Angular displacement is usually express in unih1pr(7kxe8(y a yphn;e0fr 2vts of

  Angular velocity is expres c 9)wfgp8+yotsed in units of

  Angular acceleration is expressed iic bm: ++u;twt+0 sqpen units of

  A boy and a girl are riding on a merry-go-round which is turning at a cgx ;kn sciu22de: 18(p-ciw teonstant rate. The boy is2 w dg-nt( ;kcpsxi eec2u81:i 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 whb,): ke-a gkfwich is turning at a constant rate. Th)ke :gkf baw-,e boy 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-rosh(4idoqc ds d z,h2*ga2a)n+und which is turning at a constant rate. The boy is near the outer edge, and the girl is cla*2i + 24ho na,) cd(szsdqdghoser to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round +da*soqmpj;3 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 centr3 + *dqaojpms;ipetal acceleration?

  A boy and a girl are riding a merry-goq *z -k/wk:k3wghd:8 mppb oi:-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to thebz/3kp :8h *iowm :pwk k:g-qd center. Who has the greater tangential acceleration?

  Consider a rigid body that is rot,od+6 (+dukh fwk1 ag4qjcfc*ating. Which of the following is an accurate stat1j+ 4dwcq,fh u+g(o*dcfk k6aement?

  Rolling without slipd)hs,mh2b/ ev ping depends on

  Two equal forces are agek4j*f)aco set+4k: bgqwwz2+ 3 nr(pplied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces a*g+ q4wg4 (zak)+coe:2bnfre 3swt kjre applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is adx0-rdjg4 o4 applied perpendicular to the door; the second force is applied x 0r-4oga j4ddat 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 first fo4aw1l: * m 5bm,dw ,vdaaegtx8rce is twice as large as the second forcew1 gd*v5am,8b axa4d, wt:lem. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to meq6xxn+grr.nnk i(v + ;asure an object's resistance to changes in rotatiq+xrg(x nn n6+.;kivron?

  Consider two uniform solid sphe 9 1mc /zi9fhc4szy+jrres 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 hzcm 9ycf91r +4ji/zs moment of inertia is

  Two uniform solid spheres have the same mass, bru,a/-iu9ya k6t gz4z ut one has twice the radius of the other.kaiu/,tu r gyzz4- 6a9 The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform2cn0duu5o/b:0ykuqysp- e d5q,/uwe solid spheres where one has twice the mass and twice the diameter of the other. Thwdb :n /q0-2k u5suu0pqeo,/yce5 duye 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. If these are increased4 f z91ujrcg6)ippbt* to 2M and 3R, what happens to the sphere's moment of inertia abuf*t9z )bprgj 4 1c6piout a central axis?

  If a constant net torque is applied to an object, y-ur lw-rr v+. i07idgthat object will

  The moment of inertia of a solid cylinder about its axis is given by :/i:row9 km. sgdxc *jw7lhf-lc8eg: 0.5 MR2. If this cylinder rolls without slipping,g efd:8/olgw:lk.c jm9: x w*h-7rsci the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass nbkvw-g 44 qt,150 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 biw-v n4 gtbqk4,ke? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radi9j8stewiiv4* j5h fq :us R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incqh:jwt v 4*9i s8j5iefline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping dozu3 yw 8d+o vdxoxp,b,. (wzq*wn an inclined plane starting from rest. The angular bzd o wu8q.y xwo,d*p+3z(,v xvelocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net exterc 6i5 ix/m0zddovj6, vnal force acts on the system." This stax06dij5md6o,i v/vc ztement is

  In what circumstances can the aj j9o/-goh( nyngular velocity of system of particles change without any change in the system'sny(ojj/ 9o -hg angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignduw 02d-p1apjt2u 7kxore any friction which may be pres uw-dpt j02dkaup7x21ent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical o kxf56; ycbrc9rbit. As the Earth moves close to thecc;9y65bk rfx Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performscningm ) ;1lk98gbb/c a pirouette (a fast spin) by pulling in his outstretched arms close to his body. i9lcg;) 1bb/ kcgn8mn What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirou,+.wl( js p v8-tsjjs poeey/.ette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational k sj se..to/ywl,v pp8(js+-je inetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) cgep73e:u5fy ;iq: cxby pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of ro:xqey 5;ueccpfi7:3g tation?

State the law of conservation of angularg,uasggm 6s 233,u bk,mrhh9 x momentum.

  What arc length does the Earthpc p0 /)peckk:h9h ,zd travel in a three month period in its nearly circular orbit abhzdcp0)pe c9ph kk/, :out the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length /c9tgth(u/qknsnw n):(8ilb of 0.30 m. What distance does the tip of the sec/t8 swklcnnh)n(it9gb/qu:(ond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivaqlab.( wle16s pm8;g bqlsq 31lent to?

  A bicycle wheel rotat)r-r -)mqh1v;4vev6svhw w lg es uniformly through 2.0 revolutions in 4.0 s. What is the -4wh);lsqwmv-)6gv e1 r vrvhfrequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequent8gszt14jbe0 fj4 s orl2gho;v 3s55ucy of 0.40 kHz. The periogur50hfg32 ; oobtz14jsl5s8ejv s 4td of its rotation is

  A phonograph record rotates at 45 rpm. Throutud*cr7 rmuu-b-8hx 9rtzg+) gh what angle does it turn in 0.20 s?tut*x)7 8 uu m -r+hdcrb9-gzr

  A wheel of diameter 26 cm turns at 156rwyh gjz,;ek, ch59k00 rpm. How far will a point on the outer rim move in 2.1 s k95er,zhycgj,w 6k ;h?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is tq co bt7vhhu.+u4)4f the average angular speed of the wq4tuuothh 4)fb+v7c. heel?

  A bicycle wheel rotates uniformly 9a 3u:w kw2m*ud4 eovythrough 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m ymau4udkvo *e39w: w 2from the center of the wheel?

  A cable car at a ski resort carries skiers a dis;b +ml6f snd0ltance 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 t6bsl;0f+ndm l he trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s r;ijofo(i2bzj re 387. What is the linear speed of a point on the wheel's ri83o(f jbrzr oj; i7e2im?

  The cutting cord on a gas-pr+ zgmcs:(u+rs hr -v4owered weed cutter is 0.16 m in length. If the motor rotates at tum+cs(gzr r+v4s r:-hhe rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a consqz1 vr:nu 3ywx 4z83sutant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on tz8run: zs1 yuwx33q v4he wheel's rim?

  What is the centripetal acceleration of a point on thmf9:yhvs u9 fq,m hi qi0r,: du(,erj7e perimeter of a bicycle wheel of diameter 70.0 cm when the bike is q u ru:7i,eh,,sv9(fjm0rq dm:9hy fimoving 8.00 m/s?

  How many revolutions per minutfybvv2z gnn7tw7m7d/1m;q f l31 )k vce (rpm) must a circular, rotating space station (r = 1000 fwvm c;yn7zb )273l tkq11/vm gvnfd7m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flwz-tuk3v j ()sat circular curve of radius 50 m with a speed of 20 m/s. The maxwzu- ts()jk3v imum 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 ciko-e)k2n - yxsrcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friy x)2k -e-konsction) 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 whib1orl 0s*zd8hvr s+g0rled around in a smooth level table. If the maximum tension that the string can withor 18sz d0gl*rs 0+vhbstand 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 withou ,smnqry/kn+2a4 uly.t slipping 10 m down a lane at 4rm +l/4nyq,u k2.nsay.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 acceleration of 4zod-ay nsfu ur;/2ge2fa 05m$4.5 rad/s^2$. 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 consi74og:m0bs en,yxe;j 9*rd x otant 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 startb j ,*w0kiz2xoing from rest and accelerating at a constan b0kxz *i2,jowt angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acs4kx -h 8a,fu l4ujd(tceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating yq9-(iz,8lg; f3hpiufk ad*s at 20 rad/s decelerates with a constant angular acceleration o dg9p, lz ay-8iuif3(khfs*;q f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speedw4 vdymu0)y5*v f lu6s of 6.0 rad/s while turning through 2.v0)5s4*6mwvyuu dly f0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m- lu qveo 6)lo:u vu i5eb726nmzumy40/s to rest over a distance of 115 m. What is the total number of revolutions the ll7uui2-n65eumoo)64 bv0uyq ez:vm wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from-eer19caypu f15h d,(fak+gw 8.40 m/s to rest over a distance of 115 m. Whkfe1 h-1(d +cw 59yagea ufr,pat is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly frizef9 ,j6mr2d om 8.40 m/s to rest over a distance of 115 m. How long does it take for the whdfi,e zj62mr9eel to come to the stop?

  A centrifuge in a medical labd/q3rpv8 c j:p2jlmw1oratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming 32qcl w1jm/p8vpr:j d 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 rmpho v/) 4dj-.vzwvb-mz2 ji,2 lq 4glequire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the forcil -jv4d2 lovqp2)b/ wg, mzh4jz-vm.e required when the force is perpendicular to the wrench?

  The bolts on a car wheel requrq yae ;wy;,bd,z(mh- ire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force ap,r;bzm(qe; w yha- dy,plied at $53^{\circ}$ to the wrench?

  A wheel with moment of i)zp- ,f*9 noy hew3eoznertia $3.00 \; kgm^{2}$ 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, mass /y kn j5)pp-d5lqrch vu(p /q62m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the orig(qynkdvp6pl/5/ p ju)-h5crq in?

  A solid cylinder of mass 10 kg is pivoted about a fri -itwzw-9m ua;*h+2w: gp ahdmctionless 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 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 cylindez : g;t2w+dphim-ha*awu-w9mr?

  A solid cylinder of mass 10 kg is pivoted about a frictionlessfsvs+*5b m)co 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 around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N dofb*s+ m5vc)s ownward. 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;jcei62 ns8wl1:a/4x a d ydvx the horizontal position, 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 oa8w l s;:xvndic2 d/a6x y14ejne end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and ma .rrg.t1;: vjl-o6qpx3om kw hss 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,.;vl:6o1ghmrq.xotprw j3-k assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped ar.7e dl1kvlbh 5ound a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratiov.dl7hkel 51b n of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionl bzyq223 ld1nlk w*3piess disk pulley of mass 7.0723q2yw *b z1l3likd pn kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store e0yz gp:uqi2-40fs gps nergy. 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 idroe.lb8 mg:3th0ayff 9) y e/nertia 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 starts2uaf ko2/:pis.9 wsgv from rest and rolls without slipping down a 1f9su2k a:pvo w2ig /.s.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 radius 0.010 m rolls withhvdsi4dg44i- 7c(a yg a speed of 10 m/s. How high up an inclined plane can it climb (d4iga -c7d4y4h sivg before coming to rest?

  A hoop of radius 0.5h g*+)hcsxkgef;.a1p9 c ddok*+yqqwkef 117 0 m and a mass 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 dist .kgd*pgy1ke s a17*f+hqcd h ekfqc9ox1)+w;ance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rollstndvdlf0vo; .r 6ao2 ( without slipping down a 35e incline that is 7.0 m long. Assume it starte2vn60f o;.ltoar d(vd d 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 mom;nuwvlk4i:ig( jl0 0l entum 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 m60 0u2kdrgo0l,f7qable mt gi+;zix6 oment of inertia 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/s with arms extended has a moment of inerwpw8lxud1*d0f 3 0n hdti0xdlnpf w31dw8hu* 0d a 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?