Angular displacement is usually express in unit1b9xqf * ka-m54oc zics of

  Angular velocity is exprel3 o )4ieh) wqfyrny,9ssed in units of

  Angular acceleration is expressed in units oajl f;0yahp34q(je l)f

  A boy and a girl are riding on a merry-go-round which is turning at a constantqv/tne 1vfks64g 8*bt rate. The boy is near the outer edge, and the girl is closer to the center. Wq4v/6nvs *ebkg f1tt8ho has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is i(c *.ua:iem9eue +irturning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater ang*:ci.rei+mueu(a9 i eular speed?

  A boy and a girl are riding on a merry-go-round which is turni u2ad9cn-qfx 5ng at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who5u- 9xad qf2nc has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constantyspa*de g :)-3bf)- t-ylm7uip*ufbx rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetp- ldgm-)fu 3stu *pxf7:i bbyya-*e)al acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant ratoz9tkm nz4vkt;+z 7l)e. The boy is near thznvzk+9t7m tkolz)4; e outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body 3rd0mm 1a5em)aau,kk u dy2:wthat is rotating. Which of the following is an accurate stateme ra1a uw2 :ydm5m0 eakdum)k3,nt?

  Rolling without slipping depends*u vzh/v,1ny sear6-s on

  Two equal forces are applied to a door. The first force is applied at the midp h5*e , un;ycutgn*d w*8v3fdkoint of the door; the second force is applied at the doorknob. Both forces are applied per; n*ynecuhgd*,5tw*vk3d8 uf pendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doork +lqro 7jr;c+onob. The first force is applied perpendicular to the door; the second force is applied at 30e to thl+r; r7c+ ooqje plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the d,pei4xv: q yp 8jk+h*ejd j4+toor. The first force is twice as large as the second force. The ratio of the torque of thep+48 ie:pe,k tdxv h+jq *y4jj first to the torque of the second is

  What is the quantity used to measure an objectm tcw+n ;8wqgn yu7*13,ytken's resistance to changes in rotationynkcwn1tgm;*y 8qtwu + n73e ,?

  Consider two uniform solid spheres where bothp iqm,8 ivq5o/o, i,;w/yoz id 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 ii/q v,do,, z5ioi myp;/o8qwsmaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radiu51zdsii 1y oi1,+e btrs of the other. The ratio of the larger sphere's moment of inertia to that of the sreb5, +isd izt1yo1i1 maller sphere is

  Consider two uniform solid sphx l 3rgo7hq1:wkuudg7 0vt2k2 eres where one has twice the mass and twice the diameter of the other. The rat:2gk72 qklr1w0gudutx v3h7 oio 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. If these are increased to(ncc 35me iuv c9rga(diq6. zw.7*l)yvv(vmw 2M and 3R, what happens to the sphere's moment of inertia about a central i e v 5r.6w(7c uccz)nq.amy(mvv*3wli( gdv9axis?

  If a constant net torque is a a 3/kq5a:qi1 gecua38h xekx;pplied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by dv 4ux;n )t;oo$\frac{1}{2} MR^2$. 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 whi2 spxl04sh0jich 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 enph0 i4s0lsj2 xergy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of ma0m:-og 2jod rzss M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the in20org zjd: -mocline depends on

  Suppose a solid sphere of masmwl3.w)dfdz b8b tn65 s M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on5 fwnbbldwz 3t)m6.8d

  "The total angular momentum of a system of particles changes whex23udeeom,x qih+d :;n a net external force a ue2md:dq+hix 3x ,;eocts on the system." This statement is

  In what circumstances can the angular velocity of system dmazakfq5c;+mu *v*.e4*if u of particles change without any change in th ;*am+k 5cqfm4*iedf.u*uvaze system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which may72i4+ h s1zgnhit67sy *)ful, kcykbg be present. What happens over timey6h, n+i 17tuis*hy 7lzb)kgs 2 gcfk4 to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an eh/.k)d qfh 9nhlliptical orbit. As the Earth moves close to the Sun, then which f h/kn)9qh.dhof the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling i9c t) 7a4lcphst ubn6-n his outstretched arms close to his body. What happens to his angular momentum about the axis of rotap6 tscatnl9 ch- )ub47tion?

  An ice skater performs a pirouette (a fast spin) by pulling in his outg.su :w we:f+yj5sa4 -rw x:mtstretched armswu 5w:yt xwm+ fse.g-::sa4jr close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pihcj m7b 5hgj rn7mu7ei+6r-k- rouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis nm5ughrh7mbcj e-+67kr j-7i of rotation?

State the law of conservation -4xg.nav+s 1 y-tcaomqr4)xf of angular momentum.

  What arc length does the Earth travel in a threadcw;o,k nj+0: iuq d:e month period in its nearly circular orbit about the Sun with c :iqun ;,jdod:wa+k 0a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the )n 2*5ejp;sg+gkpj phtip of the second hand sweep through in 3 mhjj 5e+gk )sppn*2g ;pinutes and 45 seconds?

  How many rad/s is 25 revolutions pem s;qbk;i,wn7 r minute equivalent to?

  A bicycle wheel rotates uniformly throu i emu7zj65i:ngh 2.0 revolutions in 4.0 s. What is the 5jumezi: n76i frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequecn5me5 vqo ,26c-fvd8qmm 3 qancy of 0.40 kHz. The period oq c m2qem 583n6,-qvva5cmfd of its rotation is

  A phonograph record rotates at 45 rpm. Through what 74+ gem yrx/9eh7vc zmangle does it turn in 0.20 s?/94 zc+r7egxmmvyh e7

  A wheel of diameter 26 cm tur2 1yzs5domh v8m, wz4lns at 1500 rpm. How far will a point on the outer rim move in 2.81zd5 yzs4 how2mml ,v1 s?

  A bicycle wheel rotatestjws1)yo td1 9 uniformly through 2.0 revolutions in 4.0 s. What is the average angular speed of the j1yt )o 9sdw1twheel?

  A bicycle wheel rotates uniformly througkmmzsrf53b -ozch *l22/nrh 4 h 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center mz h lck/4 3-5or2s2zb*nfrmh of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. Thh3oni+3f vf.34r k4 nzsx6pyve 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 minutes?zko3nfrh v.6xiy3 s4v4 p 3+fn

  A wheel of radius 1.0 m is rotating -0 *pjibr3 tfbywo 3i7with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wh3owrybijtb7 f pi-3*0 eel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If tok5 j9sl9ci r)he motor rotates at the rate of 20 rev/s, what is jiol)sk 95cr9 the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constan,zlw h jrf6y2u 2bl;x6t angular speed of 2.0 rad/s. What is the centripetal acceleration of a poinl26;h z 2lruyj6b xw,ft on the wheel's rim?

  What is the centripetal acceleration of a y7g n)uec+taa9 h-aj8point on the perimeter of a bicycle whenyue79cth a ja)ag+8-el of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per ;ba*au ,voyh5 minute (rpm) must a circular, rotating space station (r = 100 yaho* avbu;,50 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curr*3fz 0 xr-, cp2iglmcve of radius 50 m with a speed of 20 m/s. The maximum centripe c*,xc2rrf- 03pilzm gtal 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 wi ;ka i gx:-+s96vdmwnzth a speed of 20 m/s. The max6vig;-m+w s9 xdzk: naimum 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 stts yv*vo;v yaqz/5;e9ring, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum yo5v*zt av9e;qv s;y/ 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 withwzqcto, 8j2no *r (*zgout slipping 10 m down a lane at 4.3 m/s.zwc*o j( r, tzqno82g*
(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 constantb.me 6be;89a vpqcsc ; 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 cocx. m425d, tjtmwseo(nstant 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 tire rotate after starting frov.z5iwbvy -xi7 y4sn(rgq g35m rest and accelerating at a constant angul.3v(s g5 qy xbiw-ngrz547yivar acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has cxwxl1 m. yi1sxth33 .an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 radb+ y310 dkzp :wwyl:gr/s decelerates with a constant angular acceleration of ywdl1+:gw 0ryp:3kb z$-5.0 \; rad/s^2$. 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 turnc)oydzhoa8s 2r r 2:d,ing through 2.0 revolutions. Wh ha,8rros22d: y d)cozat is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down unif3q jcuzwz( tu)r9h- it )u6yf8ormly from 8.40 m/s to rest over a distance of 115 m. What is the tot6ru-ttqy f i83cwzz)u9 j)(h ual number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly 3+u*g cw ;zf*s+pd)3i-aqwtvlse.z j from 8.40 m/s to rest over a distance of 115 m. What is th+vs -dc j3)*uq3 slg az.e;w piwzf+*te angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ove ylq s66 ,cmzf6,ag)xm* h,pamr a distance of)y6gsh ml cf* p6maqaxm6 z,,, 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medicap:36ewpmf.cmtw7 x q ;l laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 5w7mpfc6 xp;q3e m:w .t0.0 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 torque of 90 Nm.3ekodtqb :,u- wi:e 9g If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to the w -ud:gito,ek: b3qe9wrench?

  The bolts on a car wheel require tighten mt1:deyqu8w5.a(du xing to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when they8m1(xd w ue:q t5ad.u force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertkscr ytw.7(q2 ia $3.00 \; kgm^{2}$ 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, ma. +m 4.,xrw3w z m.smv+ mmvrg3haq3rdss 2m is at x = a, and, mass 3m is at x = 2a. What is+w.q3mv xmmw h 3gvmsrar4.+ 3zrm.d, the moment of inertia about the origin?

  A solid cylinder of mass 1 ky6 hwin*p08)jn(u; i zpxqx,0 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer rp8kn ,0 ip) h wqxi(j;6uyxzn*adius $R_1$ = 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 b0vj md9y4r,na frictionless axis thought the center O. A ropeydn 0vbmr,9 4j 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 e/ xg t tx,tk84,jjwq*: am+l.qujjt b8nd. The rod is initially held in the horizontal positxk g+/l t4jt:8ma,w jb8tqjqt .xj*, uion, and then released as the free end 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 anuks +sa3nq55d d mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 205 aqdsk3sn +u5 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 massuxru.u o 752aj 7.07 kg and radius 66.0 cm. .j2x rua5uo u7What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wa;j abt(*;: a 3cvqdfdrapped around a frictionless disk pulley of mass 7.07 kg and raaf av:;bja3;q*(dcd tdius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it i2.tlv9ceg ov; s 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 in8) wi-a gmt/ 97qxhezeertia 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 frt ( bna9paar i0z65-p xgop 6imw-rn78om rest and rolls without slipping down a 1.0-m high incline nmr6 g-ia0wn9a(rz876tobip pp-5xa d 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 radius19 xh fuwzvzs4bf)5o 8 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming t1uvbh)zo 8 49w s5xfzfo rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released, +5hj7aeifa s from rest and allowed to roll down an inclined plane. How fast is it moving 7,j5h +eiaas fafter dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg ant--hetk-ue7b p1 ,/uwakv)ctd 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 s ce,)tkh au7-t tw1k/ vb--eupphere 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 )9b oa5, p serkv1b3qql2 kxki rg;p/8momentum 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 of inertia ofz 3ro51k6vw )tup o.xcmd0c mge )7;4obg*kmk $5.0 \; kgm^{2}$ 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 b2d- 6k0u,k)vgm4ra gwv6by1abes b7 at 5.00 rad/s with arms extended has a moment of inertiae, 6)wuabadkysrkb7 vb 6 g102v4-gbm 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?