Angular displacement is usuallysxt(jornk 1(-4v+ yvqq/b j49u2gp ek express in units of

  Angular velocity is expressedp 80di*7geyk gxio2vw (dca1. in units of

  Angular acceleration is mtg:i 3eeo4+qlm idjtwn.j3ez(6, 6k expressed in units of

  A boy and a girl are riding on a merry-g/c jt(icw8vz ,o-round which is turning at a constant rate. The vcwt, iz cj(8/boy is 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-g75mv e6kdv r is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who hav-dr 7ek5vmg6s the greater angular speed?

  A boy and a girl are riding on a merry-go-r6b 0nfvv96u8x;2s 3ar a zydlgoam*k ,ound which is turning at a constant rate. The boy is near the ou dua;x6o9sn8rm fzaavk,l3gb0v y2 6*ter edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round whic(k tjw(4qx-hk 7a j 8*c*bglluh is turning at a constant rate. The boy is near the outer edge, while the girh4 gc*8jwlj 7*aquk(lb(ktx-l is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which isqy4,vi)lba7to1uun0;y vx f : turning at a constant rate. The boy is near the outer edge, while the girl is closer to toiay) n47t0y:;,1uv vf blquxhe center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotatince xq1pm p2o8ba,)go/g. Which of the following is an accurate st )po8xeqagob/pm 1,2catement?

  Rolling without slippikiy) a a2za l: ,yqz3i7cbat4/ng depends on

  Two equal forces are applie0s w9aj ;0wsmdd to a door. 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 exews 0 9jw0ad;smrts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is isuvvj( uw8;(;d)b wav+wie9applied perpendicular to the door; the seconi uwd) ;v8iwaube9;vv(wj +s(d force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a door+0zwm.uadl;4 s0i25x2w qsksiurw l 4 knob, perpendicular to the door. The first force is twice as large as the 2 wi40s4.u ;waqzdkm5rlu+w 0s xi2 slsecond force. 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 resis 7h9rgk-o-f8 zbddk g-tance to changes in rotationfrg-g8 bo -7dkd kh9z-?

  Consider two uniform solid skqj81p zb ;lp2pheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inerti;k1zqp2 jp8lb a to that of the smaller moment of inertia is

  Two uniform solid spheres have thencfqs1;hye,sx9* c 1/ hpdop6 same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphe6 c ,e;y*x1/9 shpchp1snofdqre is

  Consider two uniform solid satanm:+ 80t*wdl rhz) 7xz,xopheres where one has twice the mass and twice the diameter of thez + 0hm a)7anldtx8 :o*wzt,rx other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere hayuqr eiti qccl7/r6qr sn(2 +i.0t;*n s mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia ab.i(rt0i* c2ru/q c e+rs ;n67yqqnltiout a central axis?

  If a constant net torque is applied to an object, that object wjkfic.:p z , i4gc8y+sill

  The moment of inertia of a solid cylinder about its ahl 0lrczo3n(4oeu.+ohj 98lz xis 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 of wdpjj-feti7 v1o4o) qw(y2w n,hich 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 t-i1o2jj q yn wofp,dvwe)t(4 7ranslational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R l lxx .x/yq)g+rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline dex+ xlq/)gx. lypends on

  Suppose a solid sphere of mass M and radius R rolls without slipping downm:* w o, l4sbrui-zp3 48iwoax53c+fcj 3ioqh an inclined pla3scfp 3+zc,*qb3a8-u hiwo4j rm:oi w4oil x5ne starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when5tond1tltc+) w 6ibz 2px0o* a a net external force acts on the sycw562dtt bx0 pa1o*z)ol in+tstem." This statement is

  In what circumstances can the angular velocity of system of particles csqdt-e 5 m2coeyxo i376l9i/s hange withooeisemc2yd/7 39 -s5tqxl6oi ut any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignor+s(guqxrz.,f22a -*db pp wfye any friction which may be present. What happens over time to the Earth's angular momentum abqfr* 2(wb2 szg+y,dp-f.up xaout the Sun?

  The Earth moves about the Sun in aocbg.f+;mtnk zr-x7g u4pp.:n elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the nb .cpx.4:fk;+ m u-pt7go zgrEarth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hijzq41n gdm8kcg0d k t/0b*(j(j(kfqi s outstretched arm(8( 0gmkcn/ dgkq 0kjdb1t 4*jiqzf(j s close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spy 5t ;5qhtw+lpin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic q t;5lwhy5pt+energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchdpw ft/0a;.1nmsl z3 sed arms close to his body. What hw/zpts0 3fs.mdn;l a1appens to his moment of inertia about the axis of rotation?

State the law of cons-sy,-9o rht)yxwk yj2 ervation of angular momentum.

  What arc length does the Earth travel in a threii: g) z,q.bjue month period in its nearly circular orbit about ,:iu)bz.gqj i the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a cteff5,)n5t95i. cziw2nxm rh lock has a length of 0.30 m. What distance does the tip of the second hand sweep through 29ztnwc5 t,h5 ei 5xfmn)f. irin 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions1s5h9+:l ie 5o1 lj0g ajnntd. ghzw;x per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 sgqne9y u5x8lbnp*s7 nn ;y)z2q i6;ta . What is thet g2; nlb8xysa5)6quqzen*ip ; 7ny9n frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz.yyfbv/ (ws 1/+e jl9mt The period of itj lfy9wm+ (/vyesb 1/ts rotation is

  A phonograph record rotates at 45 rpm. Thrv1:ajwj0e 4 dnough what angle does it turn in 0.20 s?4ej1wv jd a0:n

  A wheel of diameter 26 cm turns at 1500 rpm. How far7 ab9 ;h0msbqzr9wxi+*o xko) will a point on the outer rim move in k9rix)z7 a+qm o ;sbwxob*90h2.1 s?

  A bicycle wheel rotatesijtzqwo vm:s9-xglbd p3 0o1 9v)ve7)9 qlke9 uniformly through 2.0 revolutions in 4.0 s. What is the average angular soie9):-tsq7 ol9 w3vqx z1gdj v0ke mbv9pl)9peed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thm;x6cshm:id ddz1b/ n:;tfg id7 f- j1e linear speed of a point 0.10 m 7nd ih gzixdmmb;:;d1jtd:c f-1sf/6from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 kgh) 2y c kmj+(c,;uvfvvz1,a8h.aqud m. The cable which moves the 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 minuvua8 mu +jc,zv d(qy;fk, chvh) 1.g2ates?

  A wheel of radius 1.0 m is rotating with a constant angul8so7bt5zvvj-eei(dcv4 g d*3ar speed of 2.0 rad/s. Wha3vdei 4(7 jo esdz-5tv8 b*vgct is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is(0n lvd1jwe0jib)0tz 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is th0 j(1jtw0dvzni 0bel )e approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constan 5(. miohr9ztht angular speed of 2.0 rad/s. What is the centripetal acceleration of a poioizmhrh.95t( nt on the wheel's rim?

  What is the centripetal acceleration of a poib/ 8e3 b usfue3uqo1rdlj 85z/nt on the perimeter of a bicycle wheel of diameter 70.0 cm 83eu lub d/qb8u3/ rf e15zsjowhen the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating fp wyy4 i vd1-a,b5gr/ttd:6hspace station (r =i5h-tt4,6 a:/rddfv gpw1b yy 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of rad*s g9x 7ta p,yk3b bjbfc)or41ius 50 m with a speed of 20 m/s. Tha4ky fb)jt1gcpx ,9 7r3b*bsoe maximum 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 mdz-fo9 uwqli 7 7)i6jcf*fdc, with a speed of 20 m/s. The maximud fci )-uol,7j *fcwi7qf 6z9dm 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 around r 2y nlsz9gg, x/k*oi2in a smooth level table. If the maximum tension that z lro,*/kgn x2g9i2ysthe 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 slippl+j 51*mvf6k l 7eusbying 10 m down a lane at 4.eyj 7lbusvk+ *1m6f l53 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 si0 p1zc yo,4td5ac1/ l8dm8 d3rhmfy a constant 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 av458qoyl ; 17s bacp f+hj+2pdo,pkut constant 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 tbck px6lr.yh rl0 6 1.jbx.a6eire rotate after starting from rest and accelerating at a b.celrj.x6 hb6 rapx6l .1k0yconstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration of5 rb a,7k)o wxycyrymg0.v5j (mj-7g y $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s deceleratef7y9k(e bt;m e sxp),gs with a constant angular acceleration of p 9x( k)eebf7m; ytg,s$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speedpr o9a90ne.ps of 6.0 rad/s while turning through 2.0 reve9p0 rpa 9son.olutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cmtpbv+x6 *xa-xamr: s 8 slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions thms*-x8 va a+ ptr6:xbxe wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.4nfyq ;73l9 dw5ax rmp90 m/s to rest over apl mdw7xa3yfq ;59 9nr distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm sobu.c*i)y: v jgfq)l ;y 1p8ynlows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long doy gjicyovb*l8f)p n.u: 1;) yqes it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational s-q wn2j, 4 d4a)y2t9re ztatlypeed of 3600 rev/min. When switched off, it rotates 50.0lda2r9,ttyj q4z 2nw)e- tay4 times at 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 ,l1tcg zo+0lktightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when0 zl1+cot k,gl the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm lo39 rfxweie ),m x fe(i:+8it.wzgeqt+ng wreiwix: g3tr.8ti(9wfee zee++fx)q m ,nch is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment h lodyg44r wlu+: y:(gof inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mass m is at the origin, mass*4er . ai.r zxlc/u3lx 2m is at x = a, and, mrci .xxl3u .*/ze rl4aass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless ax6p16gd4akwzpl ,4r j qis thought the center O. A rope wrapped around the outer ra q,al1 rkjw66gp4 z4dpdius $R_1$ = 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 frj :y2583y 1l(e+h ov-vjta qoe*mbbkbictionless axis thought the center O. A rope wrapped3(kjbytaol+bv* yj8hv q: o1be5em -2 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 initially held in td+o)fxe 8oo+ phe horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (The moment ofo+od)p8+ exfo inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel torn92gdc; /bp c j1 t8o*x0pzk* y2eknv be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentia 2 yok*0zgx/92tc 8*pnvenk jcrb d;p1lly 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 bg kd ug,e7*:n ygt+o;obr-*tdisk pulley of mass 7.07 kg and radgg*ut;yntk* :b7ob -ge dr +o,ius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frt5 itc,;j;any ictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acce5;yc i;tan tj,leration of the mass?

  A rotating flywheel can be used to store energy. yl3ar i13 95dl 1 f8mqs*vewki 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 inertia ci)oczteb1 , t 024z9wzwes m*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 0.2xal42zljvge lpf fvp) k/v9i3:l4)a010 m starts from rest and rolls withouvv)z3ve4p)p ala9lf4/igk:2lj2f l xt slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg as ;3*n)b l4xd j0kkmtvnd radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it cl0n d*j )vxk; mt4sk3lbimb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 krhedtr7; cu.wh1c -krz7h,p 9 g is released from rest and allowed to roz7u re,1hc .-dh rhwt 7p9r;kcll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slclqq3n2jm j,r. 8-xvvipping down a 35e incline that is 7.0 m long. Assume i. qvv-8cq xjj32nl mr,t started from rest. The 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 momentum changes x/hzy*9o: y( e-b6 lmjvm;f9djr,m hh 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 mov sc4wqu5id rbzs 79987pfl)kment of 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.eh lnh:2m snx *ee:w) arms extended has a moment of inerti)ehhm2.:ee*wxl n ns:a 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?