Angular displacement is usually etjr6k f(3,zi 1plfu7txpress in units of

  Angular velocity is expressed in +p+ k05r f,m gtzdu7txunits of

  Angular acceleration is expressed in u( l j+cdfv6ntd7zi )3tj0 p3c2zsprv ,nits of

  A boy and a girl are riding on a merry-go-round wrbkb kjjf3dsb:2/1 1njcbo ez21 f0z0hich 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 angular dispb nof1 0kj212c j kjzb3:0 bsf1ezrb/dlacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constk+z oko*q,gnd/)i j d;ant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater jo i,; zkqg )/dod*+knangular speed?

  A boy and a girl are riding on afwh vj/1f +2pj1uzon6 merry-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 has the greater linear speed f21jvwun/h j+o6f 1pz?

  A boy and a girl are riding a merry-go-round which is tur8(mvmvo.il p v h.i-a.ning at a constant rate. The boy is near the outer edge, while the girl is closer to the cilv.iom..-(v havm8penter. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at ksm0t6m u4w*i a constant rate. The boy is near the outer m i*4mtw6ks 0uedge, 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 is an accurue f9m5 ybn;f9ate stbn9y f; mu5e9fatement?

  Rolling without slipph-x08zdrj4o p, c6rphing depends on

  Two equal forces are applied to a door. The first force is applied at tkitrwfn, a(d5 /9-nughe midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular tok5u fi a-d,rng/9wt(n the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first fo t+v phelqb0: 6cv1gr38tv(ddrce is applied perpendicular to the door; the second force is aqdlp rged0vtb6th :cv+ 138(vpplied 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. Th,b6f1nu yt1 fse first force is twice as large as the second force. The ratio of the torque of the first to the torque of the 6y bu11,ftfnssecond is

  What is the quantity used to measure an object's resistq2ljo/2:4 zla i uiqc;6epr0dance to changes in rotati;dlq 224c i/i0q ue6ol :rpajzon?

  Consider two uniform solid spheres where both have the same diameter;2dux2-e(y.bjzibz d1w/anv+ wp u5c , but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller mo d;v 1b(b5wd2epwyn/a.cu j2ux+ zz-i ment of inertia is

  Two uniform solid spheres have the same mass, but one haoeg0m0k -slkn.6 :;byr voyo-s twice the radius of thev;6on.gy0bom- ok ke0:-s lry other. 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 and mgs+uw.zy ,s5u *w9(h/uw skxtwice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller momen9xm5(w u/ gu .s,+whzy k*sswut of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2 vt/1sj r,gxqz8pxxp)6p (; zeM and 3R, what happens to the sphere's moment of inertia about a centp1j qz,xe 8txs)g6z;r p(vp /xral axis?

  If a constant net torque is apple5q5ft ui-tu1ied to an object, that object will

  The moment of inertia q7,mwl0fbvhu2p6*gbfs3p) d of a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic enep2 b0ubqfm,g)7vf* dwhp6 s3l rgy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 kg / qe3pk,la8i qand a radius of 30 cm. Whkl3 /aeq8qpi,at 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 ro 6ozl6f2o;si(b3lfo rd gj9h:i-r4t. qq; jnglls without slipping down an inclined plan zgs6.9hl 2j: dg irfi3;4-jq; rfolonqt6bo (e 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 slipping down an i/5cxn fv,e7 ulnclined plane starting 5nxe,c7u/v l ffrom rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a sy( j 6d.bfv+wbostem of particles changes when a net external force acts on the systod+(wvj6b. fb em." This statement is

  In what circumstances cahh:vm;w2 zaucc* 87lln the angular velocity of system of particles change without any change incva8z2ch; lm :h7ul* w the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore anyh6xzd n6grq5:n3u 3sf friction which may be present. What happens ov z x: n6qhu3fn36r5dgser time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth2s whr 1vbfu;u,nle;r 85 0y:lbhn8k j moves close to the Sun, trv bs l8kj8;be 5u,wnr0;2nu1yh:lfhhen which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outv2paht5) ob c*stretched arms close to his cth5b)ov*2pa body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a piros 4d9iu19. d6inqweo zuette (a fast spin) by pulling in his outstretched arms clo iq9i964wo.ddu1 zesnse to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by puhvx u3yf674n ;;dt vmhlling in his outstretched arms close to his body. What happenvfv6 ; ;xht md73n4yuhs to his moment of inertia about the axis of rotation?

State the law of conservation of ,z/ ma34k5u ykpf hm8dangular momentum.

  What arc length does the Earth travel in a three month period in its nearl2zwkn7xppp a vfv425,y circ z524pf,v xvk2wp7an pular orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock ha/kv8 9w x0/rcyg-6w+rlm wy ris a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 4 yiw/gwl + r6-8wyk09rm/cvrx 5 seconds?

  How many rad/s is 25 revolutions per minutbq3z3gh:vs 5d m ln188hxhp c2e equivalent to?

  A bicycle wheel rotates uniformly through 2.0 r;1pc d nw)hu2qvva1gnmm )-w3s jxc +9evolutions in 4.0 s. What is the frequency of the wheel's rotagc - ;dwpm9n1h2mvxavu q))cw1jsn 3+tion?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Th)shof(ac3v 1pe period of i 1(svo p3hacf)ts rotation is

  A phonograph record rotates at 45 rpm. Through what angle does ithjtto,z5 )u 2 q 3,:zvvgfg:lw ry)l;j turn in 0.20 s?qwz,uy: v2 jzlg ):g3hl t;,fr)vt5oj

  A wheel of diameter 26 cm turns ati;c(;rdw 26g1 7tdf rsd brhq5 1500 rpm. How far will a point on the outer rim move67wqd2r hb dr scir( 5g;1tf;d in 2.1 s?

  A bicycle wheel rota0sifk*jj6d v t0 l,sm*+vq 5sjtes uniformly through 2.0 revolutions in 4.0 s. What is the average anguls 5 t0vf,*i* jjv6dkjls+0m sqar speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 ., qm 5tea2kozs. What is the linear speed oem2t,oqk.5z a f a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distant(kgn4l) exca x)f.o:ce of 6.8 km. The cable which e(t4n.a kx:fgxoc l))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 minutes?

  A wheel of radius 1.0 m is rotatg vvqov l+g/.m 5cj0kkaw7( x2a2km +oing with a constant angular speed of 2.0 rad/s. What is the linear speed of a wkkvc 5m0l2ggq+7 + amvj( ovxk.ao2/point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 09m v ve :1i4aeclwwy6op7*x f;.16 m in length. If the motor rotates at the rate of 20 rev/s, 1eo vwlfcxp*67e m;:va4 9 ywiwhat 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. 1p8skmns /x.3c) )kt 0yeak bb What is the centripetal acceleration of a poibs8ms .10xk)be/np)k 3ytka cnt on the wheel's rim?

  What is the centripetal acceleration of a pointozh6p z:-w nn9 on the perimeter of a bicycle wheel nz-op w:hz69n of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) ikn3o4 pmzrnk.2)i(gje z b *)must a circular, rotating space station (r = 1000 m) rotate to prom n p43)gkrn2ibjo * )ze(i.zkduce 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 q.dx1uqo((s w. The maximum centripetal force (pr(q owd.s q1(xuovided 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 spzgi- 01/0z mcaretmie 6d.cs(;dc wl( eed of 20 m/s. The a;ewc-tziri1gz0cml d/.sc(m6 (ed 0 maximum 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 whirle(x x 0v;esge,vd around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then(;,se0gevxxv 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 without slireaivs 0 :39ejpping 10 m down a laier9e vs:03ajne 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 constant angular acceleratt t. kh1 w;or;.r+xqffion 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 acceleration of3d9 iuov0:stpfkoi cy (+fj-9 $4.5 rad/s^2$. 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 zjo zwmjvb4:m )d*p..v,b/ ch starting from rest and accelebz jm,b).p v/hwzo.c*md 4j :vrating 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 accelerzft3xpzdo p/eh/)4i9a: a/7eyz hq6,q axgc-ation of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a /-imif jw1h5x constant angular acceleration 1w5 fi jim-/xhof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from jnbbe exv;09 swj*4f3rest and reaches an angular speed of 6.0 rad/s while turning through 2.00;b3x9 *bsj4 wvje enf revolutions. 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 rest ov.:2cb rn w:bx88jpn1ehl b c6ber a distance of 115 m. 6brpxeb8.hln:21 :jnw b c8cbWhat is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rn9g+cxe m1( cpest over a distance of 115 m. Whag9e(xmcc n p+1t is the angular acceleration?

  A wheel of diameter of 68.0 cm slows d ut9sbor)d +ey/e+ mpy*i-/sp own uniformly from 8.40 m/s to rest over a distance of 115 m. Hy/i o- +yepdpm+/)br*sut e9sow long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotati g*sf8q(tm-v tonal speed of 3600 rev/min. When switched off, it rotates 50.0 8qvf-(ttms *gtimes 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 requirmz :jjha,3b0 ce 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 ishzbc30 ,:a jmj perpendicular to the wrench?

  The bolts on a car wheel require tightening to a tor sop kyy/v ( :;o4/ w3zxcw3dv8lhylm3que of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of thec8( y 4dv xv3 3sw3 okp;hozy/yllw:/m force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertdtu6x3o7 gi+ve*f ;tiia $3.00 \; kgm^{2}$ 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 at the origin, m8 0gvn nnmqf7d9bgh2 696nglbass 2m is at x = a, andbqbn6nh0mlg79gnd2 ng 98f6 v , 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 fritv+iy*y;g7 di sic )4gctionless 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.)g ivc+4syi gi ;t*7dy50 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 mascc7 nl4) j t/sdr1ju3su a1.zvjs9g)0a*wm qes 10 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. A second rope wrapped around another section of radius R2 = 0.50 m exertm.w9)cja uv )d4a3ce/ 0 jsz*1gstqjl rsu7 1ns 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 i7 cs 2ngt31edmd o0*finitially 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 od gedi f17nsc2mto *30f a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of ragy,c8l6qn-fe )2y mx6 l8pv etdius 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 ff-e6ng,el2 )q vlxyy8t86pc mor 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 dz3dkx /ugzd, vetbwc9cc,/,9 isk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration u9v9e,cw /d ,cxdbzg/c3ztk ,of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of lq-uoz0,q*gtse;80 +hlhrw a mass 7.07 kg and radir ul 0*gqw+z ,s8qt; 0-haelhous 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If*gd6qtw t);9yccf e5w 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 ofso i07o8koacrl.o4i ( $5.00 \; kgm^{2}$ 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 from rei s0s5fgob.a13qo d)rst and rolls without slipping down a 1.0-m iogs135rqosd .ab )f0high 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 speed o6 fx-sjfxzrq uc939a: f 10 m/s. How high up an inclined plane can it climb be u-r3qsa 9zcfx:jfx96 fore coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and-f.j grhyf 3c- allowed to roll down an inclined hfc3-yg.j r f-plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.skj wku1aje0 i /7 so5u i.n3+yv5rx4l5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assu5x/u ojy ei5 1n kkia37rs+4suwj0 lv.me 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 momentum changgx3; *mg xei+nes 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 inertis(p;hhxw5iq s-t:d8,l)tf r j a 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 mo/fm s 41+ff gftc5s/lig86wb bment of inerti/tg m l+ig8f f5sb1bw/64ff sca 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?