvyvmt-x*ef ;6xua4+j es f the wheel shown in Fig. 8–39. Assume that yve+*ufae r xv- 6u( tj;x;4msa friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rxi+ gp2 h0xsz,od which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this systemzgxihx, +0 p2s.

  The bolts on the cylinder head of an emnl3vj9m2oi -ngine require tightening to a torque of 38m3 l n9-i2vojm $m \cdot N$ 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.;x rtecv:/+pp- c)ixwx6 tw/j:jpvg, 8-kg sphere of radius 0.648 m when the axis of row )c/w,;tpg+jx:r/viecpxj:x vt 6p- tation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diametew.ln t /flrrwk0mq3cz* ,;vl2r. The rim and tire f twr/lw 3rv0m;l z*ckn q,.l2have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the *wic)paa x*1t end of a thin, light rod is rotated in a horizontal cicix a*t)aw*1 prcle 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 bowlq6, llxcaq2n) on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The fricti2lnxq ac)ql6,on force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects sk:a6 (zd e-o-v)dkkeqdxi :k1hown in Fig. 8–43 abou1 ekd-::e) v-(diqk6oxadkzk t
(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 z;x5e7h+r st iggpni.w fn,r/-h7n.ls $5.3 \times10^{ -26}$ 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 cylind6ffh q/8jb93d9tqsd drical satellite spinning 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 isd/6dj8h3bfq99 sq t df the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cyli,-1udd tln)oq nder with a radius of 8.50 cm and a mass of 0.580 kg. tn oud)q,1d -lCalculate
(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, accelost frd2t.e/ u0hc:8.whl4+ tm mx;gwerating 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 onbh;e a1wnfw8 c.p+b )m a small 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 t ab8h;)1efcnw.+bp wmwo 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 ap( lj*+remeeb 5*nn 8-jssvl(t 10,300 rpm is shut off and is eventually brought uniformly to rest by a fs j-e*vlm s e(e+(n8nb*l5pj rrictional 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 at 7 :y0lb21ziubnd08sv c$m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the foregk8dpesfhd/ ,b30 ( pvarm, which rotates about efk,(/3 0sdvp g bpdh8the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as sholmxcow1b71,iog8o i54 qe ;kywn in Fig. 8–46.g7cqo1i i185,;welmk 4 b ooxy
(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 consisv+ (c606xqtw.p1i uj)ulvni ats 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 four full turns (r iu:xz6fn 97tqevoux n 9fi6:qz7tlutions) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia of w8 ij*d qj*rf,$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops 9 gb +eppnobw8ie*g76/dzmb51r1wkea torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 c3hccvenb )r s, t9p3 3han.8nom rolls without slipping down a lane at 3c 3vonns thr.3p b n8cha)e9,3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respj h 9qscc 8mu8w3v2/czect to the Sun as the sum of t2/hcj c c98mszqvu3w8wo 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 jg8p2se a49rowl l.f+ 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it fg w9.8 +jparo4elsl2 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 mass 1.80 kg starts from rest and roll uxqchqb w29au2pq3+2s without slipping down a 30.0 ab c3p hq9qu2q w2+u2x$^{\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 fall and itsgqok+ y;lb7y. 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 k7oq;b +yg .ylconservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thin stv5) ,r xdhxnt3ring in a circle of radius 1.10 m at vxx3,)nh5rt d an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angulaf ki eay2;4:uc 92uqytr momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpe :uyy4fcq;t a iku229m?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating de j:*kzi2tth2 sq8.c(4cvaz5u5rq pat a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreasezc ikr.tc5u t4vadhs:2q*j8(5zq ep2s 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 x(yga*ey4jbyi:r4 -f zrqt 82of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 yegf:yq*itbjr r4 x2a8 -y 4(zrotations 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 spgkq6zkz*we: d n55.at in rotation rate from an initial rate of 1.0 rev every 2d 5keq .6kwa*z5tnzg :.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 9h1,/zq ssa5vx*l rr2ac vc:y 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 pott19*rx:,2lzavsc rvs/ ah5c yqer 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 momentum of a figure skater spinn*zv(q 5 cjfl28e 9codcing 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 of the Ear4gbqug,r jy3 vrn.ex hvkvc62-a/y+.th
(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 a )dxd n-+ha4t.yep an/n identical disk rotating at angu/na4e - x+d p)at.nhydlar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at y* tnw;qjt *q:y1 m0qm2.4 $rev/s$ 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 3vk8:z()lviywop;3 ye ejlr (kg stands at the center of a rotating merry-go-round platform;j(yv k l3l(r:y3i8 eewzo) pv of radius 3.0 m 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-go-round is rotating freely with an angular velocity of meoj6qszy 654qia-gn 759bdh51e dlg0.8 - ieq hd9qzg 6lo4as75djbymng 5516 e$rad/s$ 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 dwa.nag-mb2 q io*rf, losing 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 would the Sun’s new rotation g.i-b*n oaq2 mrate 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 1 wuz bs-kg)f5excess 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 3vtnm u;thbox /w4x60xt17ue $ 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 ro 9cyf/6*sa cwstate freely without friction. The moment of inertia of the person plus the platf6wy9cf*/asc sorm 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-m4cb phd9;c 34xjk*vw: x4nlr d diameter merry-go-round turntable that is mounted on frictio;rh :4xdcjx4v4k 3d l *wp9bncnless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on tdi 1 (+l*urn1ox(wmiar p,1.uxih x 5the ground with the end of the rope lying on the top edge of t iurdiph ri w,ao (x.+1xtmnx(15l*u1he 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 center of mass move?

  The Moon orbits the Earth such thaqf e +rdzs .1h*oss59pt the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Ea*+s5hp ofs e1drz9 .sqrth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of ,ssm8v mthd+2 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acb41t k7fod3ck quires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the toro3bc7kdk4 t f1que delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of m3d3h (2u z8axttubkdg :q)np 8ass 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 oxh82k qptgn8)3t( ad du3buz :f 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 jb4 11z(mtk nf(f8r onn032msmec:nd speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but wit 4 ;jfddyh 8gi*yeu+j1h mass 8.0 times as great, 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, l 8fe*gdyhjiy 1u4+ jd;osing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energyh*t0*7gfq lhmjapm ,x6+gth 3 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 be able to travel 350 km without nee 76m tg3lxq, 0hp* jtahm+gf*hding 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 an8wk x 2b.f 6rbbysb(4d bj+et2s 1aiu1 $H_2O$ 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 ho8 ya*lz3tlam .eig f/7rizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L cazm5y *2ztvl1))gaxam wc, z)sn pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54.a) ct )5)vzzzxag,y mm *lws21 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 shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has cuz/lsggev 22( /lqg+mch9/yp6-fqn ctx)j5radius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has heigl2ng g+ qj5x()-pcu s c6tcgh9yz/2f vmeq/l/ht h, where h

  A bicyclist traveling with speem4/s ynhu0x+bd v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and+s4hy0/xnu bm 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.+z c1)uhzjk y45 m and begins 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. Whacz)y+kh4z j1 ut 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 as thin romsakf +r 957vfds, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater wi59 mfksav f+7rth outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plat9 x,j;dajj/u.a.q-vt nwc 3z tes, of madwjcujna;va j -..x,/z9q tt3 ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 Fig. cvn d . 8:ie mp6iz7o7adk1*pz8–58. What is the minimum value of the vdpz76odpzckn7: *1i8. ma eivertical 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, bqmbhe-3.om yi6p 9+zeut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly tm8nh-o o92u ifrom 90km/h to 60km/h Tht 8oumn- 9iho2e 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