Angular displacement is usually express in unitlmkmji8(5 x 7p qc1 a2;4p6,cjzdmmk cs of

  Angular velocity is expressed inz0.wyl*2ik nmjgvt4 23 4j(v sz++ghw+ ssib j units of

  Angular acceleration is e6at+)a 5uw- -xuliqzcxpressed in units of

  A boy and a girl are riding on a merry-go-round whi7t)+h/aam45as a dzs mch is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the4a ma)zha/7dts+m s5 a center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a /vqse* r 1rf(wconstant rate. The boy is near the outer edge, and the girl is closer to the center. Whv qr er/f1(w*so has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constanjk*tx.co(sk6 +wd g h vc8t98ft rate. The boy is near the outer edge, and the girl is cltc6otsv*xjk.9dc8fgw 8 ( +kh oser to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round whic esr +imat:ubn22p+( hh is turning at a constant rate. The boy is near the outer edge, whil+e(mtup 2rsan:+ 2hbie the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding ax.i fud x dwp6*xie*b (ev;ocga h,716 merry-go-round which is turning at a constant rate. o f.*dgue1 hb7a;dixxwpcv(,xe66*i The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is )bv3pp.w;j,a 6eo kyy an accurate steav jpkpy ,ob .)y63w;atement?

  Rolling without slip 1 1cgd32ank*ku(k8ptvq0 d kx)t5 odrping depends on

  Two equal forces are applied to a door. The firstpny*e8kr2ev-hb r9 uu6 y) d.l force is applied at the midpoint of the door; the second force is applied at the doorknob. Both foby2dl 9 * -6e)yvu8.rphnurkerces are 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 ubsx9rhveu /dc6(ud2a h;qm.1; z w)jis applied perpendicular a .jxvhsdhw m)uq6;beu1(u9z d;/2rcto 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 doorknob, perpendicular to the door. The first fo qfsu7q-u)y8ub qp6. 7yfvco, rce is twice as large as the sqv-uf6 )q u,7bf7yqy c8u.pso econd force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to mihtjny, /ve i (hnq,gn+/ uo8,easure an object's resistance to changes in rotation?,n8i( g,nvju,o t/hih+ e/yqn

  Consider two uniform solid spheres where both hap+udc5v:8sp 2kcpkrn un3c02lvck :) ve the same diameter, but one han 5l0):8ncvpkrdu3 cp p+2 v kscck:2us twice 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 tw- vept4p8lkqwtejvvk*54f2 q5v 3b (1fwzj9wice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smallej *w8w 4et k1z5b(lq pfveftq-4v vvj 5p2k39wr sphere is

  Consider two uniform somv3 .lbm w5c+uoud,e 6lid spheres where one has twice the mass and twice the diameter of the other. 3o6lu, bedc+m.wmvu 5 The 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 t/,;bolm at0sdzm ,s1lhese are increased to 2M and 3R, what happens to the 0ms;otlza1/ smbl ,d, sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an objeu+:4h ujagv y )yth,;mct, that object will

  The moment of inertia of a solid cylinder about its axis is given by npu/s.o hxj76$\frac{1}{2} MR^2$. 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 whefw -b kv14ax kj+hc4(gel 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 bike? Assume the wheels are un( kfck+x- g j4wbha14viform disks.

  Suppose a solid sphere of mass M and radius R rolls without slippinge46 /kyec wim: down an inclined plane star4c/mwy6: eiketing from rest. The 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 dow)wydew-h ,4nqe unv .z:z-k4cn an inclined plane starting from rest.q:-e4,nudycz)- ww4 v e. knhz The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum ofzsco *;gvma(joj -2 i: a system of particles changes when a net external force acts on the system." This sa-i(2zc; joov j s*gm:tatement is

  In what circumstances can the angular veloc1 h ndqg.45 ylrarc66bity of system of particles change without any changgra6.byc6h q1 4nl r5de in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orb9 +m7f5ob6( x2zu)t v ncqitoqit. Ignore any friction which may be present. What happens over time to the Earth's angular +5xufn9o bq6vic qz2()tt om7momentum about the Sun?

  The Earth moves about the Sun in an ellipticad92 wgyk n p+:xsx4io6l orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth aboutknogy 49 :xsx6pw2 d+i the Sun?

  An ice skater performs a pirouette (a fas7r i4qfcazc-j(( e 3riu t-p7at spin) by pulling in his outstretched arms close to his body. 3z jaqe7- ( rfi(7cri4tc pau- What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrzyfho: fncf0c9v2d+szug,,1 6y v c3tetched arms close tsy0z2,1zvn 6 g,vfcoy c3h :9dfu+tcfo his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs afoibx n vn cii4;2646n pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his momeni46f24b6c ninxiv;o nt of inertia about the axis of rotation?

State the law of conservation of angular momentum(pgdk e+sp+ta o, 5;tf.

  What arc length does the Earth travel in a three month perionhgff, x.4xydm n+d :2d in its nearly circular orbit about ty2 x:4,.dhnx nd+fgm fhe Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. ))* bko:dz ymip63d/qvht1 h nWhat distance does the tip of the second hand sweep through in 3 min v)ypm6*nob3/:kdh) hq zdti 1utes and 45 seconds?

  How many rad/s is 25 revolutionslk my7i n lx-v8d5+zpc33jyl8 per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 y l .sar3y4jn mc6 ;;auc)hku6zs03zrs. What is the frequency of the wheel's rotaty;ru3 s;a)jc m3n.zlahr64 kuy0zs6 c ion?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 4+u/ f9ufmxsgkhj4 xhvr+ ht-+0d ff .kHz. The period of its -4+s4 ru 9x+h/x g jufkmtfvd f0+h.hfrotation is

  A phonograph record rotates at 45 rpm. Througul;gb 7jw.m4c h what angle does it turn in 0.20 s?. lgjw7;mc4 ub

  A wheel of diameter 26 cm turns at 1500 rpcvkfn/ ivn f0y,;d;g(;qpu, om. How far will a point on the outer rim movdn ,/po0fgvy;v(fu; q ;n kic,e in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the2:xn-+ps uw8rd 5efs y a:sx58ewyps2- rufn d+ verage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. W z-5m)j vpk(x dcbysmq.0f6n,hat is the linear speed of a point 0.10 m from the cen),ky vnsmzcfm-(xjp6bq d.50 ter of the wheel?

  A cable car at a ski resort carxwzn :j bavw3nr0,y; 1ries skiers a distance 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 puller, :3;z1njavwnywb 0x y 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 ofv6;bg (i+xen 5ayj0l f 2.0 rad/s. Whb+avjg0 (;5 nx6ilf eyat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in jvk dpb +*5 l3s,m)njk86wso mlength. If the motor rotates at the rate of 20 rev/s, what is the app6sn *3k+s pw,mo v5jm8jdb)klroximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating wmj9htf)zke : 9ith a constant angular speed of 2.0 rad/s. What is the centripetal accelerah 9jm )k:etzf9tion of a point on the wheel's rim?

  What is the centripetal acceleration ofc;* 5q8m xqenrlh 5e;u a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 m/c luqm;qe xne 8h55;r*s?

  How many revolutions per minute (rpm) must a circular, rotating space sta20rfw didb 4.9odsz n7ix *tk/tion (r = 1000 m) rotate to produce an *bdd2n xki4fd9/.ots z wri70 artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circu1)bm , 2 dvq1rposat0qlar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal,)rvo1 pqtd2s b0q ma1 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 speed ofmy kd4doc6 o/4wnr- 7hcq1pp8 20 m/s. The maximum centripetakqw p4dnr 18hoc d -y7mpc64o/l 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 stringl(nzehe03x k /, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximuh l/xez0(ne3k m 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 sosz9od9oslt c.2. ll+ lipping 10 m down a la.o.s odtscll99z + o2lne 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 angularuy,qhu+ 1e v0w 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 accelsnf,7hx hv*wj/r7c(5 m3qwn ieration 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 asv7oj s0 fur8+tg3w4ffter starting from rest and acceleratingv3t gur7o 0wf8 fs4js+ at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has d3g-n0gkr38u mai4 e han angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating ngk-p(ad8xp9+xvz w : at 20 rad/s decelerates with a constant angular accelera zwxd9:p+k vg 8n(-apxtion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from restf/66rpyag-e k/3 yz qf and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolut y3/yrqazg 6kp-ef /6fions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly fro*+81 ngvwn fb8xwq mt 1lf9bk5m 8.40 m/s to rest over a distance of 115 m. What is the total number of revwkfbltqxg91+ 8 8fb n n15wvm*olutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over aju2 rt njwn,0mw-/.b y d0 rbm-nt2jw .j wyu/,nistance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly f87ct o9y+bmci27rx r ,ns:vriq*9 fwfrom 8.40 m/s to rest over a distance of 115 m. Hyv c7fw+r: ,*ixc 9n92fs8tqr7m roibow long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotatiziks iv*(w3eluzb71f2poe( s x(k, j/4sb8m uonal speed of 3600 rev/min. When switchede k( (jfuu*i 4vo l/kzpi7bw1 szes3b(82x,sm off, it rotates 50.0 times 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 tig9jl z0u/.w vn r/yf10erz es6hhtening 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 is perpendicular to thezl/j0vyr0.fnz ehe1 r s6w 9/u wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If (6kr/5eyym,vvaep- x a 30 cm long wrench is used, what is the magnitude of the force required when t(kreympx5 6yvv/ a-,ehe force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o 2ht x xsd-hdn3h4*iv0f 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: mass m is at the origin, -* r 1,)ae)b haldeoijms81ce mass 2m is at x = a, and, mass 3m is)ije mbece ) r1,haas8*d-l1o at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is3c*nl7/mi nx bcq41 yc pivoted about a frictionless axis thought the center O. A rope wrapped around the cnq n/i3b4c*yxcl 17m 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 pivoted a gvq cl:a7.2rybout a frictionless axis thought the center O. 7ag .2lvqrc y: A rope 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 initiallzby k+3 3 bdye5a.k2qcy held in the horizontal position, and then released as the free end ez y 3k.yq2ab+cdb5k 3is 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. Neglebfndjul 8*0vsg0 ce *1ct 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, assuming it rolls without slippingsvdbne *0f l801g*cj u?

  A 1.53-kg mass hangs on a rope wrapy*)pf m4+ ald,3tgfu hped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of3h*mp4t,df)g yfl+u a the pulley?

  A 1.53-kg mass hangs on a rope wrapped aroundwrf2pbh*kb;.: o si e. a frictionless disk pulley of mass 7ibf*h e: 2krwo; ps..b.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to store*y3ixkau*xyxcrn)em 2n3 / , )3 gdiuv7. vnex $1.00 \times 10^{6} \; J$ 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 8duxnif9btu;7z0;tq inertia 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 radw vkg9fi9f ob v1d;g5,ius 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 9,div9 wfgf5 gkb1 ;voof the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rtwgx ;9,cz7 ncolls with a speed of 10 m/s. How high up an inclined plane can it climb before co ;ztcn,wcx97gming to rest?

  A hoop of radius 0.50 m and a mass of 0.jk,kg,nh2z ; s20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distzg;,, k nhjks2ance of 3.0 m?

A solid sphere of mass 1.5 kg and rtds fud82a*v( adius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started f*8(uvd ta 2dsfrom 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 cmm ()mhq:1cp n 1iukh8hanges 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 iv o (g+9.ne5sqa+qv/dsj/l binertia 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 rotatih jxx(k4 50jhtng at 5.00 rad/s with arms extended has a moment of inertia ojt( 4x0k 5hjxhf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?