Angular displacement is usually express kn9mr0t hw1c+.r 2* qazlt-ra in units of

  Angular velocity is expressed in sp .7liozn zt,,4z0cpho0kw+ units of

  Angular acceleration is expressed inh1gh*/kphrl df1 t3:y units of

  A boy and a girl are riding on a merry-go-round whichb,kz3khum// m:wuzh 7 is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. ku3bm7,/zz uh/k:h m w Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a con82zp)e3 ldix pstant rate. The boy is near the outer edge, zpdl2)ep 3ix8and 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 turning at a constangie o td7w95b3dk::z ft rate. The boy is near the outer edge, and the girl is closer to the center.5 wed7o: bk3 fig:9zdt Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round whicual52xa +)a vqh is turning at a constant rate. The boy is near the outer edge av)52la +uaqx, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding 7bfu: klmsy1-a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is clo fbusm-:7 1kylser to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurate bzfadv81gcr*7t pd)( st)*cda v1fpz8( rbd7t gatement?

  Rolling without slipping t(q j98,eujpw depends on

  Two equal forces are applied to a door. The firstc6 /xu12 nb*ldg3gsqx force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to tcdqg6bs2 g/ u1l*xx 3nhe door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first forcetsb,b/om,j dxv2;3 c9ifm0 u u is applied perpendicular to the door; the seb2/u3jxfmbso i,c; ,md90uv tcond force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first5oh7 fw ov8s)twbtib8ni 7 57i force is twice as large as the second force. The ratio of the torque of the first t78b 7w5 vitfowbioi ) 8st57hno the torque of the second is

  What is the quantity used to measure an object's resistance to chan4wuw6i1bkkqg ;. 6 hc ;zm-/*dfqfqxpges in rotati 6gqkh;fqi w;w-zpfbm*c d1x6ukq/4 . on?

  Consider two uniform solid spheres where both have the sam0tzw bxkdhvtn.(0 i5 4lz a 1cs0do*b ga-d(x;e diameter, but one has twice the mass of the other. a0s(txc0h g 1a d;dbv0 zzk il-wond45bx(.* tThe 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 twip aov n16w4am:4el4juc)el8k ce the radius of the othka:a c184emw l6e n4o )lup4jver. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twiceof d0uuok :z/- the mass and twice the diame :d/f -uk0ouozter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R./, fho*t): w k)a2vz kyip+w7xx0uhnu If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about u+zwk/a,f) *t :np 2x7iy whxh)okvu0a central axis?

  If a constant net torque is applied to an object, tha 5eb -u75orl/i;g ypszt object will

  The moment of inertia of a solid wn n, 583zi ptrrjug2yd5ze qa/j;x kc2i)(/kcylinder about its axis is given by 0.5 MR2. If this cylin;5xrru 8yc jk( a2e/tiwidpj/z ),gn5 q32 nzkder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150j/ 0my,bglho .e -t1itor4x6i kg, 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 energy of the bike? Assume the wheels are u,t6 h4ij g01rix .yt- lome/obniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slk/0jt9sc 1i sbipping down an inclined plane starting from rest. Ths/9s0c ibt1k je linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withoutxw: ntce.n62 f slipping down an inclined plane starting from rest. n.fntc2w xe: 6The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles change5(crxso2w- cgi kxrg*(,xon-s when a net external force acts on the system,(2 isr-o(5rxw -nxcgc x g*ko." This statement is

  In what circumstances can the angular velocity of u9 )0u6xor6uep3dqc 1r xyjj-u ooj 2+system of particles change without any change in the +qcy96o3u1pu 2oo 0dx)rxu6u-jjrj e system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which maev5 rvi 4vb,u fbg0s,/ trfa)*y be present. b,art,svv4 f/ e b0r ifvug)*5What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the27a5u7dexx e3xecl9sln- 8 mb Earth moves close to the Sun, then which of 3dnex5mex 2cxll7b8a-s9 e 7 uthe following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fas48 sy nu)-pipet spin) by pulling in his outstretched arms close to hi4 np-yu) 8episs body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his oh ewpu n5k+w35utstretched armspek5nu h+ w3w5 close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirh83+dx dp2k)exjp ko4ouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his mom okxkd dhpe4)x832p+ jent of inertia about the axis of rotation?

State the law of conservation of angular moment 9k,wj k. mx+ rsk45.wuk3a;ksqx(tlis16 yv xum.

  What arc length does the Earth travel in a three month period in its nec1k5a*j t e-vfarly circular orbit about the Sun with a radius o e k-tjfv5ac*1f $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. Whatii ffbhe)5n/jn )j0 k3 distance does the tip of the second han/i h)jjf )5bnf0ine3kd sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minuted/xkjds) z,;7czg. fj hakj (6 equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 sgiu :o sn( kp 1 i0g:qsr9vw8gsk+om48. What is the frequency of the wheel's rotp( ir8mw:s89oku+v0i:4qk gs sng1 ogation?

  A pulsar (a rotating neutron star) emits pulsesuv.h4t:hhu*aq2zz - zfv.2m6 w+tkqf at a frequency of 0.40 kHz. The period uhk 62zzvfq-+vm hft2ua.qwzt: *4.h of its rotation is

  A phonograph record rotaolsz z:2ij8)jdmtg 9( tes at 45 rpm. Through what angle does it turn in 0.20 s g(8ljzijm d:s)t z92o?

  A wheel of diameter 26 cm turns at 1500 r7k rd, 1owzzo9 72:(n gsitwzmpm. How far will a point on the outer rim move in 2.1o(72t:1w,o zrgs7 mz 9kwndz i s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What :fl r5inn5rqmxe n,4, n4 ee)zis the ) zrml4e4re, nn5 n,fn:i5xqe average angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.l4j/up7h8(3kffrz er 0 s. What is the linear spe3/zfhr (uplkrj 84f7eed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a d xnmbi((x+edn;of7kxx 1,rl)istance of 6.8 km. The cable which moves the car is driven by a pulley with diameter7r + d(,xx 1xe( ;imn)xlbfonk 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 constw1bnd82+hmq etvb t4+ant angular speed of 2.0 rad/s. What is the linear speed of avbt 2het+q1nwbm48+ d point on the wheel's rim?

  The cutting cord on +i(fgfi9h-pthtb 0m/a gas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear s 9- hb/fi +itg0f(hpmtpeed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant monymhm5ps ,44sf8r; iuf.k/r c1a k7angular speed of 2.0 rad/s. What fk7 p48 1msy,54mr.knimf;horu c s /ais the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a b e(6n5mjgd+ubicycle wheel of diameter 70.0 cm when the bike is moving 8.00 m/s?deg(j ub 56n+m

  How many revolutions per minute (rpm) must a circular,yh+++qyz:s ,s *ftj 2gcu23weuhfao 5 rotating space station (r = 1000 m) rotate to produc2hzs uh:e,f35 q2cwa+ tsyfj* +uog+ ye an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve k9d+n.hj +m qb h0iu)kof radius 50 m with a speed of 20 m/s. The maximum centripetal force (prok+ hi).+qdu90jk nhb mvided 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 withyyuxk.b/ sy 3: a speed of 20 m/s. The maximum centripetal force (provided by k./y yuy:x3s bstatic friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached , +wvylg gsp49to 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 speed can the mass have if the stri,+9 gyvl p4gswng is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slijumkre ppiy; 1br*85r;gx2o,pping 10 m down a lanube imrg;51; o,rpk py8*jrx 2e 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 constan3i:8lpv3j2ui zyxb. o/vb p,qt 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 a63xzdep( o 0lo 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 radiu6.kc86h aq kfxs automobile tire rotate after starting from rest and accelerating at a constant angular ack a.6xqk6hf8 cceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration o fsp5q,fcmzw4* *t0njm)0vb3gfgp1q f $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/njzuef 84 0kd5. hgvo)s decelerates with a constant angular acceleratij40zg5eu .o)f 8 kdvhnon 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(7/erkfpf - gz while turning through 2.0 revolutions. What is the average angular accelerf7 e(g/-rkp zfation of the wheel?

  A wheel of diameter of 68.0 cm slows down unif g48(ilw62b+/a :(ewkowo8qgqmvhx d ormly from 8.40 m/s to rest over a distanceo(vwdm+xw4g(w h/oqi k 8alb : 6g2qe8 of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows dowv1c*dp+z8gzf ,oc8vxn1 a:zf lgn;i 3 n uniformly from 8.40 m/s to rest over a distance of 115 zd+, iaf x :31lpgv g1z8;ofnvcz*8cn m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down unifvs5a 2.lh:me oormly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to the stop 2has.:e v5mol?

  A centrifuge in a medical c.*n24p,ijdurnsdf0 laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accelerf 0c i2*srdp,.4djnu nation 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 tvil.7vfyz b*t5 +0, x hbevvq)o a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitudi ft* le+0vbvv.xzy )qhvb75,e of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tig(vr5bl2kl5 b bhtening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the (rblb l2kv b55force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of vbwnv 9 ydq d,y/:y9c3w mwpi :g+)m8ginertia $3.00 \; kgm^{2}$ 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 iseknac *l.l 4a4 at the origin, mass 2m is at lae lcn4* a4k.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 etm,,u, sd7j)drc/ n+pfq- bfpivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 =fu cb-spf +emt ,,rqdnj,d)/7 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 acceleration of the cylinder?

  A solid cylinder of ma8+)gggasm v:.)n0 a pb; m*cnboxvb,fss 10 kg is pivoted about 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 arobc ;vn)bapf,* g s.+ 0g)mxngoabmv:8und 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 inyc+ xhc fg ormi;azy3 1j;f74 hfv67,p the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as ic6i7a3myfx+ff1prgy47j;,hz c; vh ot is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel toae(qbdl) +,wa5u0g bp 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 tangentially to a sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve,qeb(, u+wdg0)pl5 baa assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frpky /rftc4q/ixe ); 4jh7lw/iictionless disk pulley of mass 7.07 kg and radius 66.0/ 7rtfiwh iq//lkc)ej ;yx p44 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pu4gejbllb/:oc -9 owc*+bw,qzc) e8m z .oj l2wlley of mass 7.07 kg and radius 66.0 cm. What is the acce *wcbcz49,zw:-em2 /gjcjloo bo)ewq l.8+bl leration of the mass?

  A rotating flywheel can be used to store energy. If it issj9 wh 6d)mdc, +bg4fl 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 st/)r l g-e+kyinertia 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 kn jp o b*,fytk,:ud2f)g and radius 0.010 m starts from rest and rolls without slipping down a tou:fy2 k* )jp n,bdf,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 and raduz.hg a0 xvllum* w9g+pp/p8 +ius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before comiamgvu0x8zglp + p+/lh*u9 wp.ng to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is rele* iv / okpdejw.1l* (8/cxufnxrz*ji+ased from rest and allowed to roll down an inclined plane. How fast is jrolw*fx ix/unj1ivd. p*cez(+/ k8* it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kt(q7l 8 +(8vsqqck2 gr4 tk j7fdjg/wfg 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 spherj+ q(8wf4 k s( j87fd7g /q2rqvkctlgte 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 changeskmgura41z 21g 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 inertiz7rm)fw f;-n jt7cb cuj(8 pgns u2+/ha 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/2x-iuur)*d oricg* wk zg-)d-s with arms extended has a moment of inertiair kzuc *2*d- -uw)-doigrxg) 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?