Angular displacement is usually expres2.+ 6)hhdd8wo racn gaw qph)0s in units of

  Angular velocity is expres )s z7m2, srnb(z8mxh)c 2bhfjsed in units of

  Angular acceleration is expressed inmc(fly4 n0 pdz,ml .:w units of

  A boy and a girl are riding 1t0psxd r (epb1w f l:(zt+kd)on a merry-go-round which is turning at a constant rate. The boy is near the outest1t +d bf1(d zr0 klp(xe:)pwr edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding ii9tl-ww(t6l 9 lzlw6 ,wr ea(on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the centel6li-lrt(ww9, l6 wi9 tzw(aer. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a comm2*gezd c*/mu78ths6 q0 iopnstant rate. The boy is near the outer edge, and the girl is closer to the center. Who h e2* 8co0/di7gm puqhmt*mz6sas the greater linear speed?

  A boy and a girl are riding a merry-go-round which is tz d 747n 3)vp:wqc(( jvouko,arx -pvpurning at a constant rate. The boy is near the outer edge, while the girxqd 4):oao(pru j,7-n3cvz v7v pkw (pl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant ratep*q :, daoqz*v. The boy is oa z* v*,:dqpqnear the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the followcusq6bi2k*u+ ing is an accurate s cq+bu i2u6*kstatement?

  Rolling without slipping demf4 z5sj ziuk((,wi 3zpends on

  Two equal forces are applied to a door. The f4,.w(kq5 tyxfphn sleim)r ;,irst force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are appliedp ts; y, qrhl4fex),nk.m (5iw perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at0 5l57 otaoo)qw+qlgi the doorknob. The first force is applied perpendicular to the door; the l55 aqw) +07oooi lgtqsecond force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, pern: clqkvw4 :h4rg4v+z pendicular to the door. The first force is twice as la+vrk4qlg4h :vn:c w 4zrge as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object'sjqse8p*zohhu* u *91*qi8mfp5gt cu; resistance to changes in rotation?up5qqo*u heu*m i*;z98t* p 1jfcg 8hs

  Consider two uniform solid spheres where both have the same diamekwk;ub7 meh: +ter, but one has twice the mass ofm; u7k+ :khbwe the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has uxlixwks8v y1z2sgh54 -2w/ek duz.:6kh:a e twice the radius of the other. The ratio of the larger sphere's mom1y w6wx8:d22.vi zaxu /gk-ess4h:lhuekk5 zent of inertia to that of the smaller sphere is

  Consider two uniform solid spheres wher( 7 z(jk55gmw; fpjoere one has twice the mass and twice the diameter of the other. The ratio ofzjfo;pj (7mwre 5(5kg the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radi dwfuk)8o:qbe002 j gtus R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia ajkw8tefu):q o b2d 00gbout a central axis?

  If a constant net torque is applied to ans8 * kinm qpnee4cu 71)3lfht5 object, that object will

  The moment of inertia of a solid cylinder abou 8tbb *;wabbq.lh3w 2ct its axis is given by 0.5 MR2. If this cylinder rolls without slib.*b bqw 3cw8h2;abtlpping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a m2( aua hr6l(2a8 tcflvass of 10 kg and a radius of 30 cm. Wh (22c(hat f8aur6llvaat 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 slle1id ; xul;53yff e8zipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline dependsd l ux;e f;8l53fiz1ye on

  Suppose a solid sphere of mass M and radius R rolls wit65(ym)ddr6nbj cq fcuez y0*,hout slipping down an inclined plane starting from rest. The angular velocity of the sphere at *mqd) 6 ybjrnf, due0c(5 6zcythe bottom of the incline depends on

  "The total angular momentum of a system of particles ctndtdzd 43 ((+lfz33cd-jykahanges when a net external force acts ondtn dyft (kd4+-za3z j d(l3c3 the system." This statement is

  In what circumstances can the angular velocity of system of pa7vwrqbws33ryx g6.qq:q pt 6a.8mk f(rticles change without any change in the systeq .86xpy:(w3rsrk qm .f 37bg awqqtv6m's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which may m gllnxo.5tpg a34 x7)b74v xlbe present. What happens ove4v xx7lt 3.nglbpoa)gl4 x7m5r time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth movelw zk nhnh*h(:p4hc e l9q-:0zs close to the Sun, then which of the following best describes the orbiting spc pw9- lhn:he(n khq0lz4zh* :eed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spiqa.3qt)vkx pqj 56a uz(s3grxh26, br 3 +yvhwn) by pulling in his outstretched arms close tgqhb,qq36v 6x3xj( k+va5pysr3 ) hu warz.t2o his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his l -kx- qhov7t,outstretched arms close to h-ko,xhv7 lqt-is body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs avg+)t nobn ( fa2vbr5up/6sx,) yh tv6 pirouette (a fast spin) by pulling in his outstretched arms close to his body. What hapxy p6+ nub)25atfvvshn6(gr o/t, b) vpens to his moment of inertia about the axis of rotation?

State the law of cons77y(h;m, xdlul(x dq ov.r hj0, tnh4gervation of angular momentum.

  What arc length does the Earth travel in a three month period in itzxaiix+vy8h()bnyroye +.2m k5 k ;9ws nearly circular orbit about the Sun with a 5;.xhnxy +i)v2rb9kyom+y8i (kaze wradius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What dis1 hx*hvjtbh*7 np 3hmhb6q2.btance does the tip of the second hand sweet b2pbx h63n*h h1q7vjbhh m.*p through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutiox6 i2dmy, oo9vf* h4ihrb/. csns per minute equivalent to?

  A bicycle wheel rotates unifo0izxwkh7c ;t 5rmly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotati x0;z 5wktch7ion?

  A pulsar (a rotating neutron star) emits pulshkwydlqg.3z. p )x-j6es at a frequency of 0.40 kHz. The period owyxk.) dz6p3h- .qglj f its rotation is

  A phonograph record rotates at 45 5az 33nibtr* e;4qkyw rpm. Through what angle does it turn in 0.20 z5r3w ; beit3 4n*aykqs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a vk,r.t. l/d6 8g p,iovn+pufmpoint on the outer rim6fk liv ur..+/8ntp ,omp,vgd move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What irku180+ymhj o s the average angular speed of the wheel uo1rj+k0mhy8?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. dq-/uqr k1q. mWhat is the linekq 1qu r.qdm/-ar speed 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 c uxotu 9w:z.9shah;*r4rz -fu able which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the .oz - ;4awsr9h:u9 rthu *uxzfpulley 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 spjeu 0sp 1cvr-409cv omeed of 2.0 rad/s. What is the linear speed of a point on the wheel's rim 9op4 1js0ec0vmvr-cu?

  The cutting cord on a gas-powered weed cutter is 0.16 m in l5. skjp l .q:fgl(ff9eength. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of tlgk fp .l:f.9eq5fj (she end of the cord?

  A wheel of radius 1.0 m is rot8 v2k3tcnr0juating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleracvtj n2u0 k38rtion of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a*xh0 *ejwpantkc u( 6mj0oi3) bicycle wheel of diameter 70.0 *e thxm*i0 03( wkj)pao6 njuccm when the bike is moving 8.00 m/s?

  How many revolutions pecjz s uxl .-0ulm5fk7,r minute (rpm) must a circular, rotating space station (r = 100zm7 lsfkl.j ,c5uux0- 0 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flapr yyexipmim-yr; v/7s8,,0 m t circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fmiy 0yppym isr-8 7xm/,vr; ,eriction) 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 l2uef,ic ,baacren/)kvq m9.n o0-6aspeed of 20 m/s. The maximum centr- n/ma ik.ea )e 9o0 2fc,b,vcu6lrqanipetal 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 strin fe-fum(be-xr/. jj o,g, 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 ebfr ux--meo. j/jf(,have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without *j0e y*qs9iz-.l - /mgci1l j fvco.eislipping 10 m down a laneyv. 9*cmj csl ii .gi-el0ozj1q*/-f e 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 consta.erpv).3/k 4kl tj1;ckg wnt int 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 n /ib4sp )d:qe800.k/6 uowccqe joada constant angular 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 starting fx.7s+e9xdoomy *e1mz47 sxt nrom rest and accelerating at a constant angular acce+tmzx. oe7eyss9x m4 *xo7nd1leration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acekc(rfo5 vz / 4hn,u-fceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates withx2uha)d zxo7) a constant angular acceleration 7hxax)u 2zd o)of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest andy8fhfbr4;. ly1.rd 5dmtj i(o reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the wrd 5yob t; .8j(mh1dyrflfi.4heel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to re3.ort,8ou/j+ylmperywve18 f lb 7p *st over a distance of 115 m. What is the total number of revolutions the wheel rotavl r*8 fyu1e/+p pye 8om,.o tl73bwjrtes in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly froo(qkw l8tx7 ; 6gcayynoa00v9 cpc 4)cm 8.40 m/s to rest over a distance of 115 m. What is the angular accelen6g0 q87p09lcy;acc(y k v a)wtoox c4ration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s skw7 qm5ct u6.to rest over a distance of 115 m. How long does it take for the wheel to come to t m tsk65uwqc.7he stop?

  A centrifuge in a medical w5:w jbe8ie(j laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant anguw5jj ( i:e8ebwlar 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 0:gtw.can (s 6 hl nuqqf9tu-0Nm. If a 30 cm long wrench0a 0wq(l q.hufntg9t6cn-us : is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 9hbj)ety okye oquq:, 0 hf6/.20 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when th) , bye.tq6ohofek j qh02u/:ye force applied at $53^{\circ}$ to the wrench?

  A wheel with moment yj dnmp 9m+il:*fee5c6r/ j2 oo. 1gouof inertia $3.00 \; kgm^{2}$ 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 at9il*sz 0h;iqfg -1 iu)konspbb1 chi9*vi*.q the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. Wvi*c0fi9g*q*)izbsk-9n l h p1 bhus;i .qio 1hat is the moment of inertia about the origin?

  A solid cylinder of madk 4z (fmt;0r wnynduipi a8:56zs 8g4ss 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped a dt8m4nw s5gi8nz pk6:aidy40z(;ur fround 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 10b.miru7tgc h. b (,g;y kg is 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. Atrb cbu , iy(h;gg.m7. second rope wrapped around another 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. T5ab8s;j zy: 2jt*jgbq he rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (The momen ;j5b2aszj:*qtgby8 jt of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to bx 58vhehjqke( /)kx 4o,5ksnke a 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 e4kxs kjeo, /q8)kh( nkh5v5x4.0 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 pulley +3fr8rgiow/ exa/. tpof massx/pagfrito3+.ewr/8 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs cvwn4h *+9m jlon a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 c94 nlw+h* mvcjm. What is the acceleration of the mass?

  A rotating flywheel can be used to sto7+32l/ot hjnrr v) -t/v2uz-hma cmwcre 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 inertias 7e0pd:s)b-y5 lq z1swtq j7l 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 x*w:: xdu4c5 0lmn 4(:vooha p(vtju eradius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the 4owd*umeuh( l oc4:0j vxxnp(:vat:5 sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls witjk jh,kx3i c fbl(y;)5h a speed of 10 m/s. How high up an inclined plane can it climb before coming toykkfb 3hxj ; )5(clj,i rest?

  A hoop of radius 0.50 m and:g /nof l. m3 :lxtqgmxy*pq44 a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m3p*: /xy:x.qfl m 4tlggmn q4o?

A solid sphere of mass 1.5 kg and radius 15 cm) bd 6 0y7xuwtbmyc)fy67hmmr w.(b,n rolls without slipping down a 35e incline that is 7.0 m long. Assume it smn7 y u(b h ) x6wmrf0cd.)mb7yb6t,ywtarted 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 changes bi84cam+izjx9:or m , 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 zz)wmt7l +vy d5j.ay;moment 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 hasm-w9l2mxu + n (dpw*bevt *6vv a moment of inertia ewtdmlnv- v 9(bxpm u2 6w*v+*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?