Angular displacement is ut bx 5n ti2cv;c5kg2a+sually express in units of

  Angular velocity is exp x5dr2xwro3z1sx7c l11rpi hl13b in7ressed in units of

  Angular acceleration jovf182y 5x9 n flinpeh9q0 h5is expressed in units of

  A boy and a girl are ridi: ni)tr7lr fx1ng on a merry-go-round which is turning at a constant rate. Thenxr:7t)ifr l1 boy is near the outer edge, and the girl 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 turni+ ,ifxfvv-3i rng at a constant rate. The boy is near the outer edge, ani3+ vvf-i xfr,d the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a conqoj 0rvcr8 ,ilcx. :1e52ijlu stant rate. The boy is near the outer edge, and the 5 olqjr0u, 8 c :x.1lrcievji2girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are ridingq m8gc o/8oth3w yf-v7 a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the cenqfomvyh/8-7 t3 8wc goter. Who has the greater centripetal acceleration?

  A boy and a girl are riding a t6. bf3xw:temmerry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl itew: xm.bft6 3s closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotv- kh6yhc*2vs ating. Which of the following is an accurate statykh* cvh-vs26ement?

  Rolling without slipping depyg.5n.pe3 c0rv.hl ee5e/t nt ends on

  Two equal forces are applied to a door. The first force is appli5qwaov3n-m/ .i5ovvpk8 9zx ced at the midpoint of the door; the sec3xw8 m.avpi-/9 vvc 5n5k qzooond 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 first force is ig. ti69pw:w(o)nkqd applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Whi w)w(k96:ti qid. pgonch force exerts the greater torque?

  Two forces are applied to a doorknob, per iutvwvu:j- gjsg60a v2yr 4e.tr 9r41pendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to gr149u6rsvjt-0 :tvwevr uig a. jy42the torque of the second is

  What is the quantity used to measure an object's resistance to changes in ry0go6fl .m1 9 5wds)bft-elvpotation?e. by- lg0f)9w51ov tplm6fds

  Consider two uniform solchmep7 r; 2c h/do-5ikid spheres where both have 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 inertepo k i7 rhdc/;5hc2-mia is

  Two uniform solid spheres have the same mass, but one has twice the ezsiflet ::3 2radius of the other. T:sf ezi: tle23he ratio 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 5 5 4xfmr:*6fw:0 fhtyn ouvnhand twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of n4 w 0mh:uhf5y :nx6to* 5ffrvinertia is

  A uniform solid sphere has mass M and radius R. If these are /y a+dkg4);11 4gpaqefe qyc pincreased to 2M and 3R, what happens to the sphere's moment of a4qpga1+y4cykpqe f/ d;g1e) inertia about a central axis?

  If a constant net torque is applied to an objeu,/rum - ib 9tnntq;4 ik1pm:oct, that object will

  The moment of inertia of a solid cylinder about igpw p)6mlz 457vl vz1r.xpu. qts axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio w uv147z5pl).mgl6q zvp.xpr of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel +;c .uqdr4ndtbv5 oo4of which has a mass of 10 kg and a radius of 30 cm. What d.4 vdcnq;ot4oub 5+ris 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 massz5t, y rbtv.vt .pi)6t ehq73:wau8jo M and radius R rolls without slipping down an inclined planej .t a6z3t7ur:vto ywhq8,e)5i .tpvb starting 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 slippin3:+a 6oq aabcpswhx,y .*qc3ug down an inclinhqa *36us:cxb3pw+aq .y, coaed plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of ce.n1e*3j7 d ayguc8da system of particles changes when a net external force acts on the syst e*8c1djnaedcu 7g y3.em." This statement is

  In what circumstances can the angular velociv2w+ y4*8fwck.t *rzqhqd/ n ity of system of particles change without any change in the system'sdz*ty+/4 w w 8nhc.f2rq q*vki angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignog)nw+,m7*f pyepf vac0.iqqo + t5o2cre any friction which may be present. What happens over time to the Earth's angular momentmfp, 0yeoqo g7i+) taq* p25. v+cfnwcum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. t*+n( j 5uj yi)vqm*e5r6fc po As the Earth moves close to the Sun, then which of the following best describes the orbiting speed ouji*q+ t6fypove5nmj) 5 rc *(f the Earth about the Sun?

  An ice skater performs a pirouette (a fast spgmu08pf 6t0a min) by pulling in his outstretched arms close to his body. What happens to his angular momentum aboutma g6080 ftpum the axis of rotation?

  An ice skater performs a pirouette (a fau5gou.;2b ea yst spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy abyo.;2uag b e5uout the axis of rotation?

  An ice skater performs a p axn ojq0a8s48irouette (a fast spin) by pulling in his outstretched arms close to his body. 8ax4a j 80osnq What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momen0xc 5b0ea4d7decj v -itum.

  What arc length does the Earth travel in a three montk+h w6hy-s eck g0-o3c.ny6gyh period in its nearly circular orbit about the Sun with a radiuc- hye 0ysgk6. g+nco-3hy 6kws of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has-flm y,wo)rc.e/uydiij1)y ne-4vt8 a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes 8w/oev--yf4t rc)m,1ndl yeii )u.yj and 45 seconds?

  How many rad/s is 25 revolutions per minute e oa r kulbvb:xk581e:rg( z/l,quivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What . gw5hqlzt9z2 h b qgj, -a4ght)v7*pcis the frettaw.p ch945h2lg)g h7* qqgv-bzz ,jquency of the wheel's rotation?

  A pulsar (a rotating neutrots/zodl t76g-u72v),imy 2 uy3uqsj: wci g-fn star) emits pulses at a frequency of 0.40 kHz. The period of it 7u y2zoucy:/ mst6s)3 l 7jgwiv-,dq2tugf-is rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.206cu5 xseie tq*o3tg/5 s?*6g5 eci/to eux5qst3

  A wheel of diameter 26 cm turns at 1500 rpm. How far willw c/vl 8 g8tg+(okbt2o a point on the outer rim move i/cwto v ggo8k b(2tl8+n 2.1 s?

  A bicycle wheel rotates uniformly thr/+x - bewymyf(0wwq-qjb 58zdough 2.0 revolutions in 4.0 s. What is the average angular spezqqemfj bw (0dyb/w5+y --xw8ed of the wheel?

  A bicycle wheel rotates uni ol8ip ydsk x 4h 2,n):ii13om-tp/*jsyhh)bwformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the c 13 ls-ns h2ih )jipwi)h y,dpxty8bmk:o*/4oenter of the wheel?

  A cable car at a ski resort carries skiers a digm5va wt-6 ;rlrxeq4x k+c3v:stance of 6.8 km. The cable which moves the car is drivx3k+gamvqlvxe45 r r-6:w; ct en 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 minutes?

  A wheel of radius 1.0 m is rotating with a consrt4blil l 9 7;s:ufx7etant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's rx77: bf;uer i9lt4lslim?

  The cutting cord on a gas-powered weed klnwb8*e +3z)bt tiv;cutter is 0.16 m in length. If the motor rotates at the rate of 20 revibt );v3+ ke btnlw8*z/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s. ppic*rw ,4b;)p cair(.ov4zm What is p m.(p woc*i)c4;rpab izr4, vthe centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a pointjx 3 rj80vc-ozat73d d on the perimeter of a bicycle wheel of diameter 70.0 cm when the bik 387zr0 cd 3x-ajdvojte is moving 8.00 m/s?

  How many revolutions per minute (rp8ia +q v pnsh ysm-;9.;br.jmpphh6h 5m) must a circular, rotating space station (r = 1000 m) rotate to pqism;rpy..5;h8 s jp-6p + 9hahmbnhvroduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m/s igcx i 51r3(w/dvfxa0. The maximum centripetal force (provided by sx3crgxid/vf 0a15i(w tatic 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 wijyez)n 2iaf4b 1xk/- ith a speed of 20 m/s. The maximuzii2y xae-n4)bj1 /k fm 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 0.750-m string, is whirled aroundydw s0-d 6x np*vge1v6 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 d gw1-0e6nvy6 *dvpxsif the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm ygj) gjs6 n,+krolls without slipping 10 m down a lane at 4g+s)jn,g kyj6 .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 acvtk342: lu j,qp3b 5u4 xfwkqtceleration 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 acag+s*b bm.25nnlk 1y wceleration 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 tirvu9f hw ;. x0u,ayfh,mr,zyl(e rotate after starting from rest and acceleratin0(;mh.y,hyavwz uf,uxf9 , rlg 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 acceleration of /6kam7ij i4cm $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates wihyqr)5sx-3vk 6e0q5nw yzts1th a constant angular acceleration of ktey z5nw-5 ssx3r0vy)16 qqh$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular ty(,wo d2.jq f2ygk *nspeed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular ao qw(t,ynd.*2 kyg2jfcceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down unshrf:zm 2 o(+iiformly from 8.40 m/s to rest over a distance of oif(r2m:hz+ s115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of)3iwov e ds:6r 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acc6o)dwr vis:e3eleration?

  A wheel of diameter of 3ty 8hzs02aw 2pgj)huyar .0p68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to the stop?hs yy 8jra02z2.3g tau0p)pwh

  A centrifuge in a medical laboratory rotates atvx qp;x8)(jk-ad ; hpi a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accelerav);ijx-px; qp(dah k 8tion 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. If a 30um yx2k .wos xe+o2a44 cm long wrench is used, what is the magnitude of the forceuemsxk+wo a 42y2 4ox. required when the force is perpendicular to the wrench?

  The bolts on a car wheel requ/lrnc 2 mcrk*/ire 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 for/*mccr k2 /nlrce applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner ov 0)+fvlcd +y-eh5vjtia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as /n 3hlco;jlv .follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the momenn3v ;jo/. llcht of inertia about the origin?

  A solid cylinder of mass 10 kg isuhs+o( i /f9ui pivoted about a frictionless 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 ofhu 9(sufiio +/ 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 frictionless axis thought cipk tv;+wrkfe4n8+/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 a force F2 = 6.0 N downward. How many radianfi+n w+p k84cevrk;/ts 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 inu okpi 3*u; *udtgnb.: the horizontal position, and t;ditu *kp:bn uu.g3o* hen 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(icemuol z:6hw2lr,2 ring of radius 30 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 lin 2iemc:6o(,l rwlu2zhear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless dpcouzuf 69.wm29g 5 ykisk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the p5u g62m9ofz c ku9.wypulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mkntxmc0 n1pco/h z3yip3-)t1ass 7.07 kg apn3my1okp- 10h 3)cnic/xtztnd radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. vpsg)8.te l; odsg k9. 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 ofb5e8n 5ekssx / 9fd7u ly1olh9 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 radius 0.0 0 h2nlfmsy*z dd2llu-j7t;.o10 m starts from rest and rolls without slipping down ahn.o7fl-dzu ls d 2tm jy;l2*0 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 mass 1.0 kg and radius 0.010 m rolls with a speezj4d8t ( m*kgdd of 10 m/s. How high up an inclined zj( kdgm4*t8d 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 anl252 d tx:4jzfozkl5mn, c/mod allowed to roll down an inclined plane. ltz oko2mfmzlc 5x/2j5:n ,d4 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 cmspv/.v 2c/xpwu;wr 6b rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. T s./cvv b2w ;6/wruppxhe 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 changes by :3alda 8v whxs gm*:n 9mv(a0t$20 \; kgm^{2}/s$ 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 iner s6 -o7unt 35x1bmk0js-kurfxtia 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 ep ma+r(q* s hk.88itzdxtended has a moment of inertia h8+qdzptai 8.*m ks(rof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?