Angular displacement 4fwlmw7er amh)6rxwi *r794kis usually express in units of

  Angular velocity is bcrd2/ygu2n ; 36 thytexpressed in units of

  Angular acceleration isu w) x/bj6rih i b807gs)r3wlz expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a consb l(e9-xx980(kfu8 tqnrwkc gsgu*z.tant rate. The boy is neafx n0ueskctzu9-(8*x(g qkw8blg.r9r 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 mpiy:: *yzzt,v-uw-g 4 4ysxwberry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who x* t--uygy4p zvsww,izy:b :4 has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which/0dx jr,oocc7 is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater ,o7cdx/ 0or cjlinear speed?

  A boy and a girl are riding a merr59*pdm+mrfy3rpn te xd as2: (y-go-round 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 accelera329m( tnp+s mdxrp:fy 5* redation?

  A boy and a girl are riding a merry-go20v .d m1visefwe/h g2-round 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 tavg2 w .v1 e2h/eidfsm0ngential acceleration?

  Consider a rigid body that is rotating9 k vu.em2wh(z. Which of the following is an accurate stau zvkwmhe(.2 9tement?

  Rolling without slipping depends qocgm:r 7gu49 on

  Two equal forces are applied to a door. The first forc wakgwyafj6hh0d.:63 e is applied at the midpoint of the door; the second fh hafwk6aw6.gyd03 j:orce is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are.z zhhai,)4 puo.: ltc applied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts tz)zu c h.4.haot,ilp: he greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The fwrk8oh8sh ;o0vz,nftvfjsg / ;.+ 5 xzirst force is twice as large as g5fz+wx h,s808o;f .zv;r tsjnkvo/hthe 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's resistance to changx+axn8 bm 60 hut4yr-hes in rotatio h0b84-mh6xuna y+rxt n?

  Consider two uniform solid spheres where both have the same diameter, but o4,bsw ohebdj x3r924c8 n p,zsne has twice the mass of the other. The ratio of the larger r,sxeb 3w4c,pb dhjn 92s48ozmoment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same ppz-sg-c-a*k 1s.ud;dvdk5n mass, but one has twice the radius of the o- s ndu;z-pcddva-*p .1sk5kg ther. 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 twq(i(5p fgls s:ifcv *r /5fu+eice the mass and twice the diameter of the other. The ratio of the larger momeqlif s/5( vpf scueg5:f(*i+r nt of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M andttjg gb0x-4(k radius R. If these are increased to 2M and 3R,t0 4gjk (t-xbg what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that objec3;k 0kgiua1 ait will

  The moment of inertia of a solid cylinder about its axis is given by 0.5gcmc+)6 3mv/ f+ikgxm MR2. If this cylinder rolls gg+/)icmvkc6mm + f3 xwithout slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mas-f vr-ffde/ c(s 150 kg, one wheel 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 of the bikef dff/vrc (e--? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping down an udq1f,we. .d9:ue k rainclined pd,qakd.e.u urfw : e91lane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass Mvn*o92y o xjygj- -q(o and radius R rolls without slipping down an inclined plane startinggyqj-9( oj *nvoo y-x2 from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momenk mr6vk-2ui2x n8y9zvtum of a system of particles changes when a net external force acts on the system.9xv2- k k ymvuzr86in2" This statement is

  In what circumstances can the angulml,-ls -x99 wc cujbo(ar velocity of system of particles change without any change in the system's angular momllwcs o,x9-j- cbum 9(entum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whit*jvw89*n idg -xzeukw 1b * kz92oq-ach may be present. What happens over time to the Earth's angular momentum aboutkv xa1*bqz*weont92-uid j89 * kzg-w the Sun?

  The Earth moves about the Sun in an elliptical orbit.d c8,9 6fkyqaevfa;3z As the Earth moves close to the Sa 63 fye 8k9vcqaf;dz,un, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spi so a4h.tl-b-in) by pulling in his outstretched arms close to his body. What happens t th.li--b so4ao his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outs)syl1/04fy jy/w kt ( y 0ajl)c.o6wjookd/e ztretched arms close to his body. What happens to his rotational kinetic o)j.(w/ z klyja1w )4/ktyo 00cye jy 6dfsl/oenergy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullcb;:fpxldcw0ja 43c. ing in his outstretched armcf0:.d pl4cj 3bxw ;cas close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conser*ug2y.kwv:dir z, /zqvation of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly 9t v1tj27er,jk zrpd 3circular orbit about ttpejr tv9j3 ,12z r7kdhe 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 distance*b4hfnkt i.y(b0m r zngb5y1) does the tip of the second hand sweep thbb fn(1ir.0)mb h5ng y* kz4tyrough in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equi h6g7r:/aoe a:n zg9iyvalent to?

  A bicycle wheel rotates uniformly through 2.0 revolu(wzj(ix2 hzp07ffgp 0tions in 4.0 s. What is the frequency of the wheel's ro2xpf(ig 7zfh( wp j0z0tation?

  A pulsar (a rotating neutron star) emits pulses at a freq2*q dh ckcj-il lke(i61rz; )cuency of 0.40 kHz. The period of its rota2ceh kzj-lc;)*k(r 6dici1 qltion is

  A phonograph record roz nb1i*ns 8tu:s.( vmytates at 45 rpm. Through what angle does it turn in 0.20 nzm 8 sv:i y1s.nbtu*(s?

  A wheel of diameter 26 cm turns k(,rmqbjkf1xuwboih .d5c 2tm ,8 ,0h at 1500 rpm. How far will a point on the outer rim movedcw 1bjhoi,02(.tumfk8, ,m k5 hqrbx in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wh) o5roi9gqs blv4 j8h.at is the average 5i srh. qov o49lb8j)gangular speed of the wheel?

  A bicycle wheel rotates uniformly through 9rvabzj4,cj bcr10cy )vy ()e 2.0 revolutions in 4.0 s. What is the linear speed of a 9, yc)0ecbr1( 4jjv avbzcy)rpoint 0.10 m from the center of the wheel?

  A cable car at a ski resort carries sk6,hz(x0kla*mh 4fo8i ta ue q3iers 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 tuhf(i3k,oh qaem0z*a t 8x l46he trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angularme ntq un8/(y) 7-pazj speed of 2.0 rad/s. What is the linea yt8p-7z(nnjmuq/ e) ar speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is9wh 8naktio12s p p:n3 0.16 m in length. If the motor rotates at the rate of 20 rev/s, whn pi8tn2a sp3w 1:k9ohat is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 j/k5 zatv2w(qh)3w cbfi.0a sm is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the whee 5bktva3swhqij0c z2(a./)f wl's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle wuj4uko *jux9+6lncrih,78ya heel of diameter 70.0 cm when the bike is movrax* o8ju6ulu+n4 h,9j7cyiking 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space i /2-c /b5lcst tr9rs uy,tt pa6qh0/mstation (r = 1000 m)i0mt/rt6t-q at /,c/ rs2hsbcl 95yup rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular cur ye1be0:9oggq 1jusyom w146zve of radius 50 m with a speed of 20 m/s. The mayo 16j1z:ow gebuygms4091 qeximum 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 79,pg r(jeag;lh 4 o:yugvd f;circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by stagg ;fp r(;dg7hoyl:4 a9ue,jvtic 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 i*hy (+1lnrn.ailpc. 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 n*.yn iil l ha+1rp(c.the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls/prdv- o57 qaw3rtlq) without slipping 10 m down a lane at 4.3pt5 l3r7q/ra-wq dv)o 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 2vdcdf 9e 9)fyacceleration 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 w7 +y sq1csv(oconstant 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 f bpacc2.*l23czgq 3gautomobile tire rotate after starting fropzclb 22.gqc g c3f3a*m rest and accelerating 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 angulesb kph*x/fm 2 +dcf19ar acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelgfv*y sm8;vk *xm:r;uerates with a constant angular accelera8;m :mx**;guvy rsv fktion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches anlq.l q5f)muz vh(ey5c 20 ki7l angular speed of 6.0 rad/s while turning through 2.0 revoluueqkllcly7 )5.5q2h z0(imfvtions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from*pl.m( ; khitlgttjs7;gnw3- 8.40 m/s to rest over a distance of 115 m. What is the total n;t mt3g*-njwl;t hlisg( k 7p.umber of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68n;uy vi.aedexy u1tmhgk2;1n1- b+u 4.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular accelerationt1;21yx; e yuk.bu1vgudai n e nm+4-h?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to restw)+j q )m:hnxj.i+ ;n8ajec8gs kwm;j over a distance of 115 m. How long does it take fohw 8nq;ji j )gxa. cjm+sm;8+)j:kwe nr the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 hwl,giwsqx( u97*;uvlrq6 8trev/min. When switched off, it rotates 50.0 times at a constant lt6 9qvruw8g;7i( hwxs *l,u qangular 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 kt6td/f h:fz:hk+k eme he6v) ;akn90 require 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 force is perpendicut hhk :e anf06kemk;6k9+ehfv dz/)t:lar to the wrench?

  The bolts on a car wheel require tightening to a torqapdn3o6- hwd u7kk 3 o+z*5m5qe f3ptwue of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the foro*3mkf35tq+5 u7 onape d 6wk-3p wzdhce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine, d( rftz; uoud-l(w0mrtia $3.00 \; kgm^{2}$ 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 el: vf6 mcy(:pis at the origin, mass 2m is at x = a, and, pf(ce::mlyv6 mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a fricea,ug 8;3,cq(urs4 5rkkngaktionless 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 4ac,qkuu8e;r (n, rk3g ag5s kanother 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 frictionless axis thought thern0;wsu( xy.9*s btk i 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 radians does the cylinder rotate through in xy b.9iu nrks;t* (sw0the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially h7 pq2udv)+i jreld in the horizontal position, and then released as the frru7vi2q)p+j dee 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 q(6du.h q9fj lujc76s 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 linear speed does the wheel achieve, assuming it6( cjd q9uf67qlu.s jh rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk / 1ht0n.z mot+kmxtj0pulley of mass 7.07 kg and +10xmkztoh n./0tmjt 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 df3y x g0mgi4s-x( l3ieisk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of th0s3m4- xif3 xl i(eygge mass?

  A rotating flywheel can be used to store energy. If it is required to sxiguy a2g dp+prkb0vp /z,0 :lj: c/8qtore $1.00 \times 10^{6} \; J$ 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 ofq nw252tp+i5 bbtb)j*1 wqnn z $5.00 \; kgm^{2}$ 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 oasw),k0:/h i6j6iik* + m xqwjqetc 8starts from rest and rolls without slipping down a 1.0-m high)i,joqks0 6i e : qaw6/8tmki*+hwcxj 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 radiu8eg7ddn.ks8 e9s */zb9sw haw s 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before conh 9ak7 e8gd*zw.bedss sw9 /8ming to rest?

  A hoop of radius 0.50 m and a mass oczm9ekq844mgwsk77e f 0.20 kg is released from rest and allowed tok7k4m9mzgwe s ec478q roll down 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 csbnn6+t:d n0p l52qwzkf10v em rolls without slipping down a 35e incline that isbkdw0+q51l z 6t:fp nsn 2ve0n 7.0 m long. Assume it started 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 kj (pa ,b/9boe 6boou;momentum 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 inerti v z9qw;ro8lv7a 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 wly/wrds9(e 6 4 p9aegdith arms extended has a moment of inertia og pa4y9e/l d e(srd69wf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?