Angular displacement is usually eotw1+ue ).gxj xpress in units of

  Angular velocity is ex1fs jzg1 nn7xtb( 0lr2e j-(bipressed in units of

  Angular accelerationk -c ni49 renel+/:men is expressed in units of

  A boy and a girl are riding ow-y6 f 6e+v2r .m0.scpodhzvt n a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and mrt-zw vdyo +c2 spf066.evh.the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are rnxz6 p7py2c +/hsr) cmiding on a merry-go-round which is turning at a constant rate. The boy ms+ p/pchx6 )czr7yn2is near the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a mewdy9 h ty .fv*3ml0v:lrry-go-round which is turning at a constant rate. vyfvhd .*twlm:0 yl39The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry9f *,z 41: iv nfdbfh0h1ifutp-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl ,0* i:v91f4 hbp z hiftdfn1ufis closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning atwpodenz. r n; 2oaicej.2g0 *kodbe 42jf;3x/ a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the an3 ed.g*c.oej4d0z2oxeorbw2jnkf;/; i2 pgreater tangential acceleration?

  Consider a rigid body that is rotating. Which of the followingl1gp+x wrodeq*f tycz 73119 y is an accurate so*g7 t1xe 9f1d3zpy1w l+ cyrqtatement?

  Rolling without slipping depends or2;ngsyndqh-sd.6 i6mt a5 *l2x1v mnn

  Two equal forces are applied to a door. Thej)a)h+h 3 jokr first force is applied at the midpoint of the door; the second force is applied aojh) )jhrk+3at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are ap 7/ gumd:2n crg-uy-hoplied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exergu 7gom-unr2dy-:c/h ts the greater torque?

  Two forces are appligsxymxu2um0) 0;k 1lped to a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to psy0xukx0; lm2u 1g)mthe torque of the second is

  What is the quantity uz2b)uw 1h2hv a a3s- spumo+a)sed to measure an object's resistance to changes in rotation?hb)zuh+3-2su2aap s v)a wom1

  Consider two uniform solid spheres where cvl2.aui8qfps(,0 ftboth have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the c20 qv8itf,lfau( p.ssmaller moment of inertia is

  Two uniform solid spheres havengau0u3oc u l8i 3g6gq)5 jl0a the same mass, but one has twice the radius of the other. The ratio of theu un0g u5q)6jgc l a3o3igl0a8 larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one l137vejkpm s q4x :1h2cl7fbxhas twice the mass and twice the diameter of the other. The ratio of the larger moment of inb 3klse:1j pc4x2fl mq17hx v7ertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these0o0g,8+lhh*dili k/cy +sm qk are increased to 2M and 3R, what happens to the sphere's moment of inertia abouh/ *chy0s0 l,o8li++kikd gmqt a central axis?

  If a constant net torque is applied to an object, that object4h; w9,uqwakr will

  The moment of inertia kl0sk pel3m;2:fzdn.y9eh n. of a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy hl0d;.kn2 mep:9fzynl3 k s. eis

  Consider a motorcycle of mass 150 kg, one wheel xgi8j,4x67a203qpfi 6dk yeluqzr* wof 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 energy of the bike? ia3zf8uq 64q2x7kdxr, g0* l6ijpyew Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M anwxm9cgt q/+q0 d radius R rolls without slipping down an inclined plane starting fro0/m9 +gxq wqctm rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of massvns,e e 5ukw;yzzi*/ 3 M and radius R rolls without slipping down an inclined plane starting fro5i e/;,3zn kswuvey*zm rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular mome324lh(3gv + d+ue7j 4yfgby mowsc/ fpntum of a system of particles changes when a net external force acts on the system+ 4d4vc3+mhoyufp(2bf sg7ly we g j/3." This statement is

  In what circumstances can xwl9;k:x 3wcu the angular velocity of system of particles change without any chaxlwk3c 9w;x:u nge in the system's angular momentum?

  The Earth orbits the Sun in an elliptic)lywh)x u 29;zv awtk0al orbit. Ignore any friction which may kth;9y2wx)u) 0za w lvbe present. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. Aso f; 2g+u vt7;bdyg4dhkx3c8j the Earth moves close to the Sun, then which of the following best describes the oy+478jgdcotx gdbh3 vkf2u;; rbiting speed of the Earth about the Sun?

  An ice skater performs a9xo; a0 uk-0aug xkcx8 pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotatuxgo k8 x;u09 ack0-axion?

  An ice skater performs a pirouette (uq nb- +tvw;7v,iysc8 a fast spin) by pulling in his outstretched arms close to his body. What happ7;vbt,ivy-s uq wcn +8ens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outsti 9nctbm+r +xiz:8u1 r d-8jpd:eowc-retched arms close to his body. What happens to his momenc+ xt+do: wn czu8:im1-9d- bjepirr 8t of inertia about the axis of rotation?

State the law of conservation of angula0fn-cttwk: ; ek)al8 kr momentum.

  What arc length does the Earth travel in a three month period in its nearly ci ke ldlov77p70rcular orbit about the Sun with a rad7llek0 dp7o7 vius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock hac5p*xv8m/ye rs a length of 0.30 m. What distance does the tip of the second hand sweep throug5*ec rvpm 8xy/h in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minutr(iw4 wvs,p jlpb5 j)lqc5k31e equivalent to?

  A bicycle wheel rotates +fb17a au3(u rqydiey4g) fs6uniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rota yag6 4fda7s3ifuq) (ery1u+b tion?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 04t(9neil vit8 .40 kHz. The period of 4(v l n89tteiiits rotation is

  A phonograph record rotates 7esp4 r clyt:*0y. t,pu 2byecat 45 rpm. Through what angle does it turn in 0.20 7tpul*te4 yccy b2,rs:e.y p0s?

  A wheel of diameter 26 cm turns a1+rzs 9yz-zrv w q:cn:t 1500 rpm. How far will a point on the outer rimc 9y:n+vw :- zz1rzrsq move in 2.1 s?

  A bicycle wheel rotates uniformly through 2 sn 3yprzsy g(f65t rrous1wzpn 8l:s7o,)(5z.0 revolutions in 4.0 s. What is the average angular speed of t6 uzy zsgowro :tssps 7yn)8r(l5r3 n,( 51pfzhe wheel?

  A bicycle wheel rotates uniformly throug +*fmb 6grcc 3dgq2ue2h 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center oqru2m36*2+ cfcg gbedf the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8p7muxf,wez8q rhm z/8 );6zv x km. The cable which moves th6,uvm8xm)q/hez wrf; pzx8z 7 e car is driven by a pulley with diameter 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 rotating with a constant angular speed of 2.0 rad/s. 2u;)pajyu sm0 What is the linear speed of ;smauy2)ju p 0a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the mc 8oay c/17eq1-m7 8rdfzwxnvotor rotates at the rate of 20 rev/s, what is the approximate linear speed of t8ofm1x ed1 /y-r78qvwa7 c cnzhe end of the cord?

  A wheel of radius 1.0 m is rotating with a constant ufxvf1mp thcf ,v7)*w :tt1+kangular speed of 2.0 rad/s. What is the centripetal acceleration o+7ft txhtfc:wp) *,mvuf1 k1v f a point on the wheel's rim?

  What is the centripet 2,7fbf snph)j,s:vfqal acceleration of a point on the perimeter of a bicycle wheel sf,hp 7)vs2fj fn,:qbof diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating zzx98li4+8qwl k0kzlspace station (r = 1890xl8iz qk4 lz+kzwl 000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circunqs5-y, cm ;xmkjd;f5 lar curve of radius 50 m with a speed of 20 m/s. The maq f;5 ,s- kmdjcy5;xnmximum centripetal 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 radius 50 m with a speed :bwxfzq- bd: 7p+ k9uwfepg8*of 20 m/s. The maximum c87edk9 +wpu xw*q bzff:-: pbgentripetal 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 0.750-m strinx j eww7y9fvg6:: 4wwtg, is whirled around in a smooth level table. If the maximum te76tw :9y4vwwj:e xwgf nsion that the string 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 rolls without slipping 10 m 3q ipjc1l9s 4avq3:ub down a lane at 43ic aluqqp1vj3 9b4 s:.3 m/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 constant angular acceleratifr*(7 h(/hruy(mcr xoon 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 constj d; 0.qp21i ie1:zc 7cz zatbwk4;smtant angular acceleration 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 0.300-m radius automobile ti3n)my, aig4 lvre rotate after starting from rest and accelerating at a constant angular accelerat)n4lm, gi3 vayion of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at res*i )g97/im7c sk9mjeydwvpb lr -6 *kgt, and has an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s deceler/wlw+ a 9 2u,),6nxgpzwmvxj tates with a constant angular accelerationv mz)n9j xgl u,w2t+aw x/p,6w of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest g5 c.kqh,9gb xand reaches an angular speed of 6.0 rad/s while turning through 2.0 cx9. qg ,gk5hbrevolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68yhgg44sbq om (gy68)44xsbyn4 glrc-mnm,7 a.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 1s4 (bman g4y ylr 7bogcm8gq-4xgns)6m4y4 h,15 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down u(f qskuy o36qx*j ;,-wv5io ujniformly from 8.40 m/s to rest over a distance of 115 m. What is the angulary3o-,jufx 5 qos6i;vkq*uj ( w acceleration?

  A wheel of diameter of 68.0 cm slows down,t i)oc(ypgm y/mv* ykt 1*qu+2:old y uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it 2y+kmdt i/y lt1qo(*comp y y,*gu):v take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at agc( 5 ;s*6rw3hezm bzg rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constantgr5g 3 zmh6bwzs*e(c; angular acceleration 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 require tightening to a torque of 90(v/kawjmx0kvkt8akk c- ;1 f0 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to the wckk 1m-kfvk x atj;aw0 /(v8k0rench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cn q 6hzwn(pj7m:a f/q5/fbu 6usxh, v/m long wrench is used, what is the mafqn zuqbu, h7f5/h /:awv6 sm(pnx6j/ gnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner dgeyrjg2 x0n+aqf(::f tz7z-tia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: m v(mor mz357 dot9hi:f x4t8zcass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the d zxm573zfo9tct(om4ih 8 :r vmoment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about bo6 :r xanp b 7kw;nl3e0g9bd/a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular accel p6g nb7xb awkd0:onbe; 39/rleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless ag tf jp5jbli( cw52*q1xis thought the center O. A rope wrapped around the outer radi5 qi21j ljbcp*tf5 wg(us R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. 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 inc6t ;w(;18.iy. l dpfz ijbuek the horizontal position, and then released as the free end is allowed to fall. We.ykucf j 81i .tpbz6 lw;;di(hat is 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 ue h s-i4,s6gzcm and mass 1.5 kg. Neglect the mass of the axle and sprh-s4u, i6gzes ocket. 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 /m4xnt 4vfr8n around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the 4nx4mrf/v 8 tnangular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless qocv:mqme2:-p i;dl1ug3 i(y qn0* tldisk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleqm:3io c-gltp 0*v:d2; ml1 i(uqyeqnration of the mass?

  A rotating flywheel can be used to store energy. If i+3sbowkqw/6 (vzlyi7 t+arfc(2yr * ht is required to store $1.00 \times 10^{6} \; J$ 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+icpnmoaq ppiit02 1;)xb.+d of $5.00 \; kgm^{2}$ 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 startsu pqn26sxil v; w.79mh from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of thh6;9 m7 .qvip2 lwxusne sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1z5 l6oey8t9 gs.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to resty5e9o6gzs8l t ?

  A hoop of radius 0.50 p3sd7iq+w(s a m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after droppin+ ads pwiq(37sg a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rsc78y xv 5og,c1vr xxzem-*d -olls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. T1gsev-x-myo,7xdv58 rxc z* che moment of inertia of a sphere 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 mve-iw: s + aosf fo-v8ie:-9qaomentum changes 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 ofwn(1r/;r i *ffyx4ipw9b 4vd .d hypj- 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 5.00 rad/s with arms extended has a 6 3o(i qgqig,+r.vsw noig 51cmoment of inertiar,gvi+ngq.co gi6o3 1sq5 ( wi 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?