Angular displacement is usually expresupjcytmk 0vpl /*12f)s in units of

  Angular velocity is expressed in qd(w:barzlc7 mdp -x 0)* 7pmyunits of

  Angular acceleration is expresyp a h xr)/a2)g itzbs870:nrosed in units of

  A boy and a girl are riding on a merry-go-round which is turn iic98j6 p8bxoing at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the grpio c9bx 88ij6eater angular displacement?

  A boy and a girl are riding on a mvg;xm8gsp10x b jw jg pl+27d1erry-go-round which is turning at a constant rate. The b71bd ;g+w2 jpx j 8vpg0mlx1sgoy 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 merrx j ri-w-oy,/e):qnku y-go-round which is turning at a constant rate. The boyjo)yr ,xi-ukwe /qn -: is near the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a mer+sl 5uo z8g5hxry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl isgx 5l85hu+z os closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round whibx ,zz/ qns z74 h15xvm-+chc,styo6wch is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the goc7,-, qh/+4m v5bx h6wxn yzs1zzctsreater tangential acceleration?

  Consider a rigid body that jd k 70)1v usjudd1tmnc mf(5,is rotating. Which of the following is an accurate statemenj(ksjfu mt m5ud11dd,0c)7v nt?

  Rolling without slipping dependsux,c0w * rvq+ zzbokzk9 s01)f on

  Two equal forces are applied to a door. The first force is appr7adep, h5ow r8 9a bm--uyl;glied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to trpuwm75er g oaba;-y8dl-9 ,hhe door. Which force exerts the greater torque?

  Two equal forces are appzt b,r0q5 i.ttlied to a door at the doorknob. The first force is applied perpendicular to the door;t.i0 tbtz, q5r 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. Thjs2 rutc8 -hq;gg9wb ,e first force is twice as large as the second force. The ratiqg,wgsht9r- 8u b j2;co of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes in ro+pzwci oo:8 cmu q/d6+tation?o+:6pu /cqm diwzo8c +

  Consider two uniform solid se, t+dq :l9voiwu ,/ippheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger mo 9 iwo,uti d:qpe,/vl+ment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, bqq) o6cdtg-t; ut one has twice the radius of the other. The ratio of the larger sph; d-otcqqg)6t ere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice th+u/)gd kbh/b) qvmp)z4iuo,ve diameter of the other. The ratio of the larger moment of iner/+mhzb)odu)vq g4p,ki u/) vbtia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increase85)p(os3ekdvml5q mxyec k43 d to 2M and 3R, what happens to the sphere's 3c o(x4k3skm8vpy l5 q5e med)moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wilo(ya 7z)0m8 awlug;vgsg-n q; l

  The moment of inertia of a solid cylinder abomcq.bo( s 4tnmse5 sb0vvek+y (a2z.7 ut its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translatm+ n7c(e.s2bmeskos t b4zqv.(yv 05a ional kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel (q,0whrmu2ml:cwx pvk 5 v: kh, q+gb.of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energw,vrq+ 5 vwh q0hkbxm(u,kcgm:l 2.:py of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of m0j-,s-y bjdm;ujdyy 65yty:mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity jby;yy-j:djtud0,msy -m56 yof the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls wit pb vwcu. -h,x:-vr*wqhout slipping down an inclined plane starting from rest. The angular velocity of -wvpcx- :qv.bw*urh, the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net ewzg92 r1vf(o sxternal force acts on the system." This statement z(v wo9sf12 gris

  In what circumstances cav3 gci*wp ;nb+n the angular velocity of system of particles change without any change in the system's angular momentu p*wb i+;3nvgcm?

  The Earth orbits the Sun in an elldk6:y2r,f8 i,el0kck/ +sm +tqm xu ntiptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum au0n r,fm8+q,+ kl:k cmt/tykesxdi6 2bout the Sun?

  The Earth moves about the Sun in an elliptical orbitaar -y//php+ c. As the Earth moves close to the Sun, then which of the following best describes the orbitic pp h-/raay/+ng speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast 4.no,chr9z ,xjk( depx59ycgz 8t) ptd(n, sk spin) by pulling in his outstretched arms close to his body. What happens to his angular )jkxe ,k(zdc 8 gtnp,tr ds4npx,zyho59c (.9 momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) bddf9+.qyg7 fellx3f6* b nr g9y pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about th* x dqgf fdlb.l6r9 ye39ng7+fe axis of rotation?

  An ice skater performs a pirouette (a fast spin) bovi-ku0j2(j xr5 icp0y pulling in his outstretched arms close to his body. What happens to his moment of inerx0ck5iprjj-2iu (o 0vtia about the axis of rotation?

State the law of conservasa b0xqhjx h *f :/zg(ug+24iation of angular momentum.

  What arc length does the Earth travel in a three month period in ; edco;2t. dqdits nearly circular orbit about the Sun with a radius;q. td edoc;d2 of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a le9 pik+a pqg7 (i9-clqjngth of 0.30 m. What distance does the tip of the second hand sweep through97kqgjp9 l+(acipi-q in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minut fep a:kz9r8r)e equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in mogbbb u-bl8+34zjz kt* xj.44.0 s. What is the frequency of the wheel's ro 8obxt3+bb.kzm*u4 b-lz4jg jtation?

  A pulsar (a rotating neutron star) emits pulses at a frequenc+5cyxgd/mj p 5y of 0.40 kHz. Thejd 5c x+/pymg5 period of its rotation is

  A phonograph record rotates at 45 rpm. Through what a0do1dmkq ig(d3pk5 m)myg1/a ngle does it turn in 0.20 s?mky ad0km( q) o11g/i 3mddpg5

  A wheel of diameter 26 cm turns at 1500 rpm. How far will8m-g(wmdy mp3xwiq4 bl*1r1)go4 pdn a point on the outer rgrmpw* -1lqbo1ym4 4gpimnxd(3d )w8 im move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is sgnm2 ,1g w0hey1/solthe/1 mhs0, ye2gong1wsl average angular speed of the wheel?

  A bicycle wheel rotates un wc9nl 9(fq)a-v 2*ec4it nkzuiformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the cente-qcn9uafc 2w *vkln9)e 4t(z ir of the wheel?

  A cable car at a ski resort carries skierse ,c3jc j(x f*uing94b fri1t;flf+;jkc3/ dr 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 trip in 12 rul ( xi;j/f;9fcfi+n1 jr* b3j c,t4fgd3kecminutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed ofbv(.otj5smwbz9k19mb ;n4.w ukk xy ; 2.0 rad/s. What is the linear speed y;;m9bx9otk(nwz mj.w5v kks4b. b1 u of a point on the wheel's rim?

  The cutting cord on a gas-as-g wlt-p(x9 s 0 d:-p9gfrffpowered weed cutter is 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 ot - l 9f:aw0rs-pgxpf(9-sd fgf the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 r 4 us319versrz(nbhe gp338lgad/s. What is the centripetal acceleration of a point on the wheel'seznb3sv 3hg(9sg e4rp83lru 1 rim?

  What is the centripetal acceleration of a point on the perimeter of a bic2. roga;gvgu2 ycle wheel of diameteg2 ;rovaggu.2 r 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm):cznfzvan +: / must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity onczn +z/fa::v f $9.80 \; m/s^2$?

  A car is negotiating a flat circularssh-jf9 h0 hrd/9d- sj curve of radius 50 m with a speed of 20 m/s. The maximum centripetal forcerj/hsfd9d0--j9 shs h (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 speefv-y /d1zn7 ysd of 20 m/s. The maxi/yndz y -f1sv7mum centripetal 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 0y -d*sc/i8bh9a qo* udeh6 eq0.750-m string, is whirled around in a smooth level table. If the maximum tension that the st*9-b/ yo6i ed0hcsadq8u eqh *ring can withstand is 250 N, then 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 9.0 cm r3dfao( 0*rn zhsyn(l3pq:a- kxo o:+polls without slipping 10 m down a lane at apn* qa-:sfp 0l r k3hox3(:yzd(+no o4.3 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 accelo)ggsme11 (.gir,y cm(e b8jeeration 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 an kpw)2p.urq g32j d4okgular 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 after sta:/kow *zpde(v:6 ;k9 vygwmo arting from rest and acce pwv: k dyemgok/ ao(;z*6:9wvlerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest,mb-6b d5m-01vmbvh1)p n p hnp and has an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s deceleratesjv-d iljecm 5*g,9 75pqrkk2v with a constant angular accelerat ivlk9qc7v5-,k jejd2p rm5 g*ion 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 m 0(l f;;ysgxx,,xx ftspeed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angul xgffsx0,(;tx;mxl , yar acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from vwfwxmmy. f-e/h/. r/8.40 m/s to rest over a d - wh./fvmyrm/x /.fewistance of 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 uoeq*h+9b p3lj 9a/jpt8hu+ jfniformly from 8.40 m/s to rest over a distance of 115 m. What is the angulaoja99bep qut8hj/hj lp*f+3+r acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from l1uwz xiybbv :(u)0k; 8.40 m/s to rest over a distance of 115 m. How long does it1 zu xlv ykw:0u;b)i(b take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 hu2ma pjyhhl/15:)jzwwu6u +0j,xdcaf5vk4 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming 4hjdcu2hy :k1,)+wa / hxufua jm 550jvz6lpwto 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 tightebh rm 1,mcgoiw/ 5l-agl1;c/ xning 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 perpendiculr;w m,15/i1ax-o/cghg l mlcbar to the wrench?

  The bolts on a car wheel require tightening to a toucyx/ a wpx4/ 81t9qpsrque of 90 Nm. If a 30 cm long wrentps9 /u/wq 84cpxy1 xach is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in5e+swcwp16x x ertia $3.00 \; kgm^{2}$ 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 ut o71:,ln wytm is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment oyt wnlo1 7:u,tf inertia about the origin?

  A solid cylinder of mass 10 kg d i5h5 m26eh 6m 86j2bnkygjqpis pivoted about a frictionless axis thought the cente28hy6m jd6kjnqm epbi6g 2h55r 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 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 frictionn,tic)+ ec l0rless 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 another section of radius R2 = 0.50 m exerts cln,t ei r0c+)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 initially hea s(bi5j 2ssa.ld in the horizontal position, and then released as the free endsas.b(i a2js5 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 masw3 u (zb8yitgqv66 p h(26nbips 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 speed does the wheel achie ph2bqp( vg66u6b83zw ( yiitnve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk p,ta-3 oufva eueq)9 7julley of mass 7.07 kg and ra7vue3 a9fjte a-uo),q dius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped ary 1tq7d-7,ynw qigh7ed y.pw;* toyc6ound a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Whayg diy6wydc1w oty,*; nq.pt77h7e-qt is the acceleration of the mass?

  A rotating flywheel can be used to store ener 8meu p:q-usu:gy. 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 oz.rcwk9 rpw v 3ko(e-6 b38nk:-rxdedf $5.00 \; kgm^{2}$ 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 fi h8;2wj)mvi(t:m ggzrom rest and rolls without slipping doh2m) mj:gvtgzii8; (wwn a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mazc -, zpz8sfm:ss 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb befo, 8zsp:cf zmz-re coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is r,cu ipcx4i8v7eleased from rest and allowed to roll down 84xuvccpi i 7,an inclined plane. How 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 without s*ji rsqz mhkvm/96e8 oj 8gsi7fjxa)6p .n1(xlipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment orn p67j8 6qamosksxv fhej /z(8 .)im9*x gj1if 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 momentugrj s( kzuhmzd7), 3:+y8qb bzm changes 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; xgevoz ;/s+jlj :u6zxyf 1zpip./o0 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 oki hp2o-kj q ;r02fai8f inertia o 0h8kia2i2;-ko rjfpqf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?