Angular displacement is usually expr fzfoizyo1)l 26/ermgp*l5,o t)9dsfess in units of

  Angular velocity is expressed in units of 5ois aacef6- p vm94tg1w5,uj

  Angular acceleration is expressed inh:kj /jtj.2 ij units of

  A boy and a girl are rid+mdpg a z(2kqz:/kgt , qx5t*sing on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. q(2zpz+gg, mxkqa/*dtk5s :t Who has the greater angular displacement?

  A boy and a girl are riding on5.7d kfun j,mmio eti ld-2)s( a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and thed mul.ike( )7 - jtmn5,osdf2i 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 tu ej9-, r6rb5 blfaag)irning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the grej 5-b)blir,6ergfa9 aater linear speed?

  A boy and a girl are riding a merry-go-round which is turning aytcw-k cxqm0 sh-3ncs4;hn; 5t a constant rate. The boy is near the outer edge, while the girl is closer n;ss-wkh xqh 30-ct 5 ncmy4;cto the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a min;4 l q9kex.nx1hho1erry-go-round which is turning at a constant rate. The boy is near the outer edge, while tnlo1 xen q4xh19 i;h.khe girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which ofcsnw qs+to*gx 1qbt)xh, 9i en*0gp(4 the following is an accurate statementexs p 0x,qw (n1 his*) g+gqc*nt9ob4t?

  Rolling without slippin rn +*3 skiak3 pms98 hk:rmx9,jttl8sg depends on

  Two equal forces are applied to a door. The first force is app omo+*r5n0fkfl ,.st flied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater t t *.5rm n0fl,+ffokosorque?

  Two equal forces are applied to a door affo;1z18kj5w*g w wcst the doorknob. The first force is applied perpendioffcjg8w *;wwk11sz 5 cular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doni p; 16vdzal; e7yu0morknob, perpendicular to the door. The first force is twice as large as the second force. ydnva;16; l 7pim0zeu The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resist5d0k3bcnxh nwr)n .9 vance to changes in rotatioknh3n5 9cw0n)v.d r xbn?

  Consider two uniform solid spheres where both havphuredk g;tso)vb1 mws 2 gz7t(su(7x*+hl5.e the same diameter, but one has twice the m.b;gu* 1(r swhdzh2gss x(epu +vtl7m57o )t kass 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 rvvex ,rg ),4eqadius of the other. The ratio of the larger sphvv4)e x,eq ,grere's moment of inertia to that of the smaller sphere is

  Consider two uniform solia6 r/egbjql ,1d spheres where one has twice the mass and twice the diameter of th ,gbqa le6r/1je other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has ma;k rz:iet*dj4 ss M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moit*4zejd ;kr :ment of inertia about a central axis?

  If a constant net torque is applied to an obl-l0pg-o:4wwbj lz1o1 uou4 ;chi u( cject, that object will

  The moment of inertia of a solid cylinder about ekgta 2uq rh(j,af8 **lq o nz 6wsm/,r+21kztits axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translato/2grs+u ,1e rwf nazja *8qtkqh6 k*zm,(l 2tional kinetic energy is

  Consider a motorcycle of mass 150 kg,gsb+:ui0c huf +fka 82 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 tha f uh sfgc802i:u+kb+e 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 without slippingmi/. rbjjob ao0+:av-3.g2wm 1qpozf down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incoajp/ o ..0w j3oifmg2mrqv +ba -b:1zline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an a;.d 3o4ptz4k4u/mwdk f: jek3j+iqi inclined plak/ip 4;kwdqutkidj za:m+f 3.4j4 o3ene starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles ch /88iwdib7o6o64ic;z o gnn pfanges when a net external force acts on the system." Thisdz/o 786pigc;bof w84 6i noin statement is

  In what circumstances can the a74/kqgbfi2 r)hfj phn8i0,pfzxj;h 8ngular velocity of system of particles change without any change in the system's angular moment) 7kz/ihg p bx j;fhp04f2njh,iqr88fum?

  The Earth orbits the Sun 9uqs0io irs 2/be) p:hin an elliptical orbit. Ignore any friction which may be pr9hp b2ro ie)s:0u/sqiesent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the S.h2 u7wc1- uwm6bbets8it 6g fun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describuww fmth6tci1g.82b ubse -76 es the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling ie0c 5dj(p g-sccczr 78c(e i-en his outstretched s j ( 08cp-i(dezc5gce r7ecc-arms close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a (1 xxl5v2b:hwzrjwcl3 tvy 1 ,fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rota 1zwxrvl1(tyxh2v jl:w 3,c 5btion?

  An ice skater performs a pirouetd+*vtumz* nxp4w-yf w, nv,u8 te (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertin,*uxvf p- y ,wnu4 8dzv+*wtma about the axis of rotation?

State the law of conservation of angular mom8g4 h 1q eou8h ,hsg/wk2ee7uyentum.

  What arc length does the Earth travel in a three month c;+p4l.v*8ol hf/n)uku k/s b,awit2s; q lclperiod in its nearly circular orbit ab/was.uh4 ;nlscb8lq ;tk/+ fk, plv o*)liu 2cout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.31 cuif3,o n-y03mza+nngabl i0ic )t.0 m. What distance does the tip of the second hand sweep through in 3 miou t-aa+3 ci nilf,nmzi3g0n1c . )b0ynutes and 45 seconds?

  How many rad/s is 25 revolutions per 2 skkn0-1sei*w5j4ghrxhlq ,g ) fdu4minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 resq7say66de w ,volutions in 4.0 s. What is the frequen q66dsaws,ey 7cy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulsk,e s9k5k 2yezeu pzlii l639-es at a frequency of 0.40 kHz. Thee ie ze li36 upkk95l-s9kzy,2 period of its rotation is

  A phonograph record rotateswsowekfd u/- (8a2hpywi8( :u at 45 rpm. Through what angle does it turn in 0.20 ade8yw kowu 8p: 2ifs(h-u /w(s?

  A wheel of diameter 2tq* -446nztjg1px cgf5vp7ml6 cm turns at 1500 rpm. How far will a point on the outer v pq l 1g7-gnxmtfjtp 46z*45crim move in 2.1 s?

  A bicycle wheel rotates unif6obs* 6 nqa(ygormly through 2.0 revolutions in 4.0 s. What is the average angular speed of the wh( oy*6nab sgq6eel?

  A bicycle wheel rotates uniformly through 2.0 ; ihh5 ;co /ozgaa:p2yrevolutions in 4.0 s. What is the linear speed of a point 0.10 m from t5zh;gio:p;cyah o/ 2a he center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 ;p gofc*tr;l9 km. The cable which moves the car isr9 ol;cg*p t;f 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 angulj+ qz 5bov lx7m ;y;gusupgd5k/z/0;z ar speed of 2.0 rad/s. What is the linear speed of a popb0 j/mqzu;s;zokxz 5/ ud+lg7 5v y;gint on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If ti7g09w5z nsl)m* n wig(63 yq eo9ypvkhe motor rotates at qz9)ygo * v7 (59inlnmgy03ip6e s wkwthe 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 with4u7emp)jm ,vhs h ib.ok5. zb: a constant angular speed of 2.0 rad/s. What is the centripetal auz bkpm,bv.4h:hi)ojs m 5 7.ecceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the peri + ot d5rxj9qn,3-uqwpwpz84w5 v/dbd meter of a bicycle wheel of diameter 70.0 cm when the83+wup-jtw, q 5d5bow d/ 9xv4p znqrd bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space sk); ba. 6po3cqcs5 abltation (r a ccqbklop3a ;.sb) 65= 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat cifvc:m+i(w2) mgw x) icrcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by stativw 2ifm (cm:w)i cx+g)c friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating8zh 2u .q:xfivh ww u*wmx1:;v a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (providvqm;1z* i x :wuwuhv8fw2xh .:ed 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 en)hzctmyed +u 4w) q.8md of a 0.750-m string, is whirled around in a smooth level table. If the m u+m z)wq8ty eh.4)dcmaximum tension 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 slipping 10 miovpxf0m ((t emdlzqc3 i;0 6h1r,w3 i down a lane at;103ih f roip6qe0w ,vdim(z clmtx(3 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 accelerat s/3wol3mjzv5d2y d9,lx1sdt ion 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 anl,o*nt 5kupwi;l q yh 69+.sjfgular 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 startbe4s +5p5 a3amff v3ug vub6d3ing from rest and accelerating at a consta+uvfb uavfbe5ad3gs3 p4 56m3 nt angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration of rp5eg 5.vi ij2$4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotatxx qwq -gu-d+/6ood7 ping at 20 rad/s decelerates with a constant angular accelerationdd6qxp go+/oxu7q- - w 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 wyclt fu. o.:*ey+vlc 8hile turning through 2.0 revolutions. What is the average angular acceleration 8o *le.lytf.+ vycuc:of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.8rf .z:-y k nyny4b) ,)j(9jkzpcu oyz40 m/s to rest over a distance of 115 m. oyn8 ,jj)yyb n-4.kypz:z cu( f9) kzrWhat is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 t4if-bk3+ng)k xv8b 3iw b1wwcm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular accelerab3w+w 3fbwk8xg4k)v -in tib1 tion?

  A wheel of diameter oni1 4r 5l1r6gcj5smojf 68.0 cm slows down uniformly from 8.40 m/s to rest over a dis j56rr 4mijo5gn s1cl1tance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/m85cy7quwrx ul4 ,,joe in. When switched off, it rotates 50.0 times x5rqy c7u,we jo ul48,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 tightenmy )3//t8qomc9uzcb(omj ;eq ing to a torque of 90 Nm. If a 30 cm long wrench is used, wh/bou/;m3) mz9c o8(emyctqj qat is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening t9m c7klvpz+y (o a torque of 90 Nm. If a 30 cm long wrench iyzk+l p97(vcms used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofusm)oq-;.0 mja g mi9s 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 asny k.rl 50 3(pg+kk)y(mhhqoz follows: mass m is at the origin, mass 2m is at x = a, and, ( rgop05lk(hh +n.kzmy)k q3ymass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass l,4x/2me wqn cg1t8ku10 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 around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) Whnm,k8c2q u /4tlg1xweat is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is9xhbv50 htd*b9 fx j;5i td.rzqfd/ u1 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 around anotdbb0 ti9xtq5dd u;fhz *xh /195j.rfvher 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. Thz13vs jgegv *gn8u7: qf6lc)pe rod is initially held in 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 abougqpgl*jv1e gs38fz v:)7cn u6t one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and masu2ynx t7fa3f7; / mu vdff+cn6upb-- ws 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a-7f;y+n nu pbd7/6 xfvfm 2u- wauc3ft 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 ,.nn8wflkem)hari r* o.8 xy 7around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is 8o iy)n 7*8hnefklwrrmx.,a. the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrlbjk-/l x);n:ha sl h)1w2k erapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mass?a)/2nh-kl1ll)k rswb;jx:h e

  A rotating flywheel canrpy4ieebxfg k5 )6d7, be used to store 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 ijm+ zq(- am/+lia ve3jnertia 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 ah3 :xco wgrw 1k;bs-b-8nho g6wrd/, end radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high incgrhwx:83e/n kb; - dwbh,ow1rc go 6-slined 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)9xcbo1/ w f7awb b2fs with a speed of 10 m/s. How high up an inclined plane can it climb before ccbw/2 bo 17af)9sw xbfoming to rest?

  A hoop of radius 0.50 m and a masmpm 6z75g, i xsjgwy8+s of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is5jg7mwi,y s g zx+6pm8 it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mas,)ee:3sv3xr ncv hgxaz o22k/s 1.5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. Thazh32k: o)x2, necxr 3g/sevve 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 cgp(ew 8*gfy)maa, j3mhanges 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 d kory6 9cfk/)z-d +cg$5.0 \; kgm^{2}$ 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 mox46p6 3j+uymlky-hpg , yn2 vsc9usf;ment of inertiuhlpu9f-j p26 kc4;+xns6g vm3y yy,sa 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?