Angular displacement is usually express ** bia7i fyq6eyi lokrx8/7b1/ mzl9ein units of

  Angular velocity is expresseo9g. 6d fvkdh5d in units of

  Angular acceleration; 34evh9 c tvy3 lksd,8plmm l0uc ;br/hu7vu8 is expressed in units of

  A boy and a girl are riding on a me:(0o cd 2qrtrn0v lnr;f3: kjerry-go-round which is turning at a constant rate. The boy isf0ro :;vjc 0n eln dk:2qrt(r3 near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a con,je+8hu5 ldc wvmdygi:l/,7 sstant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular , ,v875jcdlgehwdu /l+s:i ymspeed?

  A boy and a girl are riding on a merry-go-round which is turning at a condqx8 ;;wf4* kfq uvvc3siizum/*r5j4stant rate. The boy is near the outer edge, and the girlm z4*v5 wxi kq;ufr/q4uv*3scjd 8;fi is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a const9vo4 qjazkgat:kx0mbr;v ;+ 9 ant rate. The boy is near the ovvt49o; kjx0g+ 9qzr:ama;bkuter edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-roundvc65/, qut+tsser i s( which is turning at a constant rate. The boy is near the outer edge, while t vsq/r, t5sseuct+( 6ihe girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating.zkazh5w66,2on;s 5yix fbz (q Which of the following is an accurate stateo6nhw,izqk5z(z5 ;xsba6f2 y ment?

  Rolling without slipping depends 0jm/ pmi j+ib3c+q4 zcon

  Two equal forces are applied to a door. The first force /jeeinwfk *)8/ avr5 kis applied at the midpoint of the door; the second force is applied at the doorknob. Both forcen* ar /jek58 )/kiwvefs are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to ,esf 55m t2/tzvk /t ovsl.zh+a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied552 v+tsfk o/,t/lhtzm vs.ze at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to th(.is shj,4ebzmcgu( 8e door. The first force is twice as large as the second forc(,(4u c.ib 8szhmjgese. The 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 changes in rotas */hg 89nyqbt)9)t k v..sccwivlt3wtio* vtki3t/h9w .c gbslt qswc.) )8nvy9n?

  Consider two uniform solid spheresp5e xhvg;ufm: * mu-gjx0j5 q6 where both have the same diameter, but one has twice the mass of the other. The ratio of tqe 5um- 5jx*0;h g6pfxum: jvghe larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid sp/:8 djhvu0y foheres have the same mass, but one has twice the radius of the other. The ratio of the larger u:ydh/vjo 8 f0sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one hw bx 5whaok-6.as twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that o.x65wwk ba -hof the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R.,y0;xzt(2,-/vrxti p s ouz/: 5avdpkpv pkc. If these are increased to 2M and 3R, what happens to th,ovzpxr;-xus.p:c/2 t d/vp ,zvi kt(p 5a0yke sphere's moment of inertia about a central axis?

  If a constant net torque is applirho*c2xa f 1u9 bbqv)f7ompf7 n;c6u/ed to an object, that object will

  The moment of inertia of a solid cylinder aboubuzsmm/)z u,1t its axis 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,xxg: 9 f87i0q ;3d cfmgjjd:rz one wheel 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 energy0j i r 9qx;f3djz:ggd8fcx7:m of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping downq iub* :9cd2aa an inclined plane starting from rest. The linear velocity of the sphere a d 29qi*cbua:at the bottom of the incline depends on

  Suppose a solid sphere of mass M and raq o a,lj8/93zky.8t1)h drr8ixn toghdius R rolls without slipping down an inclined plane starting from rest.3 g8yhl9to xr/ h81razonk.id)qj,t8 The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of e.2cpmngcf ui q;-3e6 a system of particles changes when a net external force acts on the system." fc. 6qinmue2-pcge;3 This statement is

  In what circumstances can the)*,8. hlsr sy2;ju rh8inbtjf nvg8 0q angular velocity of system of particles change without any change in the system's angular momentum?8,h8nb0ijg*hu8trsvj)s;rln fq2.y

  The Earth orbits the Sun in ano.h b:dx(/n dy elliptical orbit. Ignore any friction which may be present. What yx (db. ohnd:/happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the S ct t/pp7qs55kdf1iw74d wccp;tp:9y un in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about the Sunppd;pdcsy9 tkw p51wq t7fc:7i/ c 54t?

  An ice skater performs a pirouette (a fast spin) by pulling in his (pgjqtbus;o -8gm5 o6./hpjy outstretched arms close to his body. What happens to his angular momentum about the axis of r.;(bgomps8 g6/utjyh5 oj p-qotation?

  An ice skater performs a pirouette (a fast spin) by pullc*zb k/7bjx *t,e1s ljing in his outstretched arms close to his bjcx,ezl *s tkj/71b*b ody. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pu;rcv 9 ekqnuhd2 d601illing in his outstretched arms close to his body. What happens to his moment of inertia about the axis of rotatiov0rh2;9 dqcin eu6 1dkn?

State the law of conservation+ 4f;.(hj n(dh*fufg q*fzzon of angular momentum.

  What arc length does the Earth,fl w9gnd87 xv travel in a three month period in its nearly circular orbigx7d fl9nw8v, t about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lenrg 4lpfe)r-5ogth of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 4 o5)-fe 4rlpgr5 seconds?

  How many rad/s is 25 revolutions per minute equivalentuso 3j eh;nhh3ge3dvqo12l5 0g u7qr4 to?

  A bicycle wheel rotates uniformly through 2.l3b: g6 nk2uw7tfioj6va)h o) 0 revolutions in 4.0 s. What is the frequency of the wh b u6)vf6o oat3l7g)w h2ij:kneel's rotation?

  A pulsar (a rotating neutron star) emits pn1 3(qquisf 0pu84t ozulses at a frequency of 0.40 kHz. The period of if 4q0n outz81u qps(i3ts rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.20wc/ 9rl3ztqpq 4ywb-* s9y/qwc b3*trqw-l z4p ?

  A wheel of diameter 26 cm t yunbr7s6af.l,zh t ,.rt55bturns at 1500 rpm. How far will a point on the outer rimtl t,.nfr b.zbatu67 srh ,y55 move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 htx j*n7p,m0 drevolutions in 4.0 s. What is the average angular speed ofm,7hpdn* x t0j the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whn: q;c) eq:zpja i(u)cat is the linear speed of a point 0.10 m from the center of the wheqp;a)c )jzui (q:e:cnel?

  A cable car at a ski resort carries skiers a distance of 6.89xjd)ivt*vluc lp5r; f 1);kuh-jw q; km. The cable which moves the car is driven by a ) 1;5rf vudulv;h -ptxkci j)9;wq*jlpulley 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 angul 8trm35h jmer6c+0hjo ar speed of 2.0 rad/s. What is tcjj+ht3m m86o rehr05he linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lengthqcwjjtpbkil9; kaf 4 6m+.9 ,g. If the motor rotates at the rate of 20 rev/s, what is the appro p.9f+ jb4kklgw9;qat6i mj ,cximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s. fod7ex ,su7 8tk )ve0t What is the centripetal acceleratt e)7et8kxv0df o7 su,ion of a point on the wheel's rim?

  What is the centripetal accel)rw5*hfqki-b 3 5os hseration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is-ssf wq*5rh b)oh53ki moving 8.00 m/s?

  How many revolutions per minute (rpm) mw7j8c /i uhey 1kli*)xust a circular, rotating space station (r = 1000 m) rotate to produce ujii )1 8l/hewcyk 7x*an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circul:/m +zbqpx ;cxlz9biu-zl9g, ar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static x;xui/pq,z9l bc- 9l+z :mbzgfriction) 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 of:.-fx :3a q fkt(7-m ikuy0que;ntfli 20 m/s. The maxiuin -tfqffa7k:3 ;mxi:(q0yetl-ku. mum 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 0.750-m string, is whirled ard/ x6 qoad0n-uound in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass have if tha/0-xo nudd 6qe string is not to break?

  A bowling ball of mass 7.5 kg and ra;rl/tb h3f8 4gsgkzm5 dius 9.0 cm rolls without slipping 10 m down a l8gblgkmr ;s5hf 34tz /ane at 4.3 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 constan2c(e m*i g:/y.7bdt(ym4vvys ysb r s(t 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 acceleratio b32cyn(qfto .9 0ludgt81tw sn 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 tire t huskdinct +3d1pl 9f)n28 yzpg0; d0rotate after starting from rest and accelerating at a cons8fpzkn 0l9+0 )h312itdn;dcytgd spu tant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rests rrb3(9 woqf+, 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 decelerates wit z :dzym(7pcys6 7n: *gp4kvffh a constant angular acceleratiov:ky7cpm7 y6pz4fz*gns( df: n of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while turnir 3v*g3p;yzn v:nz*b73rq seh ng through 2.0 revolutions. What issnn3:zhy qrv3;grep7vz * *b3 the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows dcwy8 ,3y iyg(8h6ahxhown uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming tox8 hh 8gyahciyw3,y(6 rest?

  A wheel of diameter of 68.0 cczow3qp) ptsqks tf* 7n.(b9 )m slows down uniformly from 8.40 m/s to rest over a distance o wp9qn7s s tb(ko)3)pc.tfz*qf 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest :um- us /s:nfcover a distance of 115 m. How long does it take for the wheel to come to-:c/ums su fn: the stop?

  A centrifuge in a medical laboratory rotates at j5(o j.0xnf+ooljn fy; -+ppq a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times (y nfn p+fo j;50lpj-jq+x.ooat a constant 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 t7i 9+6prsutb xnxp0k +o a torque of 90 Nm. If a 30 cm long wrench is used, whaps7k nu x0bi xt6p9+r+t is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30-4/ vdlescww ik2c5mxx2 1e7x cm long wrench is used, wh7m 2x 1 lvcd-xiek5we 4/2scwxat is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iy*m/hx q)c -ji;uih+w 5h5s bpnertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: 2wr-k c4+cf owmass m is at the origin, mass 2m is+ w-cw r24kfco at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is nt0kk( d,t zh4yk9+ 0e;4irv,dv yisvpivoted about a frictionless axis thought the center O. A rope wrapped avrt k0 zdt0v yi49i ,(,yehnv+sk 4d;kround 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 i)yhntsxr* rz/y + ug7 -)ffd5about a frictionless axis thought the center O. A rope z+dr/fgn*f) yyr7ut h)5x -si 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) 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 initially5/mu ; ,dn:7/ njenivg(o z( f4idi 3umh3pgwi held in the horizontal position, and then released as the free e fgnv:o74ddz/mmj/(,i3 ( h p5eniug 3inw u;ind is allowed to fall. What 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 cm zoksh4z 1)6pu and mass 1.5 kg. Neglect the mass 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 1s)p6k zzho4 ulinear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped aro7+mjo xgnt i9.und a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the x.g9nom+7t ji angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of nj+ )oo3i2u hvmass 7.07 kg and radius 6 iuj3on vh2)o+6.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to storeg feg7zph 5p4yz:xa-3 energy. If it 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 inertir9 izba :hy9a4a 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 starts froe *x5z: f 6aw9twr2wudm rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it2r5 6 x ze*a:9tdwfwuw reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls3- jn 36xi 0bfrkyr2db with a speed of 10 m/s. How higb -rf3k dj6iy3 n20rxbh up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and all k3a+1p;vqw2pl5yaz jowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance oavzp215 ;pk3a+ylqw jf 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slippi3g +genm j8) 5iybzeci82ha if,6:c dsng down a 35e incline that is 7.0 m long. Assume it started from rest. The z s286g: yii)afebci cj+g8n3d5emh, 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 momentuy12mh+ 6p:om d vr0qnnm 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 ozz+4k tt6xf+p/+daxl f 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 moment of ini*m jnf d;k5) vu+sc eh4du*-xertia );kd 5 fu4vexd+ji -cnush*m* 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?