A bicycle odometer (which measures distancej4 p 7nnn /qke9)f :vtj9m8lahmy h4p- traveled) is attached near the wheel hub and is des 7qf9hvjlea/) pyknjnm48 -m9pnt 4h:igned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at conss3bh2 i v3wpv;k q:5,lm/wx 9q ouxo:2ne kut)tant 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 accelerati32 uxq eto hns: 2kp:kl)uv9q b,ixo /w3;wvm5on? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular vgu,gi-pq i(b 3elocity $\omega$ Explain.

Can a small force ever exert a greater torque than a largk+c 50m c ngj7fe)ke:zer 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 youj tdghh 5*7)wer hands behind your head than when your arms are stretched out in front of you? A diagret hw7gh* j5)dam may help you to answer this.

A 21-speed bicycle has seven spgbu2 wq7hp14a rockets at the rear 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 front sprocket?hba427 qg1puw Why?

Mammals that depend on being able to run fast have slemwjlp0 g3 07zah2,m z; 2pwzvqnder lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this z3ml2ajpmhwgp z; 7z00v 2,qwdistribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carty1d4q jk60gtv7 fp+iry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net -bim.c.g i9ip torque on a system is zero, is the net force zi gmp.9i.i -cbero?

Two inclines have the same height but make differentr;-u;n w nn,wc 5mu w0n+knwq7 2.pmas angles with the horizontal. The same steel ball is rolled down each incli nk2p 0 a;mw7n5w-usq ,wmcnr.wu+;n nne. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an+d )ntwl rhw.7 incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has .hl rdt)w nw7+the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They sta3 (ksdqu6mz0/uz6iy ike k/j3v9v2 gqrt from rest at thev0vkk/3 ze jimukgzy6 s d29/ i(uq36q top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or ro+mwc, w o-u9:l huy.zes 92xopkh- f8ztating objects eventu ypu9- s cwz mfxzw,l.k8+:oeh9-o2hually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, *6 gx7thm:9 2oiyu5 (ijsy ibfhuwe)*how would thism(oigsxi:5)e 9thuwf jh 6y27u**iby affect the length of the day?

Can the diver of Fig. 8–27vn/zfb;f(s6gbs ,os9 do a somersault without having any initial rotation when she leaves the bb;zn(vs, os 6g7fsf/board?

The moment of inertia of a rotating solid disk about an axis through ito- twvgl2khh; m4e1e0 kz/9nfs center of mass ith9 nh2;l k-eo0vw1m/kfe gz4s $\frac{1}{2}WR^2$ (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 rotaty0ngqbf+se 62fce:ypk6)gu*6 ( h g tging stool holding a 2-kg mass in each outstretched hand. If you sudde cn2*g6q6eyhf( gpuy0t +:bkg )esg6fnly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollq aauvbmh1c d.b3m+if -+5(lx ow and the other is solid. Describe-q+um+(f c1xi m. v5labbdah 3 an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle pointhdye+k* - rfpa88 *dags west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed inca+e gk**fhd8d r-ypa8reasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntabf0fpfgcipme)- 1f3e x rifk *c6g;1a7le. What happens if you walk toward thefx1*-ag ip3r67k fpmcfgci;)fef0 1e center?

A shortstop may leap into the +owqw5p f(oau 6k3o5eair to catch a ball and throw it quickly. As he throws the ball, theo(e5woa+p 5 owf q3ku6 upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular mo f 4uzy sr 7i4.iq*uhjlog33,nmentum, discuss why a helicopter must have more than one rotor (ohul,4o*33ry .s jnzgufi7 iq4r propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a45t d.jim l+mrnc g ydq/g)k*3) 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. Calculass 3fol;3 vq:cte, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.;3 qs:vf3cols
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Ev;ggk ul/ zstd64;nw(b0 y8gvarth. The beam diverges at an a (vwvt 4g6z0gdu /;lkbs g;y8nngle $\theta$ (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 the motor zy8ncgs*z p:.96q5wkpcbl3d is turned off during op93 8 ny6wq pdz.s*5klzcg:pbceration, the blades slow 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 a14gw3ubai i xl .t0n0u level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its .u0gwu x41ialnbi 0t3diameter?    m

  A bicycle with tires 6llhv4 s)r -z2y8 cm in diameter travels 8.0 km. How many revolutions do the wheels make s-)ry2zv4 lhl?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculdj,cml6 j cs+9ate its angular velocs+j9,c6 dclm jity 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 revolutiv bhvet 3/l) s.vxc65kon in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seals6)3e5v k ct/h vbvx.ted 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 .3 m2( ijb(u7/tcyz- x jhcizd: xdu5fthe Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point ;t /.oki 3xsc ;rsih)l
(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 t+kbe ,z/ v3 p4dntzre,he axis of rotez,,bd3e nkp 4rzv /+tation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acceleratemup gs eq6q5:;s uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determs eg6q:q5ump;ine
(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 radiu3nm*jnb xyjnb49nn d+ cf c830s $R_1$ 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 put themselveeoz, - (.(a vihvg(efls into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of f(( ee-g(vl zia,oh .v8.5 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 res*kvjwyw-v 9r rvg;x,-s(uv (st to 15,000 rpm in 220 s. Through how many revolutions did it turn in w( x;v -v 9 swkrr*u(v,gyv-sjthis time?    $rev$

  An automobile engine slows down from z g8s eg)g ,6/4upgihw;(4rk) bdo ceo4500 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 highsqlaalr.j (pj/j -.jb )peed jets in a whirling “human centrifuge,” which takes 1.0 min to turn througj(br a ql)-l.j.j p/jah 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 diametex ph gtim,or3eme02k0 j84 rv9heq y032 .akncr accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the whe89 hx omk3 3 ceirr4na q e0h2,tp2m.gy00kevjel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 rev40nyw hw2nk)9mzc0 ttiox 5p/olutions before it comezo5twwi4p0 n90)n mcy2 k/xth s to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car re+pm:egf1f ) 7yn2y lmdduces its speed uniformly from 95km/h to 45km/h The tires ha) 1+fd l:m 2ne7mfpgyyve 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.zw;xml9rh8 y the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0h8lw.9 x; ryzm.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbing a ha,w jpa h/0g:m2m)cnr ill. The pedals rotate in a circle of radius camp 2wha:gjm,)0r/ n17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. kd6 6lcltyj-vf/5: jfvif7 e/What is the magnitude of the torque if the forcev:e7k lc/v 6tj-li / 65dfyjff 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 axk4cb bni99k2 xbz1oa v 9htj f8x6c/*gle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.4 k2x9/x9jkzabg4ibh16f 8 otnb*v 9cc $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mas6rj 66h jntt0zt 8i)lls 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 thet0 66 jjl8)nit6lr hzt magnitude and direction of the net torque on this system.

  The bolts on the cylinderd85gxev xq*di( 4hgb1 head of an engine require tightening to a torque of 38 8x1 gdb5g4* v(x eihqd$m \cdot N$ 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 radiusgc 9w e5arfa szub8o2 0/bci*qur,o6. 0.648 m when the axis of rotation is througawu0uc6.fr,e92sba5/cq* bzigro8 o h its center.    $kg \cdot m^2$

  Calculate the moment of inertiavayd 8x8g-2wck6 mo *c of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg yx2k86w8*-g cdo cvam. 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 r;b, w b)t,iyzpj9s4ml otated in a horizontal circle of radius 1.2 pw, il)zbtm,b4j9;s ym. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating zkop ne; *exp 0a9(e-wat constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N tot p*0 kwxe;en-9zop(ea al.
(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 inertiaku pd0lhwvge55 (-h6r of the array of point objects shown in Fig. 8–43 about5vhp6dw hk-l(0e5urg
(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 toa x,(zy x*6lls0mqm;(lgx h 9ltal 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 cy9uz4*g,ww (hd ea0hrdlindrical satellite spinning at the correct rate, engineers fire four tangential r94 h*waw 0zd(uge,d rhockets 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 satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a masqu i aa;,*w4hvs of 0.580 kg. Calculataaui w;q,4hv* e
(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, accelerating it frojt bb.oam2(9-ro9ff :y smee3m rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven mey+qd8konz f kk2mt-/8rry-go-round and is able to accelerate it from rest to a fr /okk 8z- nkf+2dt8mqyequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300iaki- 5t2tq7 s:llp/s bb0hg, rpm is shut off and is eventually brought uniformly to bsq gls0alkt5/,b p-i 7h:i2t rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3*6(uziop/oe 2:t fdl :emce7 b.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 tpmplwn/ :lakr/:j+; 8evk8cb hrown 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 to 1r8m v/ek :bw/c l p;kl+j:8apn0 $m/s$ 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.4yq9to9zzvf jd:n) n thin rod, as shown in Fig. 8–46 n4dotj. z)q v:f9zn9y.
(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 uxmxyo5)k 4 y5c2pcg2 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 accelerateh5kldfjrr. wu7*e*q* s the hammer from rest within four full turns (revolutions) and releases it at a speedqu fk**7 5weljdr.hr* 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 inert-yrdu tw- :g5rzt4xf 1ia 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+dy /)gcdh2agf 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 k*sh2jt0zf 7 b*q 0fhgq7pdx.zg and radius 9.0 cm rolls without slipping down a lane athhq7sg 0fzpxq2 f j*0dbt.z7* 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun asw 6 vhi)xnoa/7t;de 2w the sum of tw2 h );6dexwov 7ain/two 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 o ox4yvavnxn. wf9g0z +v5-+gt f 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution p ya5g9 fnwvg0xo t+n .x-4+vvzer 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg : ij+0gz2smz6pxd ht4 starts from rest and rolls without slippit j+2i gs4dzm6xzp0h: ng 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. Iews-.4g.+f y4 qcxh bx) gzkb9t starts to fall and its lower end does not slip. What will be the speed of thc4k ge .9-fyg+)qb4ws.bxh xz e upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on t6z8n u)yrp j:1jj*:d pvuk(tzhe end of a thin string in a circle of radius 1.10 m at:1p k) n8pz*j:tudj zr( yvuj6 an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of 3c* h+uksu nvtwd,66t a 2.8-kg uniform cylindrical grinding wheel of radius 18 dkuc+nh,t 6us*tv3w 6cm when 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 a 09ryto/yio8vt his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decrea y9 otyvroi0/8ses 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 momevf 7+k;t3udjbnt of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s whu+t 7dvb3f;kj en in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate fro(u+ of oemv;mkm1txn((ro. - rm an initial rate of 1.0 rev e;mm(tom n+(r( - ofvkxorue1. very 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through+1u3 y7qqdokd its center at a frequencdq kq3 oy7d1u+y 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 the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinnin es )b zq,d:w2cddqcd0hb8(7hg 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 Earth :4um;2,d/vzjltw hpy6sj c4z
(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 gvx90q f8or-*-:iyjrc rr d8q inertia I is dropped onto an identicr 0roq r-grxcid yj:* qfv98-8al 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 .k.cga6 m rusg*-plb: 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 jq i o.cs hsw(9*m9t8t1 s6qaostands at the center of a rotating merry-go-round platform of r*6ojchq9w 8si (ot.1a q9mst sadius 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 jq+kypp olz:, l0hg4m(vs 4- yis rotating freely with an angular velocity of 0p -0:+hs(lyzvjmk44 ,opyqlg.8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing x ,egclo): f.kv4oc*mabout 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 rate be?(round to thefvocml x*g)4 oc,:e.k 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 excess6s/ hb fga2a9 )lrwlatxu+ -a3 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 ;24 qaqampb+je: opathh*c -x95;z hh $ 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 re0..tbhl;rg; gpojdak*v ) ,phst, that can rotate freely without friction. The a lt.0;gkd)rhj.*;b,ho pgvpmoment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6km7 q(o31pi g h5k*ceu.5-m diameter merry-go-round turntable that is mountedhm3*7 ep qgik5k1uoc ( on frictionless 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 (8 *uiri67nxwt9yrqm+xawd*v i h01jon the ground with the end of the rope lying on the top edge of tqji*( 97rvw rw06hu+n dtx8xaim1i *yhe 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 that the sanyhyi4 +ob(+vlfu5j : me 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 4ljn+o i: u(hvb+fy5ycase, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from resx(q/gy 5s: ue uw7d6uqt 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 shape of a uniform cylinder of radius 0.20 m acquiea5bhq3 v+l8jres a rotational rate of from rest over a 6.0-s interval at constant angular acceleration8lh5jeqa+v 3b . Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical diupw g uu4c 0 .:b,v0jkcsaj8z(sks, each of mass 0.050 kg and diameter 0.075 c .j0: s( wcpju0,ukb8auvz4g 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 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 re5,c*fef : neifar 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 (w *,xm/l zebts 7gdv03 hc av1ac*m0dmass 8.0 times as great, were rotating at a speed of 1.0 rtxa (dh0e*vw7g sb0z/*1dlm,c m a 3vcevolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for iaj wi08 9gi6a,(5fhol)kz fs at to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a z0fa5kf lw9hsi ga i68(,aoj) 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 illustrat1ulh xme/q;:rn 9 ,clhes an $H_2O$ 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) is42 g9 9+l1lsktgq ldvy rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., wuoki7*+a */en(jvvkdhz)s7n e4oxj . e ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and t dv+v7)s jaoe*jz.n 4keoi*/7hnuxk( hen 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 flobqs y,g+yl)s 0-ojff /or, and we want to exert a horizontal force F at its axle so that it will climb a step agaiqsl fbj yf,o)+ys/- g0nst which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling wit*56r x+ig xttfh speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on thrt5*g6f+itxx e 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.ewe 8fek- 1 9(gqelbm750-kg rock into a sling of length 1.5 m and begins whirling the rock in ae8mq1 9efbe (-kweg7l nearly horizontal circle above 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 arms okmq zo o,r)0v1g1vtli0r8w)as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds fwk vtm l gv,)1qoo0r8r10ioz )or a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch anuccn/n 7w 5/ lnf0n4ossembly which consists of two cylindrical plates, ofl5nn n/04ocwn fc/u7n mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fiejb4e qa;)eweu4a3 s1 g. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest a ea1seje4;bqu3 )w4epoint of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do ;cdg:m aebk2pq);(pzr .t:(dz /iqzs not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly flifn3v 6) df)v4iu, wjrom 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each t i3l6d)uvn)v f4iw,jfire? $\approx$    $rad/s^2$(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