Angular displacement is usuall4mdx iy vhoj jpm,qg.k;,uz -ik)-8j2y express in units of

  Angular velocity is expressed )djtk8 eels:( in units of

  Angular acceleration jicpdc:jx k (5 xx bji:jgd/qk46*m0)is expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a cx*c-.ixfz / uzonstant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular discf-ixzu. /z x*placement?

  A boy and a girl are riding on a merry-go-round which is turning asx z.zaed u-75-tbp xk/lc/w :t a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angulardazz7:/sbklc5. - x/wpx et u- speed?

  A boy and a girl are riding on a merry-go-round which is turning at a /dcsclq y9 ir2n)4gc3constant rate. The boy is near the outer edge, and the girl cncl 2 q/r4i dyc3)9gsis closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-roundgam ( h*,qd utei87mw7b e.di* 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 greater centripetal acceleratme *dd 8,*i(tu7ahgmebi. w7qion?

  A boy and a girl are riding a merry-go-round which is turning aez85n 150yy5 ud i 2xxivrbev(t a constant rate. The boy is near th1er x85n( z0ivy5b e5ydivux 2e 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 following ipzc*(t 7z(*eromo- pis an accurate statep( pci-**tmoze z(or7ment?

  Rolling without slipping depends onlf5nlly,g xkiy+e+8 , pfljpj9*0 7kk

  Two equal forces are applied ikidnm51n+j f;zlb8g6 c (+zq to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular1b5jk 6zgnzqm;+8cnif d+i (l to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorkhiz nk45(bokjq7a osuwy2/(k*zu h 7(nob. The first force is applied perpendicular h yz i(sz n( /4k77uoak w(qbh*jk2ou5to 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, perpendica 9 ob xeq.;pkf(gp,6a xaq52fular to the door. The first force is twice as large as the second 69q.ap x(foe5 x2fkb qa,;agpforce. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure mrv d(6 dy+vj/an object's resistance to changes in rotationrm ( v+dvydj/6?

  Consider two uniform solid sphp:;mvt,rw- qyymg5fy4 z 9sb 1eres where both have the same diameter, but one has,1z y:95mwfg;syrq vymbp 4t- twice the mass of 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 twice the radius of th9ajc u fr k0(c/t-9zjrt hke./e othet9ru (h ke tc-9jj0//f.z cakrr. The 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 adofrs f0 9wy:8;4bcgznd twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inerti0 ofs84wfydg :r;b9 cza is

  A uniform solid sphere has mass M and radius R. If these are increaslgp-6+8 dqklllv7mq3ed to 2M and 3R8dllqv6gmllk3-7p q + , what happens to the sphere's moment of inertia about a central axis?

  If a constant net toz+wj wxw0 6gt0rque is applied to an object, that object will

  The moment of inertia of a soli;t uttp9 )ut6(ix8u)u qlrq b9d cylinder about its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel,7jp9k 0.fw8a-syk1n a jcd5ps ac ln5 of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy okaf,- dyj0pkn p.81 cs7l9cnsa55ajw f the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass6i 20 qyd/jbto:ajxb i.(6hn*vdiyp8 M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the dvi*y bj/.dtph6q8:yioi j60b(an2 x incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slkb c*k2:ahg; hz4,k r;bmaso 0ipping down an inclined plane starting from rest. The angular velocity of the sphere at the bot;gkbs :hbh c;ar*a2,mk4 okz0tom of the incline depends on

  "The total angular momentum of a system of partsor8wb68 f9.ssciz*p icles changes when a net external force acts on the system." This8rbss9pof 86*scw .zi statement is

  In what circumstances can the angular velocity of sys- urmed6 ,b3qltem of particles change without any change in the sb ,mdluq r-3e6ystem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fris3b itj4mk rbwm;- -d0ction which may be present. What happens over time to the Earth's angular momentum about t-sj ;iw4k3b0rdb-mm the Sun?

  The Earth moves about the Sun in an elliptic9kj f zpb6tb 0 .e1s dbx1n6+ w265orilxpvdj8al orbit. As the Earth moves close to the Sun, then which of the following jsx6 1or pl+6f nept5k 2bd8b ixw9vdbjz .160best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pum: x8z o3nane/lling in his outstretched arms close to his bodyem:zn3no xa8/ . What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretc ts;-xzb39 sy e.jlt2bhed arms close to his body. What happejs t ezxt b2b-.sl3y;9ns to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstj47gb8)mm; v icbo,*c m:mc jdretched arms close to his body. What happens to his m jmm c7cg;,vmbci o: 8)*bdj4moment of inertia about the axis of rotation?

State the law of conser 2 k 55ixp,,wvvquxd hcqb/s.0vation of angular momentum.

  What arc length does the Earth t djxbyxh22a.e:kjs/-p- r) eqravel in a three month period in its nearly circula2:j/d.p q)k -erx2j e xsyhab-r orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What dis7gu dg/iq3ghkdw n0:wpd )n6mkr-b.4 tance does the tip of the second hand sweep through in 3 minutes and bgk wm 0)ph3/dr6qgkgd.d un: 7w-ni445 seconds?

  How many rad/s is 25 revolutions u1zcpnbo4/72 nst t2a:( psk)tssg (v per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolut, p/.s-h:xen4ai a ivfions in 4.0 s. What is the frequency of the whp/a sn,f i.v:4eia x-heel's rotation?

  A pulsar (a rotating neutron sta(eh se /a, /c5:ofp w5h.z-b ut4tyeabr) emits pulses at a frequency of 0.40 kHz. The period of it,uefbba-.ethzp4/(:t5 scewaho /5ys rotation is

  A phonograph record rotates at 9t 0rexuvhskrm) ;k9545 rpm. Through what angle does it turn in 0.20 05 k)9 vsmrt9khuxr;es?

  A wheel of diameter 26 cm t c es:gzn 3g4-23lzdbci5js*rurns at 1500 rpm. How far will a point on the outer rim move in 2sicr 3ejs3b42d-nzg :zc5lg*.1 s?

  A bicycle wheel rotates un0)r2xcy qinloziqoc/n8; y+8iformly through 2.0 revolutions in 4.0 s. What is the average angular spnnoy0/oc2xzlc)+iq8 i8; q ryeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutvp 6o8-zzwfn4fsu*( p ions in 4.0 s. What is the linear speed of a point 0.10 m from the center of pw(8ffz4 novsup*-6zthe wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The ekoi.2c6b3 c/ wh.szxgr/ cb *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 cab6oc kbi*exczrgsw.3/b .2/h cle car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotatikk4*r8hl/ abk2n 1eifng with a constant angular speed of 2.0 rad/s. Whhkf r 4a1b/kk2 8e*nliat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cu6cf dcs:)kgd kj n*,, x6jmo+atter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of tdo: ,6)gjmk 6 j,xsdcf ka*cn+he end of the cord?

  A wheel of radius 1.0 m is rotating with aex0n1rcd-a klx .7xm9 constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a poi 0da19mxl kxcrn7e x.-nt on the wheel's rim?

  What is the centripetal acceleration of a pox431te4n c,zrd0ldm-jqs 8hrint on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is 4 slhm031-rqrcxe,zdn84j td moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotusjzxb1vj*l2e 2-0 t bating space station (r = 1000 m) rotate to producjus0-*2vxbjz1b elt 2e an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with)pmutb ;(+tmh a speed of 20 m/s. Tup(;m) +mt hbthe maximum 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 circularn3 zp53bqk3if2p cjis0r0aq; curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) nk5rj03 s2 pqiba3 ;0i3pfq zcis $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750-m string, is whirledxq 8lye369hmk9sn)dh around in a smooth level table. If the maximum tension that the string can withyhnlmsqd8 39 )96kexhstand 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 rolls witho; c76 hfj2mo: adakr,nut slipping 10 m down a lane at :6;72,jaoh kn mafdr c4.3 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 w+neqwl z jygruf16p 31e9vy04ith a 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 w4 h8 +uidze6s3 tjw2ynv 8wxz2ith a 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 rotatnzupy1w2e/f(w t6: k qdyqv6;nmr* +m e after starting from rest and acceleratin yzvtyw/6w1(+r k*pmnq2qum ;6enf d:g at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, anj ysd a.3hf:v.d 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 dece. tvll +8mb)lhlerates with a constant angular acceleratlb v)+8ll .htmion 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 speed of 6.0 ray cvmkr )qfe2+zi /n5ctn v2h. 7izu8;d/s while turning through 2.0 revolutiontynui; nv2hiv/cr58 zq 7 2.emfcz +)ks. 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 y(srn:wmpswtk(e ,qeh- 2+. r rest over a distance of 115 m. What is the total number of revolutp h ew2sw n+.rqmys,((: tre-kions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm bjb 9 wksouox79q)x8 1g3c* qcslows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular accelerox)x8 wo 7kbcsq99c31 ujgb q*ation?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s toa fh ; (uj/yyk0z-ip9rgxc 1y2 rest over a distance of 115 m. How long does it take for theh1;x rg9/ ykzya u-pif0(j2 cy wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a ros l 1*o5kfv o2nyx(t/rtational speed of 3600 rev/min. Whenn r lkso/xty1 *2v(o5f switched off, it rotates 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. If a 30 cmbd4nv .oa 8p9eoo.8mz long wrench is used, what is the magnitude oe8z4.dnoovb a.9m 8pof the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm lob1z jm;cc5 s)hng wrench is used, what is the magnitudez5mb1sc; jch ) of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia mu.3a clx.f1s$3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: ga a16*)ceqda mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment )qa ce*ga1 da6of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a fri,(kiu)ak dh 3i hwjvr9df 43o+ctionless axis thought the center O+ df kd,93h 3 or(h4ijuiv)wak. A rope wrapped around the outer 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 11y/bm7ka( uc37o 0s;uz tu xzd0 kg is pivoted about a frictionless axis thought the center O. A rope wrapped aroundk7uz(0b z/7d13o a;usytxcmu the outer 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 rod is inpfc 2ycz0b:vngk 3 89eo 97:+e eqjcnjitially 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 moment of inertia of a rod about one end is ML2/ pyo:ne: kjcc 32ebgzq9fe+0 cnv8 9j73.)

  Consider a bicycle wheel to be a ring of radius 30 cm and.nu+ d*jxn ei- m/16vd+ kzsr1duinusq-0 t8j 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, what0 1jdvi+-*6dtq inrnx/- s+1edsm8j. zuun ku linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped arvwft m520epz q+4m;g jound a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acce gpz+54j wvt;fmm20qeleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk o0h1)ocb tn;zgexy /iz(9+ xk pulley of mass 7.07 kg and radius 66.0 cm. What is the bt g ;9e/yox0kxczi(hzn o+1) acceleration of the mass?

  A rotating flywheel v0n fv;ar *xs-can be used to store 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 inerti) z-pnx5zerr)(.bzff a 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 rajdg v ofmj,; 6 kt6k(gkiak2 m/.x(a.exz+;yldius 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 reaches the bottom of th6mz;(gmlx .xoi;kj .k6kkda/g, v+ayf2et( je inclined plane?

  A solid sphere of mass 1.0 kg andtr76mhkmnp()fi r 3-g radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb b km )irf76mhg3-nr (tpefore coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released0*s wqbuf z4r9 from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?w94* 0rufszqb

A solid sphere of mass 1.5 kg nl, 7vwazn( d6and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from restazn dnlw6v,7(. 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 chih+* *sovar* oanges 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 inertias-y /b0,qpmwcgm/eg+dr nd ( 33k9jgf 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 exten)r4l:1gc j2du uo8iel: zkt /vded has a moment of inertia oc:: guu rvikoz8t241lj /)del f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?