Angular displacement is usually express in s /,+udfw peklbov/(r)gcw; 8units of

  Angular velocity is expressed in units m 8l)l(r,m tyxp3y(sbof

  Angular acceleration is expressed in units o7p-gh v:xcl2cf

  A boy and a girl are riding on a merry-go .:avpxc on5 +y2.5k hjq 5li;vfpm8sm-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to t.qsj mvh5p ;: vlyxnf+kpo.585 m2aiche center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-rounz9phg 4jc62o uz3a j1wd which is turning at a constant rate. The boy is near the outer edge, and 6cojapw u4zj2z 31h g9the 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 constant rramu 2 m7h4xc1ate. The boy is near the outer edge, and the girl is closer to the center.7mc r4a1hxu2 m Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is q )jmuys7 ;kongp8;dsm7e . hjw edv4jc1m559 turning at a constant rate. The boy is near the outer edge, while the girl is closer t7mwmv q 5oyjn 7jj48g9;kded.cemuh p5 );1sso the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constantveaeocd5l5 nt/; /ya 3 rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater ta/aence53; l yov da5t/ngential acceleration?

  Consider a rigid body that is rotatingcoe zas.n:58lp*,v5 fo9dhvgq /c*e d. Which of the following is an accurate statementdcv e* n:q5zoead h,* f58.c/s9gvolp?

  Rolling without slippi/vc,ki 12 vyhgng depends on

  Two equal forces are applied to a door. The first force is applied at the m5/qhhr9(1k8wzd d eykg 4w 6raidpoint of the door; the second force is applied at the doorknob. Both forces ardheqkhw/ (g5 zdary6 4 91krw8e applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applizg) whj r;h4hw-, g*ered to a door at 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 the greaejw4h z)h*,r-ghwgr; ter torque?

  Two forces are applied to a doorknob, perpendicular to the door. ,t,/qten .fojThe first force is twice as large as the second force. The ratio of the torque of the first to the torque of the secon,to.qj tnf/,e d is

  What is the quantity used to measure an object's resistancx4el2 ugo o,z0j8r0d f3 coe-ce to changes in rotation?4lxco,o820o r egudje c0z3f -

  Consider two uniform solid spheres where both have the same diameter, but kto6qk); f hrw+7otu y58ni)none has twi tk+5r))honi6;tq kf8 yno w7uce the mass of the other. The 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 twice the radius of t4a5 hfnxnb 1c 1:()8oauluxazhe other. The ratio of the larger sphere's moment of inertiaxz) b8naon4 a(xuhl:fu1 ac51 to that of the smaller sphere is

  Consider two uniform solid spheres where one hoacp p*n .(csd31h 3e xqe4yo2as twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of thse*oyep .qn32p(xa3ohc 1dc 4e smaller moment of inertia is

  A uniform solid sphere has mass M and radius R.sundynnjw*1 g/p1f 4; If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a c41ns /p1; gwufy*n ndjentral axis?

  If a constant net torque is applied to an object, that ys5c1v.uy( jhp6)zkk cw sz+k2q(cf, object will

  The moment of inertia of a soli7h)efgu+ qt x is w(.ej7brzd;d ,c,h;d cylinder about its axis is given by 0.5 MR2. If this cylinde)hudeb,;t+xc.7sw jrehf 7(qdzi ,g ;r 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 mass of 10 kg an*g6iem 97ueulm2(.u hp:l k zmzn2y*pd 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? u*.7 6mg2kl :mum(uz eei2y pz*hpln9 Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls uc :pmp8g+2yemgq-u0 without slipping down an inclined plane starting from rest. The linear velocity of the sphere at tm+u 2 pg80 pc:-guqymehe bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an inchytst8nb3 n.)sw dz 55:ur7 bglined plane starting from rest. The angular velocity of the spher)rgbu.h7n3:n 5t 8bwsd5y stz e at the bottom of the incline depends on

  "The total angular momentum of a system of particles change di/+ ;c 9ut.urcfbh 7-.5tuianifl*as when a net external force acts on the system." This statema*iid a.uclc+f9i 7u/ n5 .fth;tbru-ent is

  In what circumstance+lljv,c hs8dz 6 zkw8(3 zqz5t/;yygfs can the angular velocity of system of particles change without any change in the sy,z l(5w86 tz83zqz/jyy +k;chld gsvfstem's angular momentum?

  The Earth orbits the Sun in an elliptic m9go:j+nk -l.bh;8jw,/mgstrj uhmr5 ( ahj4al orbit. Ignore any friction which may be present. What happens over time to gra s4jjkmbm,huwj9ng. +-t hl5rj m/(h 8o;:the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. 3 ypihj x,mhu)kn,+ .s As the Earth moves close to the Sun, then which of themikh3shu . xp) ,j+n,y following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a piroue11dm zpgopcs2qx7* e-ps. 1b gtte (a fast spin) by pulling in his outstretched arms close t1q2 * 1g7g .cozpx-epsdp ms1bo his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fadki8:hjbazasc+2o 1 *st spin) by pulling in his outstretched arms close to his body. What happens to his r8 1:*+adhioaskzjc2b otational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in of edanks5; lm,2mtayyoa69,22a+f dhis outstretched arms close to his body. Whmyln2a2ymdad f2aakto o6 5e,+s;,f 9at happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentum.snwgd /w:t9dlw- gi, f*v(v; c

  What arc length does(+fzru+ u7y ll the Earth travel in a three month period in its nearly circular orbit about the Sun with a zl uf+y+ lu7r(radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m.3)a9pa p jw9z6vgrfrin 6x:,f What distance does the tip of the second hand sweep through in 3 minutes and 45 seconz ,rrf)fpjp6vwix9g9 :aan3 6ds?

  How many rad/s is 25 revolutions per minute w9gf n* t7yvo(equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s)zbk: la9jp.m . What is the frequency of the wheel's ro.:zam9j kp) bltation?

  A pulsar (a rotating neutron star) emits pulses at a frgid mb zc .*+r6(5syt)gc k d,*sdv;tgequency of 0.40 kHz. The period of its rotationy(ct;dri,).6kc sm gvd*t* +s dggz5b is

  A phonograph record rotates at 45 rpm. Through what angle does it tu y3sok4 v iz(4okf*pr6 j*cv;jrn in 0.20 zkv**j4p y46 (c f;vrs kjoio3s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outer23fn-xne5u dk)r.hgi d 4dm 7h rim move in 2.1 sfnh7xd4md )uer-g.k25nh di3 ?

  A bicycle wheel rotates uniforalsd0/ ge ;pg)(eje 9wmly through 2.0 revolutions in 4.0 s. What is the averag)el9d/see 0(gpwj; gae angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whatzit qoith6eh3r,8x;xdn ,/ 1y is the linear speed of a point 0.10 q61io,inhez;8 t yt 3/xx,hd rm from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of tne5fo hz f - 8gynmj5gf9s7596.8 km. The cable which moves the cargf -z89 nj ten79hy5fsm5og5f 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?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 ra 5clkda0*fb0p kx3tf*+0 gtuk75c a5h/ kbpeqd/s. What is the linear speed of a point on the wheekk t*aub3l0c0dbkage h xk 5p 5t/fcpf5 0+q7*l's rim?

  The cutting cord on a gas-powered weed cuttere-9bw k4wnar5 is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the wr59bn4w-k ae cord?

  A wheel of radius 1.0bkafst fu90-, zwlv. , m is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acc0vluz kta bfw ,sf.-9,eleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a gxl+*i s/06tkk5;a usb(j esm bicycle wheel of sajxk+ g; *5ls(0s/tub i km6ediameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (x nqtnz+dz q 6tj76.8krpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial qj7 x6ztkndn68 z +t.qgravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve 3kfv dzopt.(p kgnag /59 :+y idgrw27of radius 50 m with a speed of 20 m/s. Thy753d(gd oi.z2p a9:nk/gfwrk gvp+te 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 c ;cy 3rzv6p-h2bgj/ aou08 qaip1t3dgurve of radius 50 m with a speed of 20 m/s. Tbzgrh32 t vja /a1pycq0-6g;3dp i8uohe maximum 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 wh*d8l, vyt4w+u :foo qrirled 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 strin*lw routydf:q4, v+o8 g is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm ro-;whgkrs* r8rlls without slipping 10 m down a l ;*k8ghwrr-rsane 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 l kcl )yar9af bn6v(69p li)3vacceleration 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 wii*szgzr v1nn: m1+. exth a 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 tire rotate suauh*0 v76tsb) xkx/after starting from rest and a6 v*0t/x k u)xhsabs7uccelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has aws9zw*de i:36cp(vz hn 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 h/ha) v-e ;wht21fgpjdecelerates with a constant angular acceleration of 2-etgw f h/jv)ah1hp;$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6 4k0,h,ck mh)yfzz,xqf :9b lb.0 rad/s while turning through 2.0 revolutions. What is the average angularh4xkb0h,,zfb9) cklmy q: z,f acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rec6ze un45 cs4 )x0 op(x0vm(gcm3mqkkst over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to resgckm3 zmx0smq)p56ve cn (44x(ou0 ckt?

  A wheel of diameter of 68.0 cm slows down unihd44 (uk*,kztoz2wo fhzx :( rformly from 8.40 m/s to rest over a distance ofu h ozr2 (fw*hkz(x4z4o td:k, 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down unif +zmukv.qz 47formly 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 stopk. fv7+zm4uzq ?

  A centrifuge in a medical laboratory rotates at a rotational spba ./b kvah( a9*o pi.)lburk-h- pf(oeed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accelera pbro-v(ai u-kp9f(/*h )lo ahbb.k.ation 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. If ;v d*mlyq69l1e avc+ da 30 cm long wrench is used, what is the magnitude of 6+q91y cdlvmvl;dae* 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. phy+ -e(o *zckIf a 30 cm long wrench is used, what is the magnitude of the force reqyz*oc(+e-k h puired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o;p arg eb+c-y,1bsof- f 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: masbonz. .aqj ,g)s m is at the origin, mass 2m is at x = a, and, mass 3m is at.,)qzn bo j.ag x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictio nb1.ou-zu)-czl(z zv nless axis thought the center O. A rbzl -nzcz- z1uo)(v.uope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 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 mass 10 kg is pivoted about a frictionless axis i*asl ig1w5ks s zew g01(uf38b. fc6sthought 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 s61g1ksag.sf0fbz w*l8s (weciu53s i econd rope wrapped around 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 in the ho2km4cyobn0 f9 rizontal position, and then0 k9o cbf2y4nm 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 and mass 1.5 kg. Ne- u a976kpmrksm. 9fyqglect the mass of the axle and sprocket. If a force of 20 N is appaskk9-uqr m7mp. f9y 6lied 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 i b6:bgtfpcz4j3(jz) of mass 7.07 kg and radius 66.0 cm. What is the anguli4cb b)jt( gzp3:zf6j ar acceleration of the pulley?

  A 1.53-kg mass hangsc u*sgs7em,e;w a/z/v r2 niu; on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 67es/mn, r;uvue sz2acw;*ig/6.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store1 jeskdem(fq*,j86 teoqp);w 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 inertia of o.0gi;q bwby 0$5.00 \; kgm^{2}$ 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 q;v -rlz,-e/qre6ref kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of theq,;r /-q e zr-fee6rvl sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 q:1q(w sjbby;m rolls with a speed of 10 m/s. How high up an inclined plane can it climb bj:bywbqs q;1 (efore coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is*giet-tqrk z3;wa; mlm4h(2f q0g7jw released from rest and allowed to roll down an inclined plane. 4 m;tl gjq3gmk*-7(;0f izrt ehawq2wHow 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 slipping down 5rs /z); saqtfpofmg2;1c mg4a 35e incline that is 7.0 m long. Assume it started from rea; m4f g2 /5)tqm;pc1grsoszfst. 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 change4a uydmx6he46s 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 of xw bpz73l(g n9$5.0 \; kgm^{2}$ 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 ha3im8fgf 1bb,l s a moment of inertia gm3b1f bfi ,l8of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?