Angular displacement is usu :qy*),osgif 6 kwrtan7u0 vibs1 3(tvally express in units of

  Angular velocity is expressed in units oj**lk/j8e n*8u0ob.f dx-e sx)jougk f

  Angular acceleration is expressed ino,w;wx( vr -bn units of

  A boy and a girl are rid37m39iucdzbbm53 fh ding on a merry-go-round which is turning at a constant rate. The boy is near the outer ed3bifud 9c 5m7 zb33mdhge, 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 iszp;1iq,/rsjbc hj sg.z 85 4kj turning at a constant rate. The boy is near the outer edge, and the girl is closer to th5z j; 4jc8bsr/zhs.kgi j1qp,e center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a ltseq;k.unjle- 2*e+ constant rate. The boy is near t+*qel;e. s nle2 -uktjhe outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are ridia zvq39xs:k gsp/d;.bng 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 center. Who/a9x vg:dp;s. z3qsbk has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant rf v n6u3pz-j9efa f0q,v5a;y tv6k/(3dmpgno ate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleratio-va3jpo5 d,e/fvu (y;nnkgz6 v90 6 tpfqmfa3n?

  Consider a rigid bod(y(((yq*1voc d j9-p jfp m ms0mavn5ay that is rotating. Which of the following is an accurate statements-1vj y(p ncm*fa((m50 yqao9vm(pd j?

  Rolling without slipping de7hpfl to6q 1*l* rb5yrpends on

  Two equal forces are applied to a door. (s7+fgh d ecz* The first force is applied at the midpoint of thecsze*hdg 7(f+ door; the second 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 ire,fctr 43+:so a/radoor 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 cef,3it4 aar: /rrso+ the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. j:rdjipl23mxqm4 -; h a(q4d nThe first force is twiceqj h4 4 3:l;miqdxa-rmn(jpd 2 as large 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's r4qhsz)lk q+5+,vy ptfesistance to changes in rotatil pk 4q+vft,q +)hs5zyon?

  Consider two uniform solid spheres whert0 vwe;5xx6 xlw 2e.zpe 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 x.x0vptew ;wx6e2z5lthe smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twic++k.p 4jia g;c2inze)ot:l pw e the radius of the other. The ratio of the lar: pjl t.kica+)2pgnezwo;i+4 ger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass a+zpsnxr v d4/ ) wte45* fzv3qj4vfn.und twice the diameter of tpd. vfn4ejx+f5rvq wn)v4z3*/s 4tzuhe other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R.nx)w i6wm(a nd3+v w)6d5fytj If these are increased to 2M and 3R, what happens to the sphere)t66fx5iwj v danwd+)n( wy3m's moment of inertia about a central axis?

  If a constant net torque is appliqhsy7u ( f1/hied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given p(d i5lwdu 5:aby 0.5 MR2. If this cylinder rolls without pua:( idwdl55slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 ke +*qkp)r 8;7v(oc)sh )urum+ vhrpz mg, 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 ki)omc8re puv++;u7s rr) hmp z*)v(kh qnetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of massmob81o) i )hl/ohttm6;fc9l g M and radius R rolls without slipping down an inclined plane starting from rest. The linear velct);/hm bmilo oto 19fg8lh 6)ocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withop k2kb8va9fme0k*7j out slipping down an inclined plane starting from rest. The angular velocity of theebkk 8*jok0 7fvap29 m sphere at the bottom of the incline depends on

  "The total angular momentl1flr z(r9 ypry b((kl9k uavo*)9x55 dcd6ut um of a system of particles changes when a net external force acts on the system." Tdyk ut9vl6l(1k) 9 uypbl dr59(fca*r5zr o(xhis statement is

  In what circumstances c*/acpd*gjrg z akng:*llmx3 +2oy )5 aan the angular velocity of system of particles change without any change in the system's angular momengx3nykg* j2a/*)5p: lcg+ a*zalr omdtum?

  The Earth orbits the Sun in an ellipti ph)) faoq-z;lp pjih w7)aj5j+d7 dk.cal orbit. Ignore any friction which may be present. What happens over time toah pwqp j-7)o)i5ljad hf7.jz+)kp; d the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ellipticnt8nj8j-m0nk1/gbfgro 7s kw o(u l70al orbit. As the Earth moves close to the Sun, then which of the following best describ kwjum8- k0 jn70 nbnt/lf(o8sg g1r7oes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchwpg * -7wpab6fed arms close to his w* g7p6pfa-bwbody. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchedn)7u2:tp e0ye(cv7ndi ln zq7 47csyk arms 0y4c7e) nui7(v st 7n:ye2cq7kpn zldclose to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pfa y,bo. bqs0:irouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of ine yba.q0f,bo:s rtia about the axis of rotation?

State the law of conservation of aniswls6*7k f- uepelx7mox( 2)gular momentum.

  What arc length does thju*zj ;psor 292iqs v1e Earth travel in a three month period in its nearly circular orbit about the Sun with a raj22ir; *p us1v sq9jozdius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a le 2dohl27k8q.0m4 qd6csg yxkw ngth of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and6d.70 k28klqsg4qow 2xcmhdy 45 seconds?

  How many rad/s is 25 revolutio/ 9x xh/rrd(afns per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wha(w, go6rqk/yp7k alkex( 4z6tt is the frequency of the w (g/7k( k4 a,yqroz6lwktexp6heel's rotation?

  A pulsar (a rotating neutronjeeh 34m3z:b-;w b9evaa*k sr star) emits pulses at a frequency of 0.40 kHz. The period ae ves9z * w3-3mha4b:krejb; of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.n z,qi)s3m8g*5qm *w g*xyecz20 s?en)3gx,w*z5z gs8mcqi **mq y

  A wheel of diameter 26 cm turns at 1500 rpme-.sunn zr).jubz(rs c-t 2t7. How far will a point on the outer rim move-u.cjbz-t 7rsz rs ue t2).nn( in 2.1 s?

  A bicycle wheel rotatesfnet6zub* 6527wwpag7egj k8 uniformly through 2.0 revolutions in 4.0 s. What is the average angular swfk g*tb 6p756gue7ea82zjnwpeed of the wheel?

  A bicycle wheel rotates unifo c ji e)c1s51w* 6mkfivlz*n)f;g :xfxrmly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of t*g :nc*wix1 j; kf6 xilzsfe5)1m) cvfhe wheel?

  A cable car at a ski resort ca214-xxvrzkl5z sjo h .rries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.-o zk1rxsvzxj4l. 5 2h0 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 constant angular speed of 2.0 rad/s.ur u5oz/g( l*yajrf e pk6;5-p What i;6r55pr(-z*f u/ogua l jyepks the linear speed of a point on the wheel's rim?

  The cutting cord on 6y e 5hkf. ob.xzka0hhqp-ic+6 x*t 5ia gas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed hx-thb q5.z.0fk+ *epx6i h6c ik ao5yof the end of the cord?

  A wheel of radius 1.0 m is rota ;(qoe5s9xi6e u3uppg ting with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of e;ge3u9o ux6 is5 pqp(a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicysm hpp ++4n.ixcle wheel of diameter 70.0 cm +xp s+i4m.hpn when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm0e 7.dmd;akb u) must a circular, rotating space station (r = 1000 m) rotate to produce0 u7.eb;ka dmd an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m wi+m n0tkx4iwr b0s5 bc3th a speed of 20 m/s. The t00s5mi kr4wx3cn+bb 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 circular curve of radius 50 m with a8zl2 (sqv ,sdbb+ oh.h speed of 20 m/s. The maximum centripetal force (phh2l8obbsv ,s.z +q(drovided 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-m9+ss;x3 g*/hf rgrtn m string, is whirled around in a smooth level table. If the maximus* h9gsxrtn rg/3m+f;m tension that the string can withstand 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 9bvx6 x2+ko14 lrt:try .0 cm rolls without slipping 10 m down a lane at 4.3 1vbt xrtxrk64l+2 oy: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 acceleran qpi/7 17qsx0oy76f ibnov/xtion 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 op 0+lo0d8u iucmyz:cv4a:8x;gb 5 qlpf $4.5 rad/s^2$. 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 au:r)6tmu4gixwwkq42 eig/no(j1 6d xytomobile tire rotate after starting from rest and accelerating at a :o(xu)1r2g g4yjt x6id qeiw/mk 4 6nwconstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular a ;lh50+yit1/qe 9cuj sl2pjiscceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating--kwf1oa latyyh, .)v at 20 rad/s decelerates with a constant angular acceleration oa)f-yk.hto1a w,-lyv f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while turn lwr0 --;.ovule3 rta7bha tq,ing through 2.0 revo7ru,3.-rh;a tlw albo- qtv0e lutions. 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 overma59w26 te i;q+hi itp a distance of 115 m. What is the total number of revoluai m+p9 i652 hwteit;qtions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows y 64*gccjp d:gdown uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angulargcjp gc*d6: 4y acceleration?

  A wheel of diameter of 68.0 cm s3a k fmong6s/7lows down uniformly from 8.40 m/s to rest over a distance of 115 m. How los 7fkon/ma6g3 ng does it take for the wheel to come to the stop?

  A centrifuge in a medical laborator, zo ,c d1xui2pzy;;hry rotates at a rotational speed of 3600 rev/min. When switched off, i,o uc;rh y,z2zpdx1 i;t 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 3gncyo 4w t-mc8ua/-1 5gi1orl0 cm long wrench is used, what is the magnii 51/c guo4lgmw8-y o1t-crantude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightnmggft:;v (r 1ening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the manvrf tmg(1 g:;gnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerti w 6shyfk+ttf3123 omqa $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as ft6t +,. +nmuuvrlx3wd ollows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is x++tltvmrwd n 6.u ,3uat x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a fric .o8rp-k60np zjnzmw 4tionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = -j.p 84kp nrnzz60mwo 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 10 kg is pivoted /3. go+a5ivcirmrl+7c :cuy ddj/w 9zabout 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 exerts a force F2 = 6.0 N downward. How many radians does the cylinder rotate through in the first 5.0 seconds, if it arm dcdzc. jvr/: 7 ilgw+oyuc+i53/9 starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially czd-f eoz oq;+ihy(,t-x(z+ y 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 c( hyz+z-oqfd ,ziy to;e(+ x-rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and makalik4un 0v:1v6ko s ( ikwbae i.o;5b-4b k.rss 1.5 kg. Neglect the.w ( bb 0a vik-5nar o46e.uiskv;b1ko4:lkik 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 it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless pv woucb9*7,ndisk pulley of mass 7.07 kg and radius pcwbu,*o 97v n66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrappedc) .:8iq qop5be+tfol around a frictionless disk pulley of mass 7.07 kg and radius bt:l+cf o8ieq).q o5p 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store l1kwmms: y:-e ovu,3lenergy. 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 i xx9dazn 0-t+dnertia 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 0.010 m starts froms b v4wz76q(rt 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 the inclin64vwsb(7 zt rqed plane?

  A solid sphere of mass 1.0 kg jj/yzm nda1-qvby2 :r6 8)qag and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to re yqb2j/a)amq1y:n 6-rjd8g z vst?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest 7o 3haae0 5ezyand allowed to roll down an inclined plane. How fast is it ma eey 37a0h5ozoving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping d(i )i7pug+t)q8ujdj oj1z5p down a 35e incline that is 7.0 m long. Assq1dd 78t)jjg u+ou )z (pjii5pume 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 rr( 95 j9ncx na9nb-cgchanges 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 momenmw )/:b:yvr idt 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 has a moment of;bpo9 au05w-ap x bi8i inertia oibwp; 8b0i9pua-ax5o 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?