Angular displacement is usually expreswqjwsr z;23hy94k i 3 *e1dotfs in units of

  Angular velocity is expressed in units oyjf 2teo196yx j ,j/1i: nctytf

  Angular acceleration is e28h+ 9a xtov9t jln06q(cqg3,bme u haxpressed in units of

  A boy and a girl are riding on a merry-,jll4j .9 l/v7jjivm ygo-round which is turning at a constant rate. The boy is near the ol,l/j .vv lmi 4jj9jy7uter 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 whic wm7du7hnge1)h is turning at a constant rate. The m e17 h7)dnwugboy is 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 merry-go-round which is turnid p gv+.x)lhk:ng at a constant rate. The boy is near the outer edge, and the giv+dlk :) .hxpgrl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-(rnp:q0alsvxana no6;xi 97 7round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centas(a9:70aorx npl6nn;q i 7 xvripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turnins(oy-g3jnb9)ra e pu5g at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the aru pb9)( 53 njy-gesogreater tangential acceleration?

  Consider a rigid body that is rotating. Which of t(6sany*- j vptl:ks2n k zs 3.p.e,v5zuv l)vbhe following is an accurate sta-lykp:nzv,k 5uszl3s v) e2* vs j p6.t(bav.ntement?

  Rolling without slip 8w hb(n4z 9y+nvu,icgping depends on

  Two equal forces are applied to a door. The first force is - hr/ (qbc/f eewkf4;japplied at the midpoint of the door; the second force is applied at the doorknob. Both ( ewkf4fbh-j /;qerc/forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door *otrhpz/ ;wbcfcv4 h 7z2c w,ogx8fe2 u+q*3cat 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 exerts t2cz f;34re* bpfuw cozw+ hqotg,c2/c*7vxh8he greater torque?

  Two forces are applied to a dx jizb67b6mb isla 9 tz9ot: 49n(2zojoorknob, perpendicular to the door. The first force is twice at79j( 4xm zb js 6io2tz9o abbn9i6zl:s large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an objecqg p3 7w:qrpu+t's resistance to changes in rotation?r:3pqw pqg7 +u

  Consider two uniform solidrv /jup;az75lr diy ,9 spheres where both 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 smaller moment of inerti7rvy9/;dlr za5 p ,uija is

  Two uniform solid spheres have the same mass, but qg+h 1wgm jk1-one has twice the radius of the other. The ratio1kg gmhw- 1qj+ of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform *d0qwj +fpst,xt+7qeuo;1nkr 9k 8 nnsolid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller mor8j7otpwtnku0* n,s 9x en1q;qf+ +kd ment of inertia is

  A uniform solid sphere has mass M and radius R. If these are incrdt2e12 * uwdzqhch +j-eased to 2M and 3R, what happens to the sphere's moment of *eq-h cwd1+uh d jz2t2inertia about a central axis?

  If a constant net torque9iuckg5q 3rfc -pv0*; q. z nc+waidg7 is applied to an object, that object will

  The moment of inertia12f 8xly a2dv nqyv. s9nrud0rm5;n8 u of a solid cylinder about 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, one wheel of which has a ma*3l8: xwcn-lwf) acasl 5lzf: ss 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? Assume the-f az)w3lcxl *acls: 5 wf8:ln wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls wkq;ibv/8 g d..ry(+nrx n0fhp ithout slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the inclin +nbkrpr /d.;0x fg8h yni.vq(e depends on

  Suppose a solid sphere of mass M and radius R roajb2l6bn 6uue ly;ag*/6:ct jlls without slipping down an inclined plane starting from rest. The angular velocity of the spherec6b6ujl6*ulbn2y j :ge a /;ta at the bottom of the incline depends on

  "The total angular momentum of a systfmw4pw .93g 4r+-rk qv1tme bstm3z)cem of particles changes when a net external force acts3cm)v9sq4 4k +pgmrfbw 13te -zr.wtm on the system." This statement is

  In what circumstances can the angular velocity of system of particmm3vrk. r .6wyoe(/ hcles change without 6eyv k.wmm3cro . (rh/any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction4 4lm)xy1qb en which may be present. What happens over t)nm lbq44ey1xime to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. Ai(ttg(5bb,rug 6v w0 gq,4shd s the Earth moves close to the Sun, then which of the ibvg 0 t ,g6sut,bd5 rq(w(4ghfollowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling *,0qswx:,p-oac yby gin his outstretched arms close to his body. What happens to his angular momentum 0*yw,:yx-, gsqpabcoabout the axis of rotation?

  An ice skater performs a 0yhg-.0m 5q z , yofcuywcu7(zohuo ..pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energ5.u-gzc yuc0f0y ooh7 u.zhym,w(.oqy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstj 8(pbacs 8k(97dw0lmrjwu j3 retched arms close to his body. What happens to his moment of inertia about the axis of rotation?lamkcdj3((9j0pwswr8j 78b u

State the law of conservation of angular mome9*szxi4jkpl( ntum.

  What arc length does tmg5du:fo kp*q2n) nf8 he Earth travel in a three month period in its nearly circular orbit about td*mnun oq2)k8:fp5f ghe Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lengt fb08 b (awimz;amftj7r*l,kti8- :flh of 0.30 m. What distance does the tip of the second hand sweep l :*k088 fir maft(fa; 7l-btjizw bm,through in 3 minutes and 45 seconds?

  How many rad/s is 25 rtrv1s l,:plcnd b: (t*xs.ll7evolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is (o (zsp sdth(7*y +bzwthe frequency of the wheelodzb+ (*(swt(zp7 ys h's rotation?

  A pulsar (a rotating neutron sta1mc+23gffa j wr) emits pulses at a frequency of 0.40 kHz. The period of its rotatma gj fcw21f3+ion is

  A phonograph record rotates at 45 rpm. Through w)*w.. )k5xxczk+l d yco /dlxwhat angle does it turn in 0.20 swd /+kdc).cx* xl)l5o.kzwx y ?

  A wheel of diameter 26 cm turns at 1500 rpptcttt8+l1dahw+q*rh 0bmtc,ey(n., lcx 4 ;m. How far will a point on the outer rim mo+c x1w,t .n(c0rmed,8bq+al;tt* t4t cp hlyhve in 2.1 s?

  A bicycle wheel rotates uniformly through y4yz1(tkwy ey5 qhv 7q.vz86r2.0 revolutions in 4.0 s. What is the average anv7 yk4 yt6zqw85vr(eh 1y .zyqgular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.. j2v,odkct 2wttl 3 jq,cas/* What is the linear speed of a point 0.10 m from the center s v,/lowd3t2k2j.tjqacct ,* of the wheel?

  A cable car at a ski resorj p1cc;db2pfv1+we q*t carries skiers a distance of 6.8 km. 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 triv q*pc1fjbc+1p2 ;wd ep in 12 minutes?

  A wheel of radius 1.0 m is rotatijp n9.szk)6fo ng with a constant angular speed of 2.0 rad/s. What is z)nsp6k.9foj the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lec7fac swsv; ), m+y5ra j3la8kngth. If the motor rotates at the rate of 20 rev/s, what is the appr 8 sl7acvc;yfar ,sk+)wj3a5m oximate 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. 0jh5tqdenes 1l5x nw))nz7a* What is the centripetal acceleration of a point on the whe* 5a xl)tq en 57zne1hwsd)jn0el's rim?

  What is the centripetebs:h*tsqj : iv/kfg4bug)31 al acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm whhb: :st1)/sv*iqgebg j34f ku en the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circulassex;qahc .c9 *n) 3ddr, rotating space station (r = 1000 m) rotate to produce an artificial gravity onxes ds d93chqc.a )*;f $9.80 \; m/s^2$?

  A car is negotiating a flat circular c d ,5q7ww1pjkmurve of radius 50 m with a speed of 20 m/s. The maxi7p ,kwqw1d5mjmum 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 curvezfd) k37y(kcl of radius 50 m with a speed of 20 m/s. The malzy3fkk d 7c)(ximum 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 tl d-bys,ay-nwa8y7* n9( , fkmj,ezblo the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear eyf-jzm9, -8nk,7badn as, lywb l*(yspeed 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 w xya-(j5htm6c0uy 7f /gl)w dmithout slipping 10 m down a lanet0 5u6 gy mclaj )f(7ymx/wh-d 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 constant angular accelera u7lmm:3av;qw ek-fn. tion 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 accelerat h ;raw.mh*8p gm:.xjqion 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 trmy18 n1tvuxz b58ai +ire rotate after starting from rest and acrui85 1 8y1nmvt+zxba celerating 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 acceleratiovrgh8z2t7f e l:/)puk n 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 constant angulthqm,f+vzjsc3cq +l)2y;8 mbar acceleration o m+,2vfc3 htjb +sy;lcq 8mq)zf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest zf qm5fmjj9fnb 93 s/2and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accelejj2 snq9m5ffb/z m3f9 ration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ove;jc) o9n;zm7 vbjxd/z r a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to )oz;9/d nv7j xm jc;zbrest?

  A wheel of diameter of 68.0 cm slows down uniformly fromqb + .: m8qv2indinw:*suld(f 8.40 m/s to rest over a distance of 115 m. What is the angular acceleration n 2sw*u qd+i:v(b:nfli.q m8d?

  A wheel of diameter of 68.0 cm slows down uniformly fro0j r40fa(f,rnkjjd2uk( e a* jm 8.40 m/s to rest over a distance of 115 m. How long doaffd k, rj jr4a*ujj 002(nek(es it take for the wheel to come to the stop?

  A centrifuge in a medical l;lp ovqg-sml 7rll50(aboratory rotates at a rotational speed of 3600 rev/min. When switched rm0s lvlpq-5ll 7(; gooff, it rotates 50.0 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 tightening to a torqueen-(n )fv7x wlo3hbzb *p8z,u of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to the wrench?)f lz w o-z*3ub7np (n8,vbxeh

  The bolts on a car wheel require tightening to a torque 4rvi-+ p0ex(kp au5re of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force x 5veue-4 pprakir( +0applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofj +uzx(ptf(rbced/ 4vv6)huluh 9;-g 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,6:nthawb 7d)q mass 2m is at x = a, and, mass 3m isn:)6w7dq h bat at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionles:tig(rnx 0h1y,y qd./.mlri zs axis thought the center O. A rope wrapped around t, mz(tndiil/1q..0 rryx:yh ghe 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 frictionles 5hjtmybjof n5rdgmw1 *94.p -s axis thought the center O. A rope wrapped around the om59 wp4-5*tnh1.oy bgdfjr m juter 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 the hb 7wg*xo1z toijw,0p9 orizontal position, and then released as the free end is al,wzj1 7bt iwooxg9*0plowed 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 and mass 1.5 kg. Negleco3yezx5u;v:ious 4 v2t the mass of the axle and sprocket. If a forcu5y; ze:4 2suo voix3ve 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 pulley of massh3ul+ qn6v1o/9ml,v w ns, cxn 7.07 kg and radiu1nllx,+6,v mc n9h nvu3so/wq s 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped arounnyhq7b8yvb0q60cs2kqq : : e jd a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Whn6:87:2yb y hqv0b kq qc0jsqeat is the acceleration of the mass?

  A rotating flywheel can be used elc 58-ks4)aek qn/u uvp*sn6to store 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 inerqznzzw460at q,vw q 62+g0lsctia 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 froy*p8,xrz urj:6 tausn k8 1bhl-k99cb m rest and rolls without slipping down a 1.0-m hly986,trkh 9 ncabu*rjzpxu b18k:s-igh 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 az k(e .,yp2 ,bp,1xg e:jo *veukdod0end radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climbpvp bge(d0*:ee ,k2odke, 1uzx,j o.y before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg *2xyxg *nli.2:k wyu ris released from rest and allowed to roll down an inclined plane. Hx2wu2g :iyrx. nl*yk*ow 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 sn ks hmy2xmqlk7 ( q./k3zyftb-f(g (7lipping down a 35e incline that is 7.0 m long. Assume g 7 3ql/((kfzhkbmynm7k2 -xqs.yft(it 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 c5; jr.odrjibj4; :c k;vriub/hanges 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 of inertia (,m y1- 3cfmla :nmncpof $5.0 \; kgm^{2}$ 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 owuqp2aqhhrxr+a /w(41 r -z 1moment of inertia /q4qr2ww1ur - o+rapah(xhz 1of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?