Angular displacement is usually exprecaexe3;,c:xaa4 *mi i ss in units of

  Angular velocity is expressed in units ,z0n- hvj1) (j)tg m0vgsh cttof

  Angular acceleration is emelk n kmw f+oxu5r;d78.0 f;nxpressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a com:kg9b4j1,g o3;o+v6v pnkvzivh np/ nstant rate. The boy is near the outer edge, and the girl pn:,v6v4gvb p19koo3mg ;kvz +inhj/ is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constant rebm-y i0w 8r2fodn14*bpheo 7ate. The boy is near the outer edge, and the girl is closer to the center. Who has the greaopdn -b8 h4b*ym rw21oeef7i0 ter angular speed?

  A boy and a girl are riding on a merry-go-rou w.wu -gfywl,jic4j3n bno0p(*d0nt(nd which is turning at a constant rate. The boy is near the outer edge, and the girl is cln4-jw c,otjg(fl n.3w pw*u(in00yb doser to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a cyk wg o/n w8y;t6fvg; kv432bdonstant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greatwyg64; 2dogfb;ykktnvv w/ 38er centripetal acceleration?

  A boy and a girl are riding a m8m6;x e mi+alcerry-go-round which is turning at a constant rate. The boy is near the outer edge, whill8emi+c6 ma; xe the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that ijb2tevsu:fqsy pg 5 b9:6.7oks rotating. Which of the following is an accurate statemeeo:.vubp5fg k 7:sjts9by2q 6nt?

  Rolling without slipping/ ddf cv*0vdg-z 4:uwa depends on

  Two equal forces are applied to a door. The first force pxwvofdc.p.s6k* -h zv +ba,0 is applied at the midpoint of the door; the second force is applied at the doorknob. xfa+hk.,cvopd wv. sz60p - b* Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The firstv(tbzbcc59 o5 force is applied perpendicular to the door; the second fo 5ovbztc9cb5(rce 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 dqdm t )e6h5:id2bp51w)wh fyqoor. The first force is twice as large as the second force. The rmq d2: qf5d)1 hwy6it 5ehb)pwatio of the torque of the first to the torque of the second is

  What is the quantity used to measure an objectamqgf.;c 68z u's resistance to changes in rotation?g ;6q8 z.mufca

  Consider two uniform solid spheres whxx:q095s esrsittl5 yg *80fyere both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertiats sls 8i yf: 0y5r9etxxq0*5g to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass,c/v5jk 6ca/et but one has twice the radius of the other. Tca / kj6etc/5vhe ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where on9 :( 7yx)rysoxjhl:f6ih,rn)ny uj:ee has twice the mass and twice the diameter of the other. The ratio y:o:(sef9 )h r,n:7 6luyjjix)h nxyrof the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid spherwr4iai1zky c03h-db n-a:omfb4a 0 6re has mass M and radius R. If these are increased to 2M and 3R, what h-14hrmab 0 yki4rf03ic:6ab -oazwnd appens to the sphere's moment of inertia about a central axis?

  If a constant net torque is ak03c, z znvp2zpplied to an object, that object will

  The moment of inertia of a solid cylinder ah v fvlv8+l v l 0qe/efhh6g.yghg+.4xz19b,a bout its axis is given by $\frac{1}{2} MR^2$. 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 wvz3aku:;.5 bx pr* hozhich 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 uniform diskz.va3* xr:5hz p oub;ks.

  Suppose a solid sphere of mass M and radius R rolls witexx q,b) m(h6ahout slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depa b),6hq exx(mends on

  Suppose a solid sphere of mass M and radius R rolls6e vq:ph0wz9xj5ovc; without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends one9 0:6hv;o pqxcvjwz5

  "The total angular momenq0 1z6j aglxur28w.p ;jmx-gmtum of a system of particles changes when a net external force acts on the system1 ;mxrmjx- u6a gq20gwpjl8.z." This statement is

  In what circumstances can the angula ( it2s7+ *oaj7c;snyyik : iwb4l(diwr velocity of system of particles change without any change in tyc 7lbki2 *jtoiw4n+( di(;:s7sawiy he system's angular momentum?

  The Earth orbits the Sunezm21l8q nlf. in an elliptical orbit. Ignore any friction which may be present. What happens1z m.ne2 llqf8 over time to the Earth's angular momentum about the Sun?

  The Earth moves about xxe+ gt 15cf./.tgjd2s h lr4;zkh7hqthe Sun in an elliptical orbit. As the Earth moves close to the Sun,ktt z ;xf5c/1xg 2ejg7lq+h.r .hd4hs then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a8g4k 2axe bxj5ajphyh8.5 5ua fast spin) by pulling in his outstretched arms close to his body. What hapb8 a5 ugj.xae yk825hj xa5hp4pens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling p rxlh9- 35jisin his outstretched arms close to his body.x5h -plijs3 9r What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling iqlex;4:o wigt/oi0o02 h*ptsn his outstretched arms close to his body. What happens to his moment of inertia about the as/l h*:oox0t p w4toegqi0 ;2ixis of rotation?

State the law of conservation ;j-l o4c7kgjm+0ucvfof angular momentum.

  What arc length does the Earth travel in a three month period in its nearqyst e jo ce2i8ht(16h9i; +hi0 qvm/wly circular orbit about tt iht+e/ sq i mo(6 hh9vj2cwe8q;i0y1he 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 dis17f l tzg21(p: rmznqq;;bnvm ,o8kwhtance does the tip ofhf;:m rqzl1 n2q 8gnw71ok vz(m b;t,p the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 rb4cg6 4r zx4pdevolutions per minute equivalent to?

  A bicycle wheel rotates u3lq-fxv dl h;/niformly through 2.0 revolutions in 4.0 s. What is the frequency of the l;3vx/fh qd -lwheel's rotation?

  A pulsar (a rotating neutron star) emits pulses atgf*e, *ds/tuz0b )aje 54otrg d o7dnilws8-; a frequency of 0.40 kHz. The period of its rota7 ) s*t/jgl* iu-adbt r4850;wgs fdnoe,dzeotion is

  A phonograph record rotates at 45 rpm.6rjqz(gc +b i. Through what angle does it turn in 0.20 s?c+rb i6qjg.(z

  A wheel of diameter 26 cm turns at 1500 rpm. How far wilc 17e6u iim5;;sjwdeujuw 86el a point on the outer 6u6s;iiw8ewj1;7e5ec umjud rim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.lzh+b*)4wgsd 0 revolutions in 4.0 s. What is the average angular speed of the wheez+ 4wb dgsl)h*l?

  A bicycle wheel rotates uniformly through 2.0 revol(f*cdfjptx -; utions in 4.0 s. What is the linear speed of a point 0.10 m from thecp;fxdf tj(-* center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8aaylr3m23r ;:7ss sm f km. The cable which moves the car is driven by a pulley with diameter 3.0 yfa;3rrm as lsm73s:2m. 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 z(tpc)6zlgiii cj2; (2.0 rad/s. What is the linear speed of a poinicig i2 zt;c6)( (lpzjt on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. Ifxok k4bb ) z:) u*9gpmiud,6jq the motor rotates at the rate of9) : 6ib,4ko pqmk*ujug z)dxb 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is2+wx;tqu0s) m i wkdz; rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a poin2w ;kq;w+s)0txu d mizt on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter*f9yqx) 1lv qk of a bicycle wheel of diamet)xyvlf*9q1kq er 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station (g(*39t yp1 b5xc igiolr = 1000 m) rotate to51cigx 9l bt*g( yopi3 produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 4)oz4f+ mbz so50 m with a speed of 20 m/s. The maxi4 zsf)zmbo 4+omum 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 radiuq qjc01 pwkjzf0.j8 -ps 50 m with a speed of 20 m/s. The maximum centripetal force (provided bfkjjz 8qw0 j 0p1-p.cqy 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 87tk9t7o6qmbo 4nzn k of a 0.750-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 linear speed can the mass have if the sttbnt9 468m qk7kzono7 ring is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls wit/4z kpgyojz, 5hout slipping 10 m down a lane at 4.3 m/s.j5zok4ypz/g ,
(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 constapj6(d g p ob9dln)e.i(jk,*zpnt angular 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 anc-h4u zge3sx24zi mvl )hse):gular 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 afms exdf8 u/s91alzr2 ,ter starting from rest and aczr u,a18mls2s/ef9x d celerating 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 ann 5rx4whqzt3 j:p i25x/rt2cn gular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 ra qk; 0i-6t4e2khwt dr3gide2 od/s decelerates with a constant angular acceleratioeth;igd-k2r kd4q263eo wi0 tn 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 )m aruog fx;z6u+g(. v6.0 rad/s while turning through 2.0 revolutions. What is tz (ugrf6;m x.+)o ugvahe average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to re 4zo 8v2ru2p/fc-bvp vst over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to restvvz42 u2po- vfc8b/p r?

  A wheel of diameter of 68.0 cm slows down uniformly fr imw(3ke(l f5; a8voww1xjz:oom 8.40 m/s to rest over a distance of zo 8 5wxewa3ki1;jof(wl :m(v 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to re/d/m i 980ba0wzy wezkst over a distance of 115 m. How long does it take for the wheel to come to thez8w/y w i9z/ ame0db0k stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 36vfop:iuae x/l86i3 j400 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before comingp / ix4liju 6v8e3aof: 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 wm o(g;lxed,1nheel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what igln,x;m1ode( s the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel n5s; /4oln bj++poffdrequire 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 applied a +pnoff+bjdn so/5 4;lt $53^{\circ}$ to the wrench?

  A wheel with moment of inertimr5;y pb8:q xja $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mode dji )5 z)y0gmxq+o0wcled as follows: mass m is at the origin, mass 2m is at x =iw) +oj0yxgq)c5 zmd0 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 frictionlesr, 1mij/g6nf fs axis thought the center O. A rope wrapmrg1fji , n/6fped 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 pivoted about a frictionless axis thought ti /c2 rx4tuox9v 6)aakhe center O. Ak a24rat6c xxui9ov)/ 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 initially held in the horizo9m : uf*e.mw ap88*1 tfk 7xdfr3zlgtental 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 roe83mrl.z*ffxat* ed 1g:9tk 7 8fumwpd about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass/fy wjq to;2ea 9yeoj op0892k 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of ra qejp0oo29ayjk2e/;9w8yo tf dius 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 onprj lkcw :0ur*l *ufae*u)iw2v7u6s6 /g e+ jf a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of thecr/kg+eu 2)u*j lw6uu * e 7i:rpj6vlsffw* a0 pulley?

  A 1.53-kg mass hangs onp 8i):kac rx(kd z;.8 bav(khn a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Whaz d)akph8n8i(kxrc; .a (vk:b t is the acceleration of the mass?

  A rotating flywheel can be used tot .ph0l2wf mm; 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 inertia of +( g,baq5:pzz vj, qlv$5.00 \; kgm^{2}$ 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 rol9 f2)t5 dtpihlls without slipping down a 1.0-m high inclined plane. What is th52 ipltd9t)f he speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 k5k5; tciwd*e :pj6frc:w:h a . wwd8yjg and radius 0.010 m rolls with a speed of 10 m/s. How high up an iw .dhric5ek8 d6:w c5;w:*yfaj:twpjnclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest a afd;fy)41 p4pxncuv0nd allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distd1fx a 4)fcuy40vnp;p ance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls wzdt n-dxp r,9,:yr2l without slipping down a 35e incline that is :rtzn rlddx-p yw9,,27.0 m long. Assume it started 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 cy;mbdn,3k0 r yo/fj*m9 4ojab hanges 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 mome0 8kdjtd;wfb +nt 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/ fm0af2 c3ugu2 b+hhb,s with arms extended has a moment of inerti hb g+3,fhu20amcbf2 ua 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?