Angular displacement is usually express-xynn hp ve0/k2z9 ;u7tdfhh7z - u7lb in units of

  Angular velocity is exprdhs)vqy 53 gd9oy 6:sgessed in units of

  Angular acceleration is expressed in of(com) n*r.cunits of

  A boy and a girl are riding on a merry-go-round which+7e8dpjpo vc/ a9gduhc wx 5mvt:e(.+ is turning at a constant rate. The boy g9:/ouj85x macw7 +(dc vd.p hevpte+ 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 )6q d+p);u-ttolck8j zedzz; which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater ad; 8)z6 ju)o-k dlqt;tzcz+epngular speed?

  A boy and a girl are riding on a ml -k 1awsl ql(gv*9q7kerry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greatql9k wvqs1allgk-7( *er linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constantek,j 2wg3p*ii rate. The boy is near the outer edge, while the girl g i,*wk ijpe32is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ridinr8pjm 46tf fean(am/9g a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. 6ajfpn/4 8tar ( fm9emWho has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following i kty:j*.1 56llzu n1su;xxuuk s an accurate statem1 tz 1xy;s6ulujn*u :.lkku x5ent?

  Rolling without slipping depenf b rp7z)t9-4ykptc8l ds on

  Two equal forces are applied to a door. The first f7vmb 6mji3) pjorce is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular 6 bvpi3)m7jjmto the door. Which force exerts the greater torque?

  Two equal forces are applii a,vjeg4i:2:u v4*ejz v2apk ed to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e k2vaez2,ipev4::aju ivj*g 4 to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, t8qlmj(7e hxc.t8hmvz 9y: *v perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of mvct 7vlhx 9*hm:tzq 8e(jy.8the second is

  What is the quantity used to measure an object's resistance to changes in rvyk h*o4vdcg)4)i 7b totationcgt)d4 kbvv yi)*47o h?

  Consider two uniform solid spheres where both have the same diameter, bvtk- ji 2,ckw/ut one has twice the mass of thkjc w/ki,vt -2e other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres.9qw58 c5lbx )t wzoslz,.ho juwz6t* have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of 95 uz,lch. 6z5o*z 8bqlwwtsx j )w.otinertia to that of the smaller sphere is

  Consider two uniform solid spheres p ycas;d ,c4p(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 smally ;a 4cd,pcs(per moment of inertia is

  A uniform solid sphere hzw(xvnwv;+w1 as mass M and radius R. If these are increased to 2M and 3R, what happens to thw1vw;x( z vn+we sphere's moment of inertia about a central axis?

  If a constant net torque is apgg-,4pfrblwp d28e 5pplied to an object, that object will

  The moment of inertia of a solid cylinder about its ac6 x6k-tv f k:xdtobtvw4)zwn9: ex .,j.q9sbxis is given by 0.5 MR2. If this cylinder rolls without slipping, the c)t6nb,.t w kj x:x4dfe-9:ok6 t9q z.bsvxvwratio 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 an51ma/kwd*hdxj jl;h- d a radius of 30 cm. What is the ratio d hxljhmkw5j*-/ 1d;a of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls hveuv7 ot- 1y7. lu,htwithout slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depehetv h71-u.uyol 7v ,tnds on

  Suppose a solid sphere of mass M and radiu)ppoa+aj (, ( gnidm m9jcak66s R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the inclinpi,ma+d o()gj6a96 j(mpc a kne depends on

  "The total angular momentum of a system of particles chanz0h eeexv4)di1f3-qpt ,xv/- o1pbqt ges when a net external force acts on the system." This statement isvbp-/xio e13 f0e-e tdth p)z4,qvxq 1

  In what circumstances can the ang;sl1f;c ggh7hular velocity of system of particles change without any change in the syl;;g c hs7hgf1stem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictowele )xs8tx yp4 m5*nv: k70gion which may be present. What happen5oglkxmwep 08:*)xse7y ntv 4s over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves close0o:qfj7 u2pqvuhh dw+) ahqbo:9 ;nc- to the Sun, then which of the following best describes the orbiting speed of the Earth abou72oc) hv un9pbqa-+o:hwu q 0:hfdj;qt the Sun?

  An ice skater performs a pirouette (a fbm/h6:xgru x+7jxwv.6 s8csp: jj i5 wast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotation? :j.6jxxw65vp7+r/ csig8bx:hsmw uj

  An ice skater performs a pirouette (a fast spineb0 6.xwvgd-o89 pqe u) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy abo8u6d ebep 9.g-0oqxvwut the axis of rotation?

  An ice skater performs a pirouette (af2srg +v-k jc:fzx0x. fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis offjgk . xvf c0x-r+s:z2 rotation?

State the law of conservation of*pvnk16 ahf7c angular momentum.

  What arc length does the Earth travel in a t;;4 qivshtrz)9 a0nplhree month period in its nearly circular orbit about thisaq;nr 4)th9p;z lv0e Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of /0.r ldbmv:r rfr9h 9q0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 ser.f9hr9v ldr0qr/b: mconds?

  How many rad/s is 25 rq y 0 3rzldg01jo5)j el6fkzhgt,y.q0evolutions per minute equivalent to?

  A bicycle wheel rotates uniformly,19rrru9 x hjnkmdt ( kn ghy3ez.7d7; through 2.0 revolutions in 4.0 s. What is the frequency of the whee d3n9 (1jgt xzr 9.7krmnkdh h,r;yu7el's rotation?

  A pulsar (a rotating neutron/dao4jem (srb f 4(9du0f7;p ynyav5z star) emits pulses at a frequency of 0.40 kHz. The pn(m4a4u pb97zy ryeja ofdd/0fv;5 s( eriod of its rotation is

  A phonograph record rotates at 45 rpm. Through whatrqdv bk5hw)c my,h ;m+b6lf,; angle does it turn in 0.20 shk6rl,bmbd; q v )ywm;5fch,+?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outerh)v .3 pk ukcjr 4jv8 gx*rk;-azir1w) rim move in 2.1 kx)v);k.rp-1hwi jcjk rv4 r3zuga 8*s?

  A bicycle wheel rotates uniformly through z. yaxbf82 ss)4dbk:b2.0 revolutions in 4.0 s. What is the average an:ab)zsx 8.bb4y sf2dkgular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolzxsr.n4 nu2 1k:5p ntjutions in 4.0 s. What is the nz2uk5r:n1nst4.pjx linear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a da0n-(pbpr6ixq2 sgs q-r nh/1 :8;y 3viobindistance of 6.8 km. The cable which moves the car is driven by a pulley with dian bhp: ap1nx2 ss3 nyibri8;d 6vio/0qg-(rq-meter 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 radxjrbko n78+wmp im l,m+ h/qk;:i3-me/s. What is the linear speed of7,bmm;ne:l-+ o+/p8 hmw iimk jqx3kr a point on the wheel's rim?

  The cutting cord on a gas-powered weed cut 4i*+0*8 pmcwzcfnih pter 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 cord?*0*i8mwfp zh4c+ni p c

  A wheel of radius 1.0 m is rotating with a constant an3f7xv:/gk lue gular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's r 7/ve guk3:xflim?

  What is the centripetal aue3o1sp. 0wo wz 3hm 6yw(ubs+s ays0-cceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is movin3oswy03m( + shybp.o0ezu 6-sawuw1s g 8.00 m/s?

  How many revolutions per min4c)dwyvwg 55 22x c j9rfvebm0ute (rpm) must a circular, rotating space station (r = 1000 m) rotate tx2wcv)0 52wmr9dv yjgef45cb o produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circuga e(toz yx3+z3/6n bplar curve of radius 50 m with a speed of 20 m/s. The maxiet/33 6nzzy +xpa( ogbmum 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 5.vq-0n7h 6trm 5snll v59a slv0 m with a speed of 20 m/s. The m0.v7v-56nnl l 9lq vstrsm5haaximum 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 .m+b *mg f(n7p g1vkeq0.750-m string, is whirled around in a smooth level table. If the maximum tensiob.* mfgq k7mpgn+v(e1n that the 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 slifjzws,dt3 y .hq8zv:4pping 10 m down a lane zy3. h ,:wz4jvdtf8sqat 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 acceyth c-7wa79o3(acf duo lfxt j63v6n4leration 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 ,qbca3+ ud6um 5 gzwr7*ve )ryangular 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 rot.yul ,1o6rm 2.sdxdii ;g 0bwkate after starting from rest and accelerating at a constant angular acceledi,1w0b. ugxdk s 2l.6mr;o iyration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acce y(5 iciv 1xeh.do.2gcleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 dy5t 95zvv(is rad/s decelerates with a constant angular acceleration ofsd(5i 5vyzv9 t $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular sgx 3s4zu/ lucg81rk z;peed of 6.0 rad/s while turning tx cg u1ulg;/34zz sr8khrough 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows y)0wnn,am8wq down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in comya n,8n0)wwmqing to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ovec 9x2qdpsljjd m 7 2gz)7r3;zar a distance of 115 m. What is the angular accelm3lrqc72zj2d 9gjs ) xp7z;a deration?

  A wheel of diameter of 68.0 kt-lje1i+u 3yi-yzt)cm slows down uniformly from 8.40 m/s to rest over a dktze yi -)ltijyu+1 -3istance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medj xa56n ;/ibodical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleratii jo;6bda 5n/xon 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 tigl,te fglhyrb r/2sm +,l+4gy7 htening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force r7l +fg2 hy/erls,,4gbm tylr +equired when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a )qves2gt8szvpnk ar+bh3z 14sq 88m)torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the fs v3ehps gmq1rt8s8qkv)24 za)8nz+ borce applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in9 vy i/ fph43f+kst5vnertia $3.00 \; kgm^{2}$ 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 isfv nb3b ik;;; yowbpxn9q945g at the origin, mass 2m is at x95bbf; iyn;kqv3gb;n x 9 w4op = 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 pivoted about a frictionless axis tscd-d2v2- sgosng7q53) ;uiek zubf:hought 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 around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is thdf i2ss) --u7gns g;ukzcde qb 2v:53oe angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is 29nvy/j *kkjgpivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius Rkj nvy9*j/g2k 1 = 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. 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 5c9 6bsgekn*t at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fnk9e*56sg c btall. 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 r9 b6ipzg6*+*nh uj iamass 1.5 kg. Neglect the mass +9 pni hzji*6g* u6rbaof 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, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a lwd kvq70g- /dc:r5dffrictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration o kldc/:0gr dfv5w7 qd-f the pulley?

  A 1.53-kg mass hangs on a)z xa5 ajse41a1bozc )pbf ta0*ir2 i7 rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acias)p) b*ix0zb2 t1re7 4zf1aoj5 aacceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to store 6 m.kes.ile486 au 8oevmcom4 $1.00 \times 10^{6} \; J$ 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 inez11yzb n4q5 obrtia 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 from rest and rolls wie /j)3kcylj ;othout slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclineo)y kl ;c3jj/ed plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 main0*;szem( d /s. How high up an inclined plane can it c(ne zds*i0 ;amlimb before coming to rest?

  A hoop of radius 0.50 m and a uj.lb(: 37r:nxwqj o h :lq1esmass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical :b3x1 hl7: wu(j enj:qslr qo.distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without sliph l6 4zd*qkp-rping down a 35e incline that is 7.0 m long. Assume it srhlqdz-4p6 *k tarted 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 by g3z977j pm7qe3)onvl4ry ul m $20 \; kgm^{2}/s$ 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 ol97/c6epw(2h ofe z gbf $5.0 \; kgm^{2}$ 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 w3r9u *gyq ,ijfd 5-- knarqr6tith arms extended has a moment of inertiaf rjdy*9ki -5-g3a tq ,ruqr6n 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?