A bicycle odometer (which measures distance traveledtbk/25ajv5dw4s vso7(y n*yww ur*. ,8sznw h ) is attached near the wheel hub and is denvzwbu 5,5swv wh 8*s/.2an*kd4s tyo yr7w(jsigned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does ggv2 3 a1 ,iqed)i6fjfa 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 the magnitude of either component of lin, )dv3jfq egif6i2 a1gear acceleration change?

Could a nonrigid body be described sl,+je0 z3kw kby a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a largl(n5ktp3ajg7-lkpre h + rv1 6er 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 behisda23ov5 gi nzo1ft6 k.+s+vrnd your head than when your arms+6 31.r f s+dio n2ozgvkavt5s are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven spr6)e 8qxbbq(r3pkt5vy bi+4s l7nj ,szockets 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 hardebei,4+r (t )qv5bbp zsn6jy3 87 sxklqr to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on bz8vpmgu) n73bt q2qv;eing able to run fast have slender lower legs with flesh and muscle concentrated high, cqpz7 q)2;nt um8g3vvblose 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.gg1 63sh7for7j.etap dru38zvic +; a 8–35) carry a long, narrow beam?

If the net force on a system3: 7 skjcs6sil is zero, is the net torque also zero? If the net torque on a system is zero, is thkcs3j l6 i7ss:e net force zero?

Two inclines have the same height but make different angles with( jaa;zz*wnj: jn5/mr the horizontal. The same steel ball is rolled down each incline. On which incline will thmj /5z(n jrjzw:*na;ae speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously e: t zgsu5;4ddstart rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bo:z5 egd4t ud;sttom?

A sphere and a cylinder have the same radius and the same mass. They start fr)yf7 1 pkwbuw7om rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater tota)up17kw f 7wybl kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are consevzwwe :8-7ipg aa+ 7w6uci:ourved. Yet most moving or rotating objects e i 7apwz:aco+6wg wuv-i7:u8 eventually slow down and stop. Explain.

If there were a great migrati m933t. xrl12(txuwuaoxze 7u)gp4ds on of people toward the Earth’s equator, how would tlxdt4x3u)r .w7s2 e3p zu(u9gmo1 xtahis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial/p yi6:c bayb4-bgg1z rotation when she leaves th:4-6yca bybp gbg1 z/ie board?

The moment of inertia of a rotating solid disk about an axis through its center rg2 5:v-jiwleof mass is5- gi:jwre l2v $\frac{1}{2}WR^2$ (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 rotatinguuwn1 r ng;g8l;:tpj0 stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will youn01n;t ;wu8rj gpug:l r angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and ha*p k55gwzcq2 cve the same mass. However, one is hollow and the other is solid. Describe an experimen wcq52g*z p5ckt to determine which is which.

The angular velocity of a w 21/tp xws 49,ve*mnq*wbpuz ze8 qol/heel rotating on a horizontal axle points west. In what direction is the linear velocity of uz/ 42vwq 8 *qb1* ltmespewnz,/pxo 9a 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 r2.vodyt2 ml /turntable. What happens if you walk toward the centery2 m/2or .vtld?

A shortstop may leap into the air to catch a ball and throw it quickly. As hnla30ampg r) :e throws the ball, the upper part of his body rotates. If you look quickly you will notr:)nlgm0a pa 3ice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a hel 7isf9lb5o 120/hoey0dp wifkjty8 1xicopter must have more than one rotor (or propeller). Discuss one or more ways the yjy0d2bihpti s7 5xfl9fk0/e1 owo81 second propeller can operate to keep the helicopter stable.

  Express the following ang 5pgu z -(,8r1 lttxcy:mqmbx-i4 2hdmles 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 amaziwo; 8apmi )8da.6ucjq*m+etmng coincidence. Calculate, using the information inside the Front Cover, the angula+wjom* d m)8;aapm8tiqe c.u6r 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, 380,000 km from Earth. The beam diverges vu9bx tnlb4 wd,;d b4/at an angle , bu/l9wnt; bvx4d4db$\theta$ (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 bpn: uc kz,q. 8pe;6)rrvpyql6 tyq;, is turned off during operation, the b , 6pvyeup6t ,r:rbl;qz8p;cnyqq. )klades 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 a level floor 3.59(gt sarx 14(me kpfqmnuaft(6, .d1m m to another child. If the ball makes 15.0 revolutions, what is its diamdm9upf.m 1q xst4rtk,6me((gn1 ( aaf eter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many rev/cm- i 6 /mh/d6kas;sh c8q tb91tpmpnolutions do the wheels make? a h /cspsh/qp- /;9m8 6ti1dmkb mnct6   $rev$

  (a) A grinding wheel 0.35 m in diameco8yjxg e8/1 y nitg::ter rotates at 2500 rpm. Calculate its angular velocitgg/ye8i 1n:tyo8x: j cy in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8a9)vg8zz k9ca–38). (a) What is the linear speed of a child sec99 8a )zavgzkated 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 around18. u)-cx: p;:rj2 vqef zqhrbil*94 fwoasfz the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spv(h)cypi(o+ gg)n(g c eed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotat1dyhj hc(;2ppba 7qj: e if a particle 7.0 cm from the axis of rotat7( jj;yb pphhaq2dc: 1ion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to.m a,tpr rajmq4w-ao /-l5z* x 280 rpm inxmazpa45rr*qwm .l/ot-a , -j 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*5b +cg+leg3ke9dae q $R_1$ 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 the4xaa8 dgsd,m0 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 cylinder with a diameter of 8.5 m,0mxd8 dsa ga4. 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. Throt gdn( ic;.0ysugh how many revolucdg ( s0nty.i;tions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm i9o *2s4kot5c -pxrklan 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 iw29,v3msf dqthe stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min tfs,m9d3w 2qvio 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 fropwd)o*5 hrgjw0q 0,hc gf .8tim 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have travhtgw.pq0ir*0w) d 5 c,ojfh8g eled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revz syzb 1a yvki)4309kqf)z ik,iv9 f0solutions before it comes kk9)109zzzyfav03kfi,s ) yivsqi 4b 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 j( lvq70tjel:the car reduces its speed uniformly from 95km/h0 7tq:ljjl(ev to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolu0d 1a7+qt)gr:v aesjrtions as the car reduces its speed uniformly from 95km/h to 45km/ )tar1er7s+dgq:0 vjah 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 hew zcas(uo2ok7) 5w6a4xb05;vq n jq rdr weight on each pedal when climbing a hill. The pedalj u (w k5wb; 5o6 z2adrx)qnv7s4qco0as 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 of 55 N on the end of a door 74 cm wide. What is the n1zfrq9( ;4p gpemim3magnitude o4(n93 1rgmpp;fe z miqf the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle ofl.xxer6vevj;; q)zn , the wheel shown in Fig. 8–39. Assume that,rqvv)e n6j.xx ;;lze a 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 rod whra ju:xe8llk+0 :j1kpej, kz +bkq+,rich pivots as shown in Fig. 8–40. Initially the rod is held in thejr:k qk 0k8:lb,+zpx u+je1ljek,a+r horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torquyrum xd a)r73/e of 38 m)/3dry7ur ax $m \cdot N$ 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 o0 bo*/ ,kye yp8*bawngf a 10.8-kg sphere of radius 0.648 m when the axis of rotation iy8 pgnba, *0/kyo*bews through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The ri tjr4+epzh/ekfd44b72kq0 yz m and tire have a combined mass of 1.25 kg. The mass of the hub can be ignoredzjr4bed40ehkz4p fqy+kt / 72 (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizvl 6uiqy4: f/y6a4zffontal ciqi /zu64fl yyf:a6vf4 rcle 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 potter’s wheel rotating at constant anm tmek xy)+ 24zt2--usswwm6 kgular speed (Fig. 8–42). The friction force between her hands and the cl- e+syz)tx-ws2 2w kum4mm6tk ay 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 i6)8ssbh ;mv5gg :ia)ic ueyi-nertia of the array of point objects shown in Fig. 8–43vyum)e)bisi:6 hc i5 s8- agg; about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whos7lw t7a-fd b.k*.opu ue total 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 correct rate, h6 b t:-5e,520ksfpshulr a e5jy,mcqengineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket ifu5m ,hc:sa p65l0 ,yskb- fqe h2e5jtr the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0ic*q() ,goj bnw:q,e 6p4n ood.580 kg. Caln:) op4*,n qj dw6 eboicoq(g,culate
(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 from n9m(8g igc 6 vgwxr60vrest 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 merw05m3 pbd 714rq*a gr :vzkdce9fi1lnry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite eachqlfng90v1r d weckz1 a3bm*pr i7d:45 other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shutscx8 nqe; y8xk jmt+cwf618*t off and is eventually brought uniformly to rest by a frictional torque of 1. x*ke6stwqnj 8x8;f1c8 t cm+y2 $m \cdot N$ 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 ballq +oc4.v9 *;hiw4uybw jrv7y(h tcc t; 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-kgzovj4 a7 p.x:w ball is thrown solely by the action of the forearm, which rotate vjo4xp.a:z 7ws about the 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 blade8 +ta+g f- lsbwhn5w/o can be considered a long thin rod, as shown in Fig. 8–46.nw5sol t-f /+wga8h b+
(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 masses, qy tnwe/0pn-nzh qho3,k) ;2z$m_1$ 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 w:n)o((l/ 0jw8 heqp kh wuu54txqg0ffrom rest within four full turns (revolutions) and releases it at lu)8:f ge4 wx nj5q/o0hu(0hq k w(wtpa 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 o;da +abe7mp /pf 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 s4 a-qsnai;g7a 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 c:s7ichvg((s bz a 7nq6 .;nhmt8j9vtlm rolls without slipping down a lane at.(v77( mtaig bl9 jzst8;q s6n:chnvh 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy o/phpfc9x q;z72j zel1ez3ww0 f the Earth with respect to the Sun as the sum of two ter ez/e7pjxf30c2q phw91 l;wzzms,
(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,im+ss3;h -g;unbt yj radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylug st-,y+ si;bh;njm3inder.    J

  A sphere of radius 20.0 cm and mass 1.80 kgm*48-keor nmg d xg(n4 starts from rest and rolls without slipping down a 30.8k-e(dnmo 4rgmg*xn40 $^{\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 startdzl l5lm)+ec 2s to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the groun m)c ed+ll2zl5d? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thim9ohw4cfijj b8 f)cf.7 4dau-1mdh q ,((nbkbn string in a circle of radius 1.10 m at an an4cbbkj-ido9 mf7 d nf(( 4,f8umhjcb) .wh1 qagular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grind,un (ujg,dulkm1w6n y*- zn;aing wheel of radius 18 cm when rotating at 1500 rpk*; ym6juuz,wa, - nu(ngnd l1m?    $kg \cdot m^2$
(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 platfv6) ,3 qh*je1a 5ed j1yrbdi b9plw(sporm that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the jr jq*96a3y15d1ev p)bsb lip e, d(hwspeed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown ifydwemg+6 69ld2dsh9 n Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing fromgs dml69ehf 9y w2dd+6 the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation 6psmfe1;80je jo 7+zh/ fc8h al4cccarate from an initial rate of 1.0 rev every 2.0 s to ac6oc8hf ca0+jm z/;7lc 4fehe8a1psj 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 its cente lq6mttx21 6y1tisios/h;db mu..t8wr at a frequency of 1.5rev/s The wheel can be considered a uniform diytsi8 bi 6mh.;s t 62mtx.tq/w11 lduosk 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 pr/u:s aezs,3u sa1 k3skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momev4tv0//j mjy ha14t axntum 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 inertiwbgo;g77 jj0/e cdz :ca I is dropped onto an identical disk rotatiejg czo;7bw7j0 d:cg/ng at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 ikwc:fkzu sp2b.+k3 7$rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round pl njmjtc8;f8(vatform of radius 3.0 m and moment of in tj(n;fc88mj vertia 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 an87/v .q6lgs)i v)pp cvro3 gwp angular velocity of 0.8) vpgv8q6 icp ropvw/37)l.sg $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about hal nxm .kd4y(jckc/i,w/pm1v +hx 19hsg f 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?hid/ksnyc ,g1+jm(k.x1v mhc9 4/p wx(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 ofqce,+p6afa1 d 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 z, lz0rfte/ hyd-(i3a6 lp4rdi lo( o-$ 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 reod +( sb 9l8moehgjck2*z4pu*x1b p3tst, that can rotate freely without fris cb+8pbz m4k2o* uj3ogxh9te ld(1*pction. The moment 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 6.5-m diameter merry-go-(xy8;2cn u2 /2h)caquv 9:hxyo cosfsround turntable that is mounted on fricuy2x; hc)/(8avn2qsu : 9oys 2 hfoxcctionless 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 the ground with the6(et9 (z;rm*gxesaiyna8 t d. end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person wii9g etaz8 armyx.(*end6t (s;thout 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 t nxw3drhb0n36stdn 4: we h/i,hat the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum e3h:3swtrx6 dw/n n4n h0,bid (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate qpm80h+fdxa 5 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.y2rs of;8br ej.vnw( vhufqw. o4*,0a20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the tor.joo,f 8 ;y(fvhurrws 04nwb*eq av2.que delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks,mg/ v vg/xe-t.nyf 3r pszt 66th8t/v; each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches /6m xtr/- ysn v3t/hveg8gvf.6t;t zpthe 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*aeqd4x3x.td sk+ax ; ($\omega_R$) 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 sr)5kxf mk a(*mize of our Sun, 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 fxkm (m5r k*)aprocess, 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-po 2m*qx1kto3 fq xhl yhew(956+ez d8pgllution automobile is for it 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 flywh83 yk2hh6xt9 m (f*ed 1wepl +qgqxo5zeel “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 illustrate l6bqbn,+c-y hs 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) is rolling on a horizontal s/ cxn ezommkl; j *c98:srv7(nurface 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 freewcm 42+6vcm dv,e1gzf4ag e9o ly (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) 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 masc o+g,g61eamz49d vefcm4 w2vs of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing v)) oqbitb ( ;ubi39ryxertically 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 h3q)yb)x9b trui(o ;ibas height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat roawb8 )korpsf9 -e i8n6.qy iyzd;)w(dkd is making a turn with a radius The forces acting on the cyclist and cycle are the normal forfi y rzqn-)k9e(8 .8yi pd)do6bwws;kce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 sli:t05olatvdg+g/ yf ;h ng of length 1.5 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. What is the torque required to achieve this feat, and where does o v :f dlt;gghy5a+/t0the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her ao-3ryb+p3:k4bjx33enu ad , sm ax;eorms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstret3e4x+ ,me;a3bn3yskpouxar3 b:o- jd ched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindricalle3sx,2fydki v.o* - s*zh k(l plates, of ma khxkoi.f-z*e3v2,lysls* d( 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 rouz hyo,b6xsqg.7- r f)jned,8pq qi9 eab /;i9vgh track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the p o,bn8/fahz6dx7iiyeb;g.,99qqs -)q jr v ehighest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do935w*oi qmp2dun 03y:y0xxq:p u prw y not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unas /pq72nhi/ yiformly from 90km/hy/ hinp sqa27/ to 60km/h The 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