Angular displacement is usj+v+dm7n9bvoycgs al(/lx b h)nw( :/ually express in units of

  Angular velocity is expressed in unitmf e;.5jgj, mp3r nm8*;kxhsns of

  Angular acceleration is 6gg r46:szcbl expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning * 1jp7icqvyc7 at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater ang 1cqvpy7*7i cjular displacement?

  A boy and a girl are riding h:bwb6uv+q+ pon a merry-go-round which is turning at a constant rat v:u+p+q6b bwhe. The 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-round which is turning at a constk. 5:tyozoi.w23pu ds m*zh. dant rate. The boy is near the outer edge, and pz h2kmowid. :s.o5*yzt u.3d the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are ris5f: *q8srgw51b8jp/fvih +yon/mr oding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to b rv1 n 55j/+o :/r*qsm8h8fpowigyfsthe center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a-g1uh y c8c2rbr1oj e2-h a)fa constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the ab-a rhrhc-ej1 f )2cug1 8y2ogreater tangential acceleration?

  Consider a rigid body that is rotating. Which of the follfpzb1 gqj3w /.owing is an accurate statement?.3 qw/zpbgf1 j

  Rolling without slippingim6jp+n q 9)pr depends on

  Two equal forces are a3m (mmvhmzo6e07 nr(xpplied to a door. The first force is applied 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 gr 6vz er(xm( mhm3mno07eater torque?

  Two equal forces are applied to a door )q vew ds)):oiat the doorknob. The first force is applied perpendicular to the door; the second forc w:)ise) )odqve is applied at 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 firs de*l(/*ore 3p /yexz/.32exi,g mjpuxazm h8t force is twice as large as the second force. The ratio of the torque of the first to the torque x*d,x a/gee yi/r* 3u o zee8m h2j3x/.mz(pplof the second is

  What is the quantity used to measure an object's resistance/krkb9t 4-a1eo oi/fl to changes in rotati4 t/aeo k-f1/9rlibko on?

  Consider two uniform soli i,;4iic .bi0 8kanqifd spheres where both have the same diameter, but one has twice the mass of the other. The ratio of tki.aii 4ic,bn8; fq 0ihe 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 ra y z5mcog*fi,y0t:v j tc+su:t:76mxbdius of the other. The ratio of the larger sphere's moment of inertiavz5c m:g*uto yims0: +yc bf:,6t 7xtj to that of the smaller sphere is

  Consider two uniform solid k4lci i-x89xa spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to tkxc 489l ix-aihat of the smaller moment of inertia is

  A uniform solid sphered 0l o3zk:owygrkl1i 2v-(- ox has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central a( y-rdvoil-xo0lkk 23w1z:go xis?

  If a constant net torque is applied t. cpp2w0(vzuk(alb tr)6it l5o an object, that object will

  The moment of inertia of a solid cylinder about its axis is given bye ;0p ;hhut++j x8j9svxuw cw; $\frac{1}{2} MR^2$. 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 which has a mass of 10 kk d i5h)d*im,mi8f8 ujg and a radius of 30 cm. What is the ratio of the rotational kinetic e )jm,58dmfk d*8uhi iinergy 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 ax( 9nhmpr-;rizxdvl )he2 :) xnd radius R rolls without slipping down an inclined plane starting from rest. T;rv (z:-rn hlx)xx9 ip)dmh2ehe linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping 86ntzy mcwz9e j5aj;v0ioo2:down an inclined plane starting from rest. The angular velocity of the sphere at the bottom n8te 0wm5vi6yo; oj:z9ajcz2of the incline depends on

  "The total angular momentum of a system of particles changes /i25finom 9 ddwhen a net external force acts on the system."ondf/ 9imid25 This statement is

  In what circumstances can the angular velocity of dai+kho3dc*je g ( 7v2system of particles change without any change in the system's angular momdv7ce2ig od+ hj3a(*kentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any 94gxvp q)7cw0 jpza6j friction which may be present. What happens over t)jp79x64 zpw cagvj0qime to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Eartu*:tui5,tuj67oysp fqk if/ /zoa ;b8h moves close to the Sun, then which of the f/67iou,abuj/p y5 qio8 t*ztffk us:;ollowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretche : z70crwaq,yz n6t j(qszp+lv03mmf*d arms close to his body. What happens to his angular momentum about the axis of sc0zy(t0m6,3*zv+:q ma7lnf qjrpwzrotation?

  An ice skater performs a pirouette (a fast spin) by ph/0i kgg1jt7je5z m2 xulling in his outstretched arms close to his body. What j5/zehm2g7jk t 0g xi1happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by puwifls fijm 1m.)c,02xlling in his outstretched arms close to his body. W m.jwl1x f2c0if)mi,shat happens to his moment of inertia about the axis of rotation?

State the law of conservatp3ozya59e ( wsion of angular momentum.

  What arc length does the Earth travel in hvw r 2u,1;eqzw4f po+a three month period in its nearly circular orbit about uvwq wrzp,fo +e4h ;21the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What d(jqmcci0 :y6gmud69a ue ( v7yl 3fwi2istance does the tip of th7mjya gu:u3vi60f cec2mdq(6l( 9ywie second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivaleng;ac(. ,rnn .5jdcxq xt to?

  A bicycle wheel rotates uniformly through 2.0 revs +/dky e,-6-jkmh dh4lhq:lrolutions in 4.0 s. What is the frequed, +ds lhkl-ekq 4h/mh -:jr6yncy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits puveh lme kyn;f fb642(1vj/q4plses at a frequency of 0.40 kHz. The period of its rotation isl (e6v; jm fvpfq2byn/ ehk414

  A phonograph record rotates at 45 rpm. Throught u9z/,ceucl xp6g -shb4f v,3 what angle does it turn in 0.20 s?g- 69cx3u f t,ep vbzuhs4cl/,

  A wheel of diameter 26 cm turns at 1500 rpmqfl4u7k(z ne7* 8m p 63sozdip. How far will a point on the outer rim move in 2.1m76u (o3 d4iezz f8sq*pn lpk7 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 zzw9ovb 3p( l2ftdn 80s. What is the average angular speeto 83wzf2d nb l09v(zpd of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions iy8pv/ oqr62 d fq5)zvyn 4.0 s. What is the linear speed of a point 0.10 m from the yq68f zo)5vyv/ rdqp2 center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6. r aa,;dwk5qku0wr)a 68 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 fakdr 5ww 6)k, 0aur;qaor the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constamg fzx12*nsx6 o0u o5drz1hps;m .1zjnt angular speed of 2.0 rad/s. What is the linear speed of a point on thejf51 xmz. sr;hxm20 ogznod *1u 1p6zs wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the motorvq,lq ; mrl3/m rotate mm;3/,r qvqlls at the 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 const1vbrf1hn) l0d ant angular speed of 2.0 rad/s. What is the centripetal accelerationrh1bn 1dfvl0) of a point on the wheel's rim?

  What is the centripetal iy10/csb566bm otrms acceleration of a point on the perimeter of a bicycle wheel of diam imt/5obb6sy1 r0 6csmeter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute s;*1twpkvmj 7f,byp1 (rpm) must a circular, rotating space station (r = 1000 m) rofs vkt1,w *b;7pj1my ptate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve/in8 x4nbd1a cv5q )smx *qf(p of radius 50 m with a speed of 20 m/s. The dfqi4*nqm 1nps5cxx /b 8)a v(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 curve of radius 50 m with a spei 2-kkkysk 8*3vif fd r)tg) n3uj7z3ped of 20 m/s. The maximum centripetal force (pr 8yfisf 3)gdtzk-jk373pu*vink k2)rovided 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. l;ffi9;6z1yzo pk/ryws k65g750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linea 6k9 skwy f1/r;oyg lf6zpzi;5r 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 slip+n-yr(tftog 8, kh1 myping 10 m down a lane-tnm+,1 h (grtyok f8y 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 anlkuxa w ,.v+;zgular 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 constant angular acceler05f/d:pm6lm d,k cv shation 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 startin.pxz15b 6fqbng from rest and a6xf zb5 1.bpqnccelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelerav46f7y prjm3w6 /hopation of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decel;uskmv2.5kz1 ibo(+ ui jgr4perates with a constant angular acceleration of um+r(i.ub25 zok s4pg1kij; v$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rae.i* dv/fd+ wod 8ak(est and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. d fkdao *a.e/d+(iw8 v What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down unwivrv/ -sgun0 +p4)s giformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wvin rpss-+g4guv 0 w/)heel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/5d xo+gsa;43fcaiu c1 s to rest over a distang1duaaf5 4x 3sc+i;c oce of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m).ac*0 / xddpdjk9km f/s to rest over a distanm.kd)*x 9/0 dcfjpkd ace of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory r ryog/xzcpd;:tc at74h n90u ,otates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a9t,au :ohxg/np7r0tc4y; z dc 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 toy0y77hn rbx 8h4.n ixurque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the 8nhnh7x ibxu y0r. y74force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tighte1rf uj8.7wg -o3wtk zq4dp g+rning to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forcezp4k8wwqo.d3jutr- 1gf +gr7 applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ay8ihgfvw0 m).g , -ywinertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as f) h5s0.r3uwths zp:dr ollows: mass m is at the origin, mass 2m is at x = a, and, masrpu)h:s .d30tzr5 shws 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10hl nl3 can rsy)18 9g )r0hj*- v:usirkux+zs) kg is pivoted about a frictionless axis thought the center O. A rope wrappe nr :)rl -n*1l0s+89)v) guyhs rsiuzkjaxch3d 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivotedoeam4:; c r7rybt:rp1 about a frictionless axis thought the center O. A ro: ry;7tmo1r4e:caprb pe 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 end. The rod is initially helf,p .e5hmcfl2ni8ml 2opfv9- d in the horizontal m52.29- hlfvcoflpmef, ip8n 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 one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.u 6y ecdbvz2x jh -e5*y*8+sml5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sproeyec 6ux hs +zv-mby2 dl8*j*5cket 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 ex my)m ,f50l:ag/dtdmass 7.07 kg and radius 66.0 cm. What is the angul, 0f g)5dat /mey:xdlmar acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionles+7fwmo6aiy v.7 q ov 1wv(;obqs disk pulley of mass 7.07 kg and radwaqvi+oq(.w7vyofv 1 o67;mbius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required m q3 ,b.y8a,jkwonm,l q 9gt(uf8xj/k 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 ofr * yxjw7ou5/q $5.00 \; kgm^{2}$ 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 y 4ct9xsi(a5k6 0eqbzh*ey*zbd;j) iradius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclineia k )4j6q bybye9c 0xhz(e;*szd5i*td plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls 9b/9qok v- wrjzy j 6efp721dkwith a speed of 10 m/s. How high up an incfjvk9qyo6wb /r- 2 9e1pj7 zdklined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is releasedk85.tl*a s3a pft(vm.-wp ru l from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 5mr3 f(.. awakl-*ttspuvp 8 l3.0 m?

A solid sphere of mass 1.5 kg and ra c f a3ol:qfbp+:nvd3ko9ko-7dius 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 sphfoko vcn7p-9a:bodfkq :+3 3lere 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 */m vyaysr+/r 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 moment6v u*axm//d-ylfbn s 1 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 acvi osts,vh 2 t-g-p+2 moment of inertig- -vpstis2v+o cht,2a 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?