Angular displacement is usually exp(c h2t a;mj6)xlxrs: aress in units of

  Angular velocity is exsim uc 6wpnn; 6z*s1 89wk;ji 3kcld4o rdde67pressed in units of

  Angular acceleration is expressed in ur2(d4i7 gwmfnmqge1y9 3rd4xq:zg; + bi8owznits of

  A boy and a girl are riding on as(3 g 1pyax3o ;1wtfzb merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angulax3b3 ;1 wapofsy1gtz(r displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constant r m i0:von-rp,date. The boy is near the outer edge, and the girl is comrn-p d0v:i, loser to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constant xw2h,fuxwse*( s vn 1;rate. The boy is near the outer edge, and the girl is closer to the center. Whhun;*wf(s2 xxv,wes1 o has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a c2zoxx n(i1) zgonstant rate. The boy is near the outer edg(g)iz2x xz1n oe, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round whi;yjhe/ 8r(urg8 si:f sch is turning at a constant rate. The boy is near the outer edgj iu ssg(:ef8rh8; ry/e, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following isquub -uta f.rma-)06d an accurate statem u6rb0 d-qmu .t-)auafent?

  Rolling without slipjqbguz o ,ea9 k2sx (9*vc)geat4go77ping depends on

  Two equal forces are applied to a doortj(,fc bm50*pyo )wwb. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greatetpj cob* ,(fw m)wb0y5r torque?

  Two equal forces are applied to a door at the doorknob. The first force is appl mynncu c7+ k:) kaq6pogf:(b8)1rfdmied perpendicular to the door; the second force is applied a)f1 cu(ncn+k:f)aypd om7kbgmq6 r8 :t 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a door f;of5 rc -en;v.ykhy1knob, perpendicular to the door. The first force is twice as large as the second force. Tcnoy-f;efkvy 1r. 5h; he ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to ce5k5f0t nzm52/ y)sv f*kqf amhanges in rotationf5z*5y n)tmvs m20ekq kaff5 /?

  Consider two uniform solid spheres whcnxby 7c:, 7 rrdh2mk5ere both have the same diameter, but one has twice the mass hrr,d by7:2mn75 kccx of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twiclz (u oras93k/e the radius of the other. The ratio of the larger sphe/uk9lo rz3 (asre's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the di(uzgu +0 h1zscefs4u1 ameter of the other. The ratio of the larger moment of inere+ fg04ch(1suszz u1utia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2) p:y+op jkvk9wjg - cx(jzv.x0h3y9n M and 3R, what happens to the sphere's moment9y(w.0okj)jhx9nc j-x 3p +k gyz: vvp of inertia about a central axis?

  If a constant net torqueds, id g m0obghhw: 17:o7c7nj is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axia d)) ofmp iag3s/n2x(s is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel,2a ea:z jl7 jxljp5mgg,( a;s of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic eneg7s le:,pza; g ax,jjam 2lj(5rgy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slippinqgyj94o;q v 1;kzmb)j: jg5qdg down an inclined plane starting from rest. The linear velocity of the sphere at the bottom ofd j qjq: yq)5;mkgjb o4vzg;19 the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipp lcw5,g8(v lkzing down an inclined plane starting from rest. The angular velocity of the sphere at the bottom o,lgwv5 k8l(cz f the incline depends on

  "The total angular momenx81rh umv ;a15j0ll vytum of a system of particles changes when a net external force acts on the system." T8 0l1 vaymvh jl51u;xrhis statement is

  In what circumstances can the angvzxyf tbqvf,4:u95is3 g/.t nular velocity of system of particles change without any chan:t54vf i/xng .tzqyvfu 9b, 3sge in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction*pki rod5b)oo2/pd0 h7cxko :u0uwg: which may be present. What happens over time to the Earth's angular momentum about the Sunrcdxk*7 kohu:)do50iub/w2 p g:0poo?

  The Earth moves about the Sun in an elliptical orbit. As the Ea3l)jn dvh/c2u rth moves close to the Sun, then which of the following best describes the orbiting speed of th/ hnld)cj3u 2ve Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by 0 byzhf poql5)7wc*bxb6l( 4dpulling in his outstretched arms close to his body. What happens to his angular momentumzbc xh l(qb7b5y6 flod)4 w0p* about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outs lm1 rup4)yq1jmy+tf:tretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotat u)11tpm4yfjyl: q +mrion?

  An ice skater performs a pirouette (a fast spin) by pulliba+ 8tapm. a.(vcysr)ng in his outstretched arms close to his body. Whaa y)v +ta(.bs.armpc8 t happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentum.56ilwal-ecfpb. s i8 ,

  What arc length does the gd30y arc0ou6Earth travel in a three month period in its nearly circular orbit about the Sun ogau06rd cy30with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 s mt8 i3p:3+ukr r:gxxm. What distance does the tip of the second hangu33xm p i :t+:rrkxs8d sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minutesl u:xz o;e(of54g gxykz6)kcp9r0 v8 equivalent to?

  A bicycle wheel rotates uniformly througf7kq:, uq- a0m7x pvvnh 2.0 revolutions in 4.0 s. What is the frq:qvx v,7nu afp -mk70equency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.4f .kl0(9eu )ydkm89a7 y k6mw.wh/b yxmr lr6x0 kHz. The period o)bywkl/87k099rmu fr(x.6hlm ykw mxad e.6yf its rotation is

  A phonograph record rotpj hn y/les iim irlmw9:*;t12ud(m//ates at 45 rpm. Through what angle does it turn in 0.20 /9ite/rm*mj p yi u1 d/2h;lm:nw(ilss?

  A wheel of diameter 26 cm turns at 1500 rpm. How far wee*s)o 0dmh4 qill a point on the outer rim movd0*4)osqmhe e e in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What ie11+ 69mw1l *xr jhdudop-uqms the average angular speed of me6 1-o w1urp xdq9u+*1lmhjd the wheel?

  A bicycle wheel rotates shoreghhluj,,+g : - 8wi3h1runiformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m3 srh+8igj e,o-,glw rh1hh:u from the center of the wheel?

  A cable car at a ski reso d96xb bbhvv) gi0yt23rt carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with di23bg90 hvytidb6b)vxameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotati b/b 5/ pru5bwhi16dihng with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's rr db h655iub wih/1pb/im?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lengt r3hc5hv3tn+b h. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cordb3+htcr5 hn3 v?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0w vrp/pn*k :b, rad/s. What is the centripetal acceleration vk , nrw/b:*ppof a point on the wheel's rim?

  What is the centripetal v9( sfxqb ,p:wazb8y/2 irdt)acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bp8q (:)9z b,t a/s x2fwdbyirvike is moving 8.00 m/s?

  How many revolutions per minute (hfz4xv 6rml +xzt*6 j(rpm) must a circular, rotating space station (r = zrxf*46(ljhzm6 vtx+ 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20zz.0 n hh wbyaqfy(m)h-dq(ib5a61x 3 m/s. The maximum 6fw0q(nbd )xq1hh5( .i3 zz- bahyy macentripetal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radiq nt k/gbgr s6l/8ou*hl 5yisg6dk /76us 50 m with a speed of 20 m/s. The ma/gb678/o nu 6*igq5kt dksr6/lylg h sximum centripetal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.74p(k5cd.pnn (mkcq t-)5ez(lzuzi 8 m 50-m string, is whirled around in a smooth level table. If the maximum tension that the strmnu8(zke5(d p)5 clti kzc4nmpq.z- ( ing can withstand is 250 N, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rjs q+za o5t43 .xhl i+qo.0rp2(k pe+pihc p-wolls without slipping 10 m down a lane at 4.3 qta + (ozqlr.ko 2phiw xe+c53pi4+0 .hj -sppm/s.
(a) Calculate the angular displacement of the bowling ball.   rad ( fill in numbers only)
(b) Calculate the angular velocity of the bowling ball   rad/s ( fill in numbers only)
(c) Calculate the radial acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)
(d) Calculate the tangential acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)

  A wheel accelerates with a constan3z b7uf)e g9nn p;aln*lqo9jt h5j-u0t angular acceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angle the wheel rotates through in 2.0 s?

  A wheel accelerates with a constant angular accelerab0xo1 1png-fxtion of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angular velocity at t = 2.0 s?

  How many radians does a 0.3007e vz4xbl2crw *fz uj1h2 4b/y-m radius automobile tire rotate after starting from rest and acceleratinfc*lzw/ yxz21bh7 4ebv j24rug at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleratiq)fyho(95oq x on of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a cox, *v bpjfn8ca.ht 6faiz:y 48nstant angular acceleration of 86jnpx8*i ffybaz4at. ,vhc:$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular sy:8j (wjmo)p pm +q/jspeed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration o+8w:)yqj s/m p(mp jjof the wheel?

  A wheel of diameter of1 sqvx ;2uzvf1 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel ru;sz12 x1vqfvotates in coming to rest?

  A wheel of diameter of 68, xatv71g 62b.ua ezfj.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular agxj17, tbfa.zu2 a6ve cceleration?

  A wheel of diameter of 68.0 cm sn4m7 qm2k./bf0 j3i* aiybu rslows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to com.f 3mibk q /mr*ajb un247y0ise to the stop?

  A centrifuge in a medickgdr2oxd 3l9-. xyg 4bal laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accelerationkrlybo2gdxx. 93 4dg- before coming to rest.
(a) Determine the initial angular speed of the centrifuge.    $rad/s$
(b) Determine the angle (in radians) through which the centrifuge rotates before coming to rest.    $rad$
(c) Calculate the constant angular acceleration of the centrifuge.    $rad/s^2$
(d) Calculate the time necessary for the centrifuge to come to rest.    $s$

  The bolts on a car wheel reqz0zle0 gl b 4h+vfmw3*uire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requi0 hz+fl lwm3v*gze04bred when the force is perpendicular to the wrench?

  The bolts on a car wheel require tigm j7y 9xbb npfq2du4o1a3cxg7(d8/u vhtening to a torque of 90 Nm. If a 30 cm long wrenc p39 gdd/y7u( jc2 ufxvamo714qxbn8bh is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i5qfnk/ycj sjh -,atvz1qh 24:nertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is xzu.ipz9u-2scm7 v+f modeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is7+v z2isz.u mf-9cpxu the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought th ejd/qi:et o v3/ q(h:gh+7umue center O. A rg hqeomq d :ihu3t7/uj( +:v/eope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a pj6ke, .pr9m ns(8cyv frictionless axis thought the center O. A rope wrapped around the outer radius y6 sr8ppe(vc jkn, .m9$R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held inx6 -ny8 +6lc5vvlx9vztxb5 pjx m:x5 5 ;inhln the horizontal position, and then released as the free end is allowed to fall. What lylt58hl xvic:nx9xzvjx ;pv mx+n-55b 656nis the angular acceleration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. -s)1t x-iym7wom(fu3oz xd 9a Neglect the maso -xs31 i-ydfoa9( ) zuwm7tmxs of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pu iz+l:ibg+css(roy5 p(qf7 ) z4blaz8lley of mass 7.07 kg and radiu5(i+cs4goiqla 7:+z lr)fby8 s bz(pzs 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless diskfwyim 9/jixe/9ia.2k pulley of mass 9 ixf ija/9my/ek2.wi 7.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to u;6 +9(hpl val cfc8j 6w(xoqnstore $1.00 \times 10^{6} \; J$ of energy when rotating at 400 rad/s, what is the moment of inertial of the wheel in $kgm^{2}$?

  A wheel of moment of inertia ofu4ascd/x- s/h4 kv+eb4vq.xd $5.00 \; kgm^{2}$ starts from rest and accelerates under a constant torque of 3.00 Nm for 8.00 s. What is the wheel's rotational kinetic energy at the end of 8.00 s?

  A solid sphere of mass 1.0 kg and radius 0.010 m starts+c.l2sz/iovh l duj. ,w5qs/ y..lxvuc/;dji from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reac;iq +zvhld u.5l..lyd/i2j.w //o c svcs,xujhes the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed ojh9 oy 9m)l3u/t ab( .bfjijw8f 10 m/s. How high up ana/joi wtlb9(m)3.9 jh8bjuf y inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 k0c pyh3vph5y5g is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of h 0 53yhvpy5cp3.0 m?

A solid sphere of mass 1.r2 /q1a: bltfu5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sp/2fq ura1 btl:here is given by $I = (2/5)MR^2$.
(a) Calculate the linear speed of the sphere when it reaches the bottom of the incline.
(b) Determine the angular speed of the sphere at the bottom of the incline.
(c) Does the linear speed depend on the radius or mass of the sphere? Does the angular speed depend on the radius or mass of the sphere?

  An object's angular momentum changbs7l;8:u ukyn es by $20 \; kgm^{2}/s$ in 4.0 s. What magnitude average torque acted on this object?

  A proton of mass $1.67 \times 10^{-27} \; kg$ rotates with an angular speed of 2 x 106 rad/s in a circle of radius 0.80 m in a cyclotron. What is the orbital angular momentum of the proton?

  An ice skater has a moment oe un8yj7x yu-r490saff inertia of $5.0 \; kgm^{2}$ when her arms are outstretched. At this time she is spinning at 3.0 revolutions per second (rps). If she pulls in her arms and decreases her moment of inertia to $2.0 \; kgm^{2}$, how fast will she be spinning?

  A figure skater rotating at 5./lz1ufg nvn 0-c4q6m72df tkg 00 rad/s with arms extended has a moment of inertikmg/0tn2v u7 l4 ff6z1qnd-g ca of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?