Angular displacement is usually exp/z w9gc4a2f-v+-m+ mist fcv e4u6tz5aw1msq ress in units of

  Angular velocity is expressed in units9s*e*voh a5in of

  Angular acceleration is expressed ;g)c xpm7fn8kiwek+ d*uz5w 4jz:b2s in units of

  A boy and a girl are riding on a merry-go-round which is turning at a conp*8aos5fp+ silq(0hl z +8dihstant rate. The boy is near the outer edge, and the gaq+i(8z* 8 iss+ phpo0lfhld 5irl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round wbb- rkql:. pj(hich is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Whbl- (jpbk.qr:o has the greater angular speed?

  A boy and a girl are riding on v m1tlvg9p 8(8bu*lg7 tiduz1a merry-go-round which is turning at a constant rate. The boy is near the outer edge7 tv8vmbp*i9z dulgl18(t1gu , and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-roundya7nm+e *7k zlr 0ok,p which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the g7k 0z prk*ml ,yeo7+nareater centripetal acceleration?

  A boy and a girl are r ax7cktzzy5dh 7t8 xe e9.-m*giding a merry-go-round which is turning at a constant rate. The boy is near the gxmzk7tcx- z *y9t7ee a8 h.d5outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotatin fjc :enbe7u2v f3fxwc h68 wo+t0f:9rg. Which of the following is an accurate statemenf8 h7x 2w3n uff0cwc9+ejr6tb: eo:v ft?

  Rolling without slippitqdw:zmn-8 9wng depends on

  Two equal forces are applied to a door. The first force is u1szwi gpy 2rml0/h*+ applied at the midpoint of the door; the second force is applied at the doorknob. Both forces a*y gmhr/p u1i0l2z+w sre 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 is jt:4l7s br-koapplied perpendicular to the door; the second force is applied at 30e to the plane b7k- ljs 4rt:oof the door. Which force exerts the greater torque?

  Two forces are applied to a doorkno0:kwaigu*ptsl *m2,6wcna )n b, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first taswaicp:,n*w lm) 60*k ugt n2o the torque of the second is

  What is the quantity used to measure an objebmcw-87 ;0jm2p sp pet;lr*gfct's resistance to changes in rotation?pbg c7j2sef;mplrtwm- p8*0;

  Consider two uniform solid spheres.8ge gkd:pk gc2wvlf:.5 n 7wv where both have the same diameter, but one has twice the mass of the other. The ratio of the larger momen7 c8 ggl.f2v:pkvn kw. d:gew5t of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the ray. jc vr- fmxdn c17s(0j4f.mddius of the other. The rati0rs7xjm(41my cv.j-. ffcd ndo of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the,7v)v 00/)dfnnf0za rv zngfv diameter of the other. The ratio of the larger moment of inert)fz0vvf nf 0v)ar0,nngv 7zd /ia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If7en9fdjdrl 54 these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central ax4rj59ln7fde dis?

  If a constant net torque is applied to an object, that object t :7r)jwj4syx)r g- lcwill

  The moment of inertia of a solid cylie)qi de83*fa+ 7b3x.qns oih cnder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic eneb3e*.7qe3 d8icfasx hqo) in+rgy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a9; ti0 u)hrx q-vi9 pvjt/cfs1 mass of 10 kg and a radius /ftqh9r9 ;jtp-i) sxiu1vc0 v 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 disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping dk/qz 1(kb t4ljown an inclined plane s4lq /b (ztjkk1tarting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M j03d;tc1 uvtt)f nux5 and radius R rolls without slipping down an inclined plane starting from rest. The angutu x );t0u5tn3cfvd1 jlar velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a*,rgbvxp nkb 7v d ),,t+iqvs5 system of particles changes when a net external force acts on the syste,d+g*, tkbvs pqxir)v,5n vb7m." This statement is

  In what circumstances caq4j. asq1v bw5n the angular velocity of system of particles change without any change in th sb4wv j.aqq51e system's angular momentum?

  The Earth orbits the Sun in an elliptizq-6/y4n9 :ued jukptd 5qln5cal orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the:k9z5dpy n -6njqd et/quu54l Sun?

  The Earth moves about the Sun in an ellipticageinn :j)1x*;g mjgg hsdn*6a (0g1rj l orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about th0;gj* iajg*: ne gg n1d)s hrj(6m1ngxe Sun?

  An ice skater performs a pirouette (a fast2:e2zop6gx i t. l +xxwztb9j8 spin) by pulling in his outstretched armx2 :9j loi2zg8 pe.6ztbxxwt+ s close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin)72(d7w(/cqmw(qhhgto -x wo zd3u7 x e by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy aboutw(tgd c(7 qdqo-(uoxwze2 mhw3hx77/ the axis of rotation?

  An ice skater performs a piry f(ng01az(l uqoj 7b2 r6xl8qouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his momenyax7 ufj2l8qr z(qo l1 g(n6b0t of inertia about the axis of rotation?

State the law of conservation of aww3(ki rap)h (:qf5p cngular momentum.

  What arc length does the Earth travel in a three month period in its nearr1 m9dj deusl n0ujc;c:nzd. )9oooj 5.,9cukly circular orbit about the Sun d)e,z ru ukccc .9mj 5;1sdnooun9o0.:ld j j9with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.3u 3rqteuw k+fdpbuv2,-:;gz ,0 m. What distance does the tip of the second hand sweep th,w2zv3 f- ;uutdkp,g+:b q ruerough in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute .dcyo66k1j idj5o r62a ) hwnnequivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What 2m 7zvwrxt :9ris the fretrwvxmz7 : r29quency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40;ok15igxkv8q g/ lncy 4.x5al kHz. The period of i ;ci5k l/5lx1n8x .aygog4qkvts rotation is

  A phonograph record rotates at 45 r6 n-hkawy el3s+23ksj pm. Through what angle does it turn in 0.20 sjynk6sla-2 3 e3 hskw+?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on tu2- mwbeb 3n hcpc6.n sliw1n813(sjdhe outer rim move ind-hc b1pe1w2nus8j.wl s 63min 3bn( c 2.1 s?

  A bicycle wheel rotates uniforah b u+-y2eq/imly through 2.0 revolutions in 4.0 s. What is the average angular speed of the w +b/yqihu-ae2 heel?

  A bicycle wheel rota nnrna6:thw-4 ))r dvptes uniformly through 2.0 revolutions in 4.0 s. What is the linear sp)wnr)6adpnt nh:r -v4eed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable n ,l eimj r9.1axr x -kmp6sezi:72(qywhich moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the i( 1-7q2rr zkjipae m,:xsy9xn e.m6lpulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angui+ l:dsrb:l qfh 0;:cqhu7-tnlar speed of 2.0 rad/s. What is ;fh:qcurin:d qslh7- b:t0l+the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter ise3. -ifzlohn) ksz ,p; ne(ybgb 7(4cs 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of thz3 enp(4 ge nk(b fblh iz-;sco,s.)7ye cord?

  A wheel of radius 1.0 m is rotating with a constant pj ) g0n6wg9 0nryc7c3ox(ulhangular speed of 2.0 rad/s. What is the centripetal accelerhln xgr79(ucwpjg c0 )0no 63yation of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the peri8)hejau6 5nz43 4jukvw9 kqld meter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8ku w953a4kd 6j)luq4 nvzjh8e.00 m/s?

  How many revolutions per minute (rpm) must a7o1fu ia(j:uaczc4;wc/w4 rg vn q(m7 circular, rotating space station (r = 1000 m) rotatanug7i c:zv c(;jaocr4mfu/47 1qw( we to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat cip8o awfxfgq0ct62a.i3w :2 zercular curve of radius 50 m with a speed of 20 m/s. The maximum centrip30 6a 2ffotp aw8.ixcz2 eq:gwetal 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 5/-z gyz* j ;ahs7dn2nm0 m with a speed of 20 m/s. The maximum centripetal force (providn h*j 2/ mzyn7-sagzd;ed by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached *1f.hcthytr7to the end 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 string is not .7t* rht1ch yfto break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without s7 -5ohhz m*fc)y.yuvrk p+( rclipping 10 m down a lavr.p-)5kc7f y*h+yrum(cohz ne 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 angular acceleration o5 yso(hs(w4f1/g gg(0n vwqoyf $4.5 rad/s^2$. 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 angulars *evwjab su1/9l w8y) 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 k + 6;bqms4snavf,3wcrotate after starting from rest and acceleratvsq;k6m3,4+fb sn w acing 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 accelerationl 6;xks5f 7. y,apxuowv8ccl( of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a constant angular acy 6dyj4 )xfis.ib)/5 bmovh;fi(pv4j celeration of y)mf4b. ij4v)b/ yiosdi6p f5vhj(x; $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of lv)l)/ egxrt8 6.0 rad/s while turning throue) )lltxr8/vg gh 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest oveij 0t4cw7 utt4r a distance ott 0tiu7w 4jc4f 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/l ; p jb)jcxkn5ihrvfx (u2 8;*p9kk(ns to rest over a distance of 115 m. xuk) ;n(; j p5fn28jc9xkri*(vpbklhWhat is the angular acceleration?

  A wheel of diameter of 68.0 cm slowza a4nyd:dfs--j j ,36 (rnqufs down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel nd a suf,fjdj6y--rq34 (za:nto come to the stop?

  A centrifuge in a medical laboratou2 )c,ne2 ;g*emiqqw5g e-btory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acce)tnqqu gegib2emo2,5we ;* c-leration 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 tighte(wl,7s1 *bwsmzw) narning to a torque of 90 Nm. If a 30 cm long wrench *wb1la ( mns),w7zrs wis used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tighte4r)xb8x/ds.x s ; g3 yndanrbxp.x i:3ning to a torque of 90 Nm. If a 30 cm long wrench is used, wh.r4) dadx :n ;x xb8y3xr3/inpxgb. ssat is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine/zo)wx5mf1nn wzr 3 0jrtia $3.00 \; kgm^{2}$ 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,m ;3/gwr: xrxcm3q xl7 mass 2m is at x = a, and, mass 3wr/ l 3;:rqc7xx3mxg mm 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 though.g iyv2hduxy aa--03.*pb uuvt the center O. A vaxg.2 y .u aydub i*-u0p-h3vrope 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.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictqqeni m3 w71vdhjiy i/h. cs8 sk7b792ionless 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 anothw ychbk97smeh7 i8. 13 jnvi/sd7qq2ier 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. The rod is initi5;-rf oy qq )nydww,*qally held in the horizontafy q )5qq n*-yd;,orwwl 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 cmuugyja:(.l0vo :a8(m9kew lx and mass 1.5 kg. Neglect the mass o0o9kyeul lmvx8( a.a u( g:jw:f 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 slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk f 00 vdh- 0fqzkvuk ygg 6fk+uss4a*z b90f,*cpulley of mass 7.07 0kfayufks6,zh*0z * v- d4g090c+gsuv kfbqf kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of 5yhu 5ga)ddlm 13g*a ef2a) iu8q xci6mass 7.07 kg and radius 66.0 cm. What is the acceleration 12camq5aufdyxuedig 6)la* 5gi )8h3 of the mass?

  A rotating flywheel can be used to store energy. If it is required to storeh7b o)c;rv1/ t2kb9 irawq zy5 $1.00 \times 10^{6} \; J$ 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 owrt;mjwpkc9:-ow:::zm( n yd f $5.00 \; kgm^{2}$ 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 r75xou u.lv 8fwjexq51olls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it 8xfq1jev 55wuux.o7 l reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and 134i+i utjkyf8) eq dpradius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane ca fidq1i+k4 etupyj8) 3n 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 allownf ;6hk.-(tgwl8say b ed to roll down an inclined plane. H g sknhly-awtf. 86b(;ow fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls withpm 27*a6rvvokout slipping down a 35e incline that is 7.0 m long. Assume it started from rest. Tvk7*rvm o ap26he 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 c zvzs8. 8(ufr+dlb: sahanges 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 mya i tshe f )hs,gzj1l1,,mwcjx +vv(g.8d)z; oment 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 a moment of in3kxh29, qbn:+adx o t5hnr1vdertia o1t,9 dradhq x+ nhonx32:bk5vf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?