A bicycle odometer (which measu.c4dej nrgi;:rmcz5 -res distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. W4drz- j: ;.rmingce 5chat 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 havr(pcz.*9nm hkza r-*rvs lt 5f0+)lzye radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangentia0 z *lz .hmy+)ars( n lrpcrz-v9*5ktfl acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be describn/e3n rk:g+ ymo5gjf 5ed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a/ o4fw 4l 6e6jbudir9f 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 to do a sit-up with your hands beh0syo+s43lv8ig3q a mpind your head than when your arms are stretche qy3sv 4aos g3lp0i+8md out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the re(gzf -4. j2fxi )jt8ljru;x+ba2fgalar wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large bz2f;)lja4xf.( j fg2ujta+8g irl- x front sprocket? Why?

Mammals that depend on being able j2plawg q 58nm c,z+i+to run fast have slender lower legs with flesh anngj5 l2a+8+m icwq zp,d muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35 nocwsq5s+dm0m1 -1gg ) carry a long, narrow beam?

If the net force on a system is zero, is the net torque a(1*a q thtnc3vlso zero? If the net torque on a system is zero, ct( t*1vh3anq is the net force zero?

Two inclines have the same height but make differe0f/e -w( rv/bruzgk2ant angles with the horizontal. The same steel 0vzfguw//ak2r -b( reball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (fromhnwm)g b 8+ fubh+5ov9)1onj d rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater +)h1 jm8n w95fbuobvno h +gd)total kinetic energy at the bottom?

A sphere and a cylinder have the,lsbd +pxcrf: w4.enq(f ano 1)m8w8x same radius and the same mass. They start from rest at the top o+.wq:fdnrfe 8 x) (alwmbpn14 o,sc8x f 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. Yet most movingcc66fn)sx0 j 7fbybo 0 or rotatingy xf0on7b60j cc6fs )b objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wou ( wjk2k:ui;sjld this afksiw: ;k2( jjufect the length of the day?

Can the diver of Fig. 8–29 dxt h.ew7 ccx2y*ak v7s 1kgu) 2*bui5n 1bas)oo a somersault without having any initial rotation when she leaves the b kk1v y hxx 5cu22u) n)7a7*oti.*saeb1cg wsboard?

The moment of inertia of a rotating solid disk about an axis through its vf;quu*36 0q yytnc, *ptbz7ycenter of m;p,c f vtb 7z0tqnu3q*y*yu6 yass 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 ykr5p:pe6k qv 74bo1ea 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increask: 4 61byoe5pq p7kevre, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hd gg6,wx7mfk )ollow and the other is solid. Describe an experiment to dw f)dx6 ,gmg7ketermine which is which.

The angular velocity of a wheel rotating on a horg y w so6f;8k/0ikwdc*izontal axle points west. In what direction *fko;s0c 6kigywd8w /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 the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating tu1eieq5clf;9 mrntable. What happens if you walk toward the cente iecq1m95e;lf r?

A shortstop may leap into the air to catch a bar qk)z,debq)) ll and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite dir q),kzbde)q) rection (Fig. 8–36). Explain.

On the basis of the law of conservatiodjus95b.mb :us bcy8;n of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways t5yj:cs ;bsd9 u.u 8mbbhe second propeller can operate to keep the helicopter stable.

  Express the following angles 3zoq.s7;r(k ptxx3 ed in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, *p)n8ra/mwec using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on E /em 8)wpc*ranarth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The bea0)ihd.m;a6, b yblc rom diverges at . dc0r li ombab,h6y;)an 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 rotate at a rate of 6500 r*(c kf9czblt 4pm. When the motor is turned off during operation, the blades slow to rest in 3.0 s.4bz9(* ckc ltf What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floocwoc3umkqr(54g3gski e0*q c* if3* or 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diameter? 0*iw msk 3q3r3g k4cieuqf**c(5oogc   m

  A bicycle with tires 68 cm in diameter travels 8.0 km. ht/und 5n*ao- 5j lym*How many revolutions do the w*ytoln ndu- *5 amj5/hheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotateg)nv(b27jt5ifhz*l3 l r/ lkl6g(f em1hn9dns at 2500 rpm. Calculate its angular velocity ilv5ie)t (d kf g/1*7l 9fjlnn3bh6mn(lh2zgr 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 one8:c 3 f rnil8j(qu1 -amszz)hz q:ec9x complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the ce mcj 8znz fa::i9-r)sulc (13ezx8qq hnter?    $m/s$
(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 itnnr4,i7yau6c* 5 f, oh*k cgjes orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a l;+e d,bya8ow 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 frcc2vc7 eta/8qf,; u q 9+oys jky*rna:om the axis of rotation is to experience,y/ cjqkso9f8t*e+rc auc n2a;v7qy: an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its centm ggu7/ 4miex7er from 130 rpm to 280 rpm mg/g x4 77iuemin 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 *sgocen2 9x+ gk*xui- $R_1$ 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 fkvlf01 rkjl)y4 /hh(Moon, 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 be thought of as a cylind4h)ff1vj hk(r 0/lkly er 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. Thrt3 bvkwcg +2o,0toe -dough how many rwog b 32otdvkc,t+ e0-evolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500g; p7(uecz+hv,l/ 3xrn j7)vio kf8gl 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 whirling g + s78 k:or gsqalupt225y)kx4o vbx.“human centrifuge,orx2p oxgs7kby 85t vl)a:s.qug2 +4k” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly fromqrjdg:p u6n+6 240 rpm to 360 rpm in 6.5 s. How far will a point on 6 j6+nurp:dqg the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850v5u 0ll,f12wyxo ur0 arev/min It turns 1500 revolutions before it comes to1wouf,lr l yu0v5 x02a 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 revola*mv9 oy vim1xl5o// tutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0l*/ v5moy9 tivamx/1o.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 t06m csp- dc 5ws9k z9ida()oejhe car reduces its speed uniformly from 95km/h to 45km/h The tires have a diamete5-d9jw)9 sm(6ckcszid0o a ep r 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 putwolta12sfo2xxph 2od75q s 12s all her weight on each pedal when climbing a hill. The pedals ro s2oal1h2 xx sw2dpq7ot25o 1ftate 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 of 55 N on the end of a door 74 cm wpsk -8 d2c(p9d,pbhg zide. What is the magnitude of the to cp , pk9ds-d(82bghpzrque 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 thej*y mk4c5v 1cf1dx(tpezehe;/7r7a7 r4ob no wheel shown in Fig. 8–39. Assume that a frictio oet5/f 7j4ode1r vm4cyakch7x *1pb; (7z nren 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 masslesfpbj joi2i1 sh(;9ph- s rod which pivots as shown in Fig. 8–40. Initially the rod is held ips(jo; i hf2phi9j-1bn the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder ha j;q/+2hww et: ne:gzead of an engine require tightening to a torque of 38 w h:z:+w etnje;ag /q2$m \cdot N$ 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 theca8xfb jh 8u:1 axis of rotation is c fx8 ah:8b1ujthrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rs,co: q 9icssd 8;(adx, oc2bjim and tire have a combined (9soaqcs,co :i82s c dx ;,jbdmass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in ys )1w s7iuf .o1dki,ka horizontalsdyki .f w7 o1,)uk1si circle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potd7 4i 4g5-(bjavdpjh 6ei7 jfater’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and thej i4ageh-vfj774ipd6(b ajd 5 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 obw;ztc c1e ,z 1paid1+mjects shown in Fig. 8–43 ai+z ,1dzpe1;c 1camwt bout
(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 t8z liumj8njd,.bn-ntmp c3.4 otal mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the coregl hp4e 3kd-;;m6qam rect rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600q3 p;h6ml ek;dam4eg- 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 b)0e3 hxi6mmaga; x)g 8.50 cm and a mass of 0.580 kg. Cal e)0ig3m)hxa a;6bmxgculate
(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 avoq 2*z )gpv:f 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 oz2v m w+ fl13bw0r-xkwn a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 01 wmkwv2 lr fzb-+3xws. 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 tm,h ehnp7+;fe n:ws( at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictionem thh+ n(sw;,7:nfp eal 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 i i* j0se8ywvp/sm-1 fcz7 t7cball 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 b6u(ydpptn;f8/yxil-k d/-e ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest tofbdup/p8 i-ekyl-(/ 6;ndx yt 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;ao7q97 con mb in Fig. 8–46.9;7cb aomo 7qn
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two mass 73n0fze i)v4zuo la;ees, $m_1$ 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 thesbt8y 39-yuws hammer from rest within four full turns (revolutions) and releasess3t9yb8sw-u y 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 mo6oeyv(i/fkvk hc3(elkiz* ;: q 0yq4sment 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 o 9uy2 e,u-e 0rmt:k6 ,h yqptdcdot-4ff 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of massl s wxd.8(:lms 7.3 kg and radius 9.0 cm rolls without slipping down a la lxs:wsmd(8l .ne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the su)viive+w:e 3 dm of two )i v eiwe3:vd+terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7otuz-wb+:mga tyk.0 l9ryz-7.50 m. How much net work is required to accelerate it from rest to a rotation ratat wy-zmoy+u:ztgr .l-k 90b7e 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 froa 23qcb7h4lp.zszjc ) m rest and rolls without slip ljzh3z.p bc)4q7sa2c ping 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 fall and bx4mlktexjjc1n3dp u0;/a 7, 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 conservation of/tbjp n u;0dxe,kl x1743ma cj energy.]    $m/s$

  What is the angular moi/ kl0ads*x ;p)ni3yik0c/hqmentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular sx/ns0pyd iki0*li ) h3k/c; qapeed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding whmeyp--w x r:q-0/yz2n whlkch3z up;3eel of radius 18 cm zyu3:w --xr pzlk- 03; hy/ph mwq2ncewhen rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a pl 2l:p5fc +tvxlatform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decrvplf :c5l2tx +eases 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. ge 3kbgcvh-g4a.,n2um+jt(f 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing fro teuc+2h n.,3 kg-gfagjm(4bv m 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/htt o*lzla.7x3y uw n6cm* q*ation rate from an initial rate of 1.0 revz lnhm.*c qo l u*67wa/ty*x3t every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating arouy w)kx4iv52z m a;ze.tnd a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a unifow;)kemi vzx4a2y .zt5rm 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 momentum of a figure skater spinning co63 ,at*kydhwy,mafn)g 8 5iat 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 momen4mji1uf*q0x hux*zt8tum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an sb7dq: )g;l hlidentical disk rotating at angular speedh:7gldqb;)l s $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atuuv1 sp*(y,ft s0. tjd 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 jvhz8d8j -mi6yxr)k6 zu a;b( the center of a rotating merry-go-round platform of radius 3.0 m and moment of inerx;y6 zuvjb 8dr h k(6j)mi-a8ztia 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 vegsy-2 dgyf3e2 )oms.j locity of 0.8djs)my2 gs3e.fyo -2g $rad/s$ 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 inbqtak)bdm e n *m501l7to a white dwarf, losing about half its mass in the promlqb7) d m*0ne 5k1tbacess, 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 rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess * jrcc (kzi9jj;i,)2 b8iwnt bof 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 zd7j ::8tmbg ik 8nqc,$ 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 fe ahevqk0 8q e7,4)ei23r eapwreely without friction. The moment of inertia o )h2kieq ee7,a4a 8e30epw qrvf the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-e; te4mnwz*e -go-round turntable that is mounted on frictionless bearinge* t;m-wz 4nees 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 ground with the end p.1 i*p-2ox9hmp e xo o)iibmj4+g6aoof 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 f-h go*objop x4i.i pmo+2)p9ixe1 6am ar does the spool’s center of mass move?

  The Moon orbits the Earth such that the sa,n w8y,nn axi0(p upo0me side always faces the Earth. Determine the ratio of the Moon’s spinpuywi,p,x ( a 08non0n angular momentum (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 xf:kfg:e 12ax from rest 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 the z9q.gp(*n)ueocbo5 ushape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest ove5 (up* oqn).zou9bcg er a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylin9n 9tx)y m*tuudrical 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 conservationn*yu9t)x m9ut of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheel (ndy8vng /u0-g $\omega_R$) 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 Suuf,w9 osg9 l *1nbq5dvn, but with 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, losing three-quarters of its mass in the process, what would its rotatsd5 bl9 g nv1uoq,fw*9ion 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 energyq2th));6x swh+w bf zz stored in a heavy rtz2+ x)hshwf b 6q)zw;otating 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 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 aaat: q cl+,vx0hd 78rp:/igjen $H_2O$ 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 horizozj2+m uu wgh)+viru 63ntal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot fr(p1y:n96awgv5z x u0fv/kmbn eely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontuzf vw v0(xa6y9 pkn:bn/m 51gally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and we wk2(gl8 y(7wbl9n ktsoant to exert a horizontal force F at its axle so that it will climb a step akn87sw l g(ybt2(lok9 gainst which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed f9of8rcom :(mgumyr 39pgd2 8v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal go d9c2rogf:f9m( 8ypm3 m8u rforce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 rooa9qi 2 d9**srrarc.9id q vq)ck into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle )9 q9.*i*coadsrqvi a9rdqr2above his 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 2jj)l*tq d)f)p5 los jarms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, osf ) *tjl p5j)d2j)lqand with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, ofmlmvo 2uq-0lr+ 9+cb;1 d vluv mass 09-+ou r dlv2uv+q ;1lmblvcm$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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. 8–58q, 3uue1r*h a 9cblg1ag2x*arun,ko+ . What is the minimum vorn9 gk q3 ub,r+ agua,2*1l*xech1 uaalue of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, by udgs z-e:i5z)p;o;fut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 re b2 92llrkkp*jvolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. *lr9pkb j22kl (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