Angular displacement is usually express in uyyh*y3+3n)lrew bhsfz)im, 8nits of

  Angular velocity is expressed iql4so6j 8ns s4,qcn2n ug;5tau )n2 pkn units of

  Angular accelerationw;wcbv s7na ,y b( *5de20yrlx is expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constan:10tfahc z:ne /p,l4yh joe9ot rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater / j4oz1lhey 0aeo h:fc9t n:p,angular displacement?

  A boy and a girl are riding on a merry-go-round wh/8 o7n,7tjrznc5u fan ich is turning at a constant rate. The boy is near the outeo7zftna8c5n nr7 /j,u r edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a xe nc.z(hbzamuju8kcm ,. :p 72-zw,z 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. Who has the greater linec b.7mkxn2ah8mzw uzzjeu. ,c-(:zp,ar speed?

  A boy and a girl are riding a mslyy+r+on8ls1c(j-fwz64 ea l l1x 8 xerry-go-round which is turning at a constant rate. The boy is l fllosl81csx+ 4exa w+ ryj8y (1n6z-near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which isz3bku)e k od qx5tt9+dy6 3ys-4mt tc- turning at a constant rate. The boy is near the outer edge, while the girl is closer to the centesxk z3-5y6t9o dmbc+tetd)34qtky u- r. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurate e,wn) 6qm1 ex58lgcwb sta5n,b 81wqe c)e6xwlmgtement?

  Rolling without slippingn (,oc9/z 5jr 8no qneakf+ lgng/i8z- depends on

  Two equal forces are applied to a door. Th arsuhi*tgyhd-w5mf* 0k0.z + e first force is applied at the midpoint of the doh*fw 5u+ir*m.-g0s k zthya0dor; the second force is applied at the doorknob. 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 fo,l- vz5zci8d1w ic) jirst force is applied perpendicuc1 5z)8 -zd,wvjocil ilar 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 doorknob, perpendicular to the door. Thkv0 1o;8/r fiyq*,2 azgo;upjh1dq ple first force is twice as large as the second force. The ratio of the torque of the first to the torque ofuqvf1,;r1;2o 0i 8 oqzgylp/ jpdha*k the second is

  What is the quantity used to measure an object's8m0ua/rv06 dsi.7sf gc( ms tu resistance to changes in rotatiof078/uus agvc(m0.ids rmt 6sn?

  Consider two uniform solid spheres where both hwot wn tl260,fave 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 moment of in wotfln2,w0 t6ertia is

  Two uniform solid sp2st0v-w a, w5fbaix8n188 ooq+ear qpheres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere io5 8 1b oa88wqxs eva0-iprf,taw2+ qns

  Consider two uniform solid spheres where one has twicec(k svns+dl16:lh: uxl 3y wm) the mass and twice the diameter of the other. The ratio of the larger moment of ins ud(+1 x :6snl whc:kmyvl3)lertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these a8;u b5rpk+ yf)*p:fowf8b nrare increased to 2M and 3R, what happens to the sphere's mom k* yaffp+brnp:u58of8r w;b)ent of inertia about a central axis?

  If a constant net torque is applieuzd*,6 fs*t,hur pmp+ug9 nx*d to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0m4fmi .mdrkgfqqw 8wf5 r w3rh4,f2: $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcyclem3wqk5 5k5g 2xdc vy5 fgbhq0)47 htna of mass 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 the5m )5qb5qhhdw0v 45ky72gc ax gkt3nf 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 slk*+m,d ;ig/xk9k 5tkafaxq8j ipping down an inclined plane starting from rest. The linear velocity of th /; jtadxmfaq59k*8 i,k+xkgk e sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius aj*x+niq(qp8k-t, ls R rolls without slipping down an inclined plane starting from rest. The angular velia kjx (sq *nt+8pl-,qocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net ex g ubimsl1jps5:k68 8dternal f p1jml8bi s5us6:dkg 8orce acts on the system." This statement is

  In what circumstances can the an:4kdb*ks- be ugular velocity of system of particles change without any changeb ks-*ued :kb4 in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. I :f; cfep om/vje8:(1wipt ri y+tk2l-z ,vyw8gnore any friction which may be present. What happens;w1 ey8/cjtyoike(rp fmv-+8,ftwz2 lpi v:: over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth mov6 4mtxi5w lhs-es close to the Sun, then which of the following best describes the orbiting speed of thx-ts4w6i5 mhl e Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstre0 *jtm+lwh*las+k-u ,asuhr 8 tched arms close to his body. What happens to his angular momen8*,ua+slas l-*h+mt ju whk0r tum about the axis of rotation?

  An ice skater performs a pir;p n n 5/8 3fsrjnuk+acwq+9zjouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetz;acn93pnj 8k++/jw sf 5 qnuric energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullign56ghzfz , .xhfrj3/ng in his outstretched arms close to his body. What happens to his moment of inertia a5f.,h fngh 6z3zjrx g/bout the axis of rotation?

State the law of conservation of angu;spuaokm 6m n58fufz+ dj,z9;lar momentum.

  What arc length does the Earth travel in a three month 2z 4ve5j uf1roperiod in its nearly circular orbit about the Sun with a r5f1eu vr2z jo4adius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does thaed spz5g393 ae tip o9deap z35gs 3af the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minutnej7al z* *4ce,l7mu xe equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is * hb/ l3ckoeq1v r/;w oak9br.the fr;1e3k.9wb clv obq/rk*/a orhequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at1(rjuuwv0 k9 xk4o0r x a frequency of 0.40 kHz. The perk r xku4(jx090ou w1vriod of its rotation is

  A phonograph record rotates at 4bobp05h ) ax2k5 rpm. Through what angle does it turn in 0.20 s)0ba b k5o2xhp?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a poinr8q m xqv8nq:)3hgd2o( *vao it on the outer rio2)xi q8(qvdma:rh*3 o vgq n8m move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What ised1,nwl)iv v4wdjxj77yu .n , the average angular spee.1,,7xi d4dy e)jwlv uw jnv7nd of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutihoi:tm*yqx4v8: l gd 9ons in 4.0 s. What is the linear speed of a point 0.10 m from the centehgy9lqt mix8 4o:d:*vr of the wheel?

  A cable car at a ski resortj0kj4 9e- s 1bwi*uori carries 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 pulley rotate for the cable car to make the js 9ijruwik *o14-be0 trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed6iq;98 fahgto of 2.0 rad/s. What is the linear8aq;6oh tifg9 speed of a point on the wheel's rim?

  The cutting cord on a gakpoit*v0 g ko3.xva7 1s-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate line.k37*oao1gvtv p0x ik ar speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a mcop/sj;rxf f 2u)(1hz-vh4qconstant angular speed of 2.0 rad/s. What is the centripetal;vprf)xqzh/-m 1fs2hc( oj4u acceleration of a point on the wheel's rim?

  What is the centripetal :d.zd)rjlr b *(+kzzsacceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm w sz(.z*)d+zk: jrbrdl hen the bike is moving 8.00 m/s?

  How many revolutions per minute (r.z.b8: n v,cvapvcq .rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial graa:z8.v pr c. ,vb.vnqcvity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 0ef1hdgw l0nxmx-. /f50 m with a speed of 20 m/s. The maximum/gfmf.ldw0 ex0hn x- 1 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 w1cxi- 1dw x4eoith a speed of 20 m/s. The maximum centripetal force (provided by static frictio-xx14 cwedi 1on) 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 whirled:ao0+oc rt.s wnw tb(4 around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then.ronw0:(+bts t4 acwo 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 9s my0:26 h4,lzdu 7h1bkhzyom .0 cm rolls without slipping 10 m down a lane ad h1 0hykmy7ob4 lzh6um:z s,2t 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. 3oh 1ums( 1uhtzs5xagle5v * constant 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 angular accele3qr;h2vvzg.e7p 1y2sx l tjl 4neh/i;ration 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 startin5 vdxokh,fo+ut lj8/2 g from rest and accelerating at a constant angular accelerav 5f2/u+,k odoxtlh j8tion of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleratio9itcr .dfx o9,n of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 2+y rdohoobz ) :z79z,dj/ (lfz0 rad/s decelerates with a constant angular acceleratio+dz zz/o:do 7r9(yhfbo z)j,ln of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and re5je;cz2vs (pw aches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the whepjevc;2w zs(5el?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to r/.c *d kwql7jzwg2;b xk)aw jbbp1(1f est over a distance of 115 m. What is the total nu2pf;1w (.xg b k*wk/b1wd )caqjz7bljmber of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.xpqk5 y4f5eajq1 ew:j6vh,x5d0 ;e ok0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 hkd4 v51,jqajx:k0 xeep fqwo65;5ye m. What is the angular acceleration?

  A wheel of diameter of ,3 1dq018uk/apsdwj e,u bmqt 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the 0sk,eb1,w qtu8m/ad ud p31q jwheel to come to the stop?

  A centrifuge in a medical laboratory rotate0h qd 8hss0+rns at a rotational speed of 3600 rev/min. When switched off, it rotdn0s hqh r8+s0ates 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 tightening to a torque of 90 Nm. Ifjncsrl6iyha0 q 3hd,7qq -* )c a 30 cm long wrench is used, what is the magnitude of the force required when the force i3aqhjs -nly*r0i ,qd6 cc7hq)s perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. hmo8k3nv6 s9m tlc; kna 0:i2bIf a 30 cm long wrench is used, what is the magnitude of the force rao s9i6vkc m:20lh3 8mk ;tnnbequired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inert;+5e1bob st+zm 1aq.wbsy8wswl9 bv0ia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mod2 );(bg67vzs oqrjk fbeled as follows: mass m is at the origin, mass 2m is at x = a, andj )s7r2vz; gfo bk6q(b, 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 frictionless axis thought the z cjr ;4tcsjyjk*:9mw i, ao2v5-l7zycenter O. A rope wrapped around the outerczyo *vz; c7j2-sj r9m:a,wlkti54yj 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 piaz35 /jkvkfjbr3p-582splu 9um k ) fpvoted about a frictionless axis thought the center O. A rope wrapped around the outekspf8aj j/lu)up53m v2kr 3zb-5fpk9 r 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 roh0om ::;c yppod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular a y:;ompo0hpc: cceleration 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 e07 vo05w4fqi( yu16rgevz,msovm ,v30 cm and mass 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 spe,oe5 vu0g ,y4vs1zivrf woq0 v7m(6meed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a x3w.70kd - 76-vudnsaqc lbmw frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration xs3kalq 7 n60wwm.udb - 7-cvdof the pulley?

  A 1.53-kg mass hangs on a rope wrapped arom1h5gp8fut + ound a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accm gft1u8op5+heleration of the mass?

  A rotating flywheel can be used to store j9/ebb k.xgg2energy. 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 tkv iq/3.lzh1ez57v/ ;as-fj(wozmf(j gn.z $5.00 \; kgm^{2}$ 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 andmt 7swk p)++y65qecx m radius 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 reac6 +xy5m7msk tecp)q+whes the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a sped6m t 5p4;vhx-bs e;nae,z4dr ed of 10 m/s. How high up an inclineven 5,abthrs4m; 4 pd-xe;6zd d 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 and allow5,a yh kd5,ytkows1 o:ed to roll down an inclined plane. How fast is it moving ayk,s5 oh:toa,y5dwk 1 fter dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping dowr 0b/ai/unfzhp k**qkyq4 m ,8n a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is giveh4/*qy n08*zq bfa,u mpk/i rkn 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 changl:de); 9 ,.c h2 /lrervzygdqyes 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 momenrr2 klmxf6d ( fd81dx:t 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 h 0 g p3)9 snnu;fyb jd7r2m+7hfpoe.fhas a moment of inertia o n.j oh p)dnb3yff+ uem72h79f;sp0grf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?