Angular displacement 7lwq/;yr bro- is usually express in units of

  Angular velocity is expressed in units ofc s.kz-i.cb )k

  Angular acceleration is expressen1rq6 3i dcsctpr 8a*49jk/ gkd in units of

  A boy and a girl are riding on a merry-go-round which is turning at a con(do/ dn)6zv xl,m+qhf0yf,rm stant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displam,xv+oq mr 0/yn,f fdh)zl6(d cement?

  A boy and a girl are riding on a merry-go-round which is turning at a constajxg/7k:jg+;pugq ewy -1o7y k nt rate. The boy is neajj/ q1k7xk:;ygp+y gwoeu g-7r the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constanwxg.8vpv9q es ; )l4cjt rate. The boy is near the outer edge, and the girl is closer to the center. Who hasjv4ex. ;qw 9)cgpv8 ls the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constan :3-yzu cl /v(cnr1i/fndlv4s wtxxy:u3f1w,t rate. The boy is near the outer edge, while the girl is closlun/w-v31c n1/vrw 3:z lc : ,xx (uffisydyt4er to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at qdgo)9ytr t: :,7li ewa constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greatergr)w:t y7il, oetq9:d tangential acceleration?

  Consider a rigid body that z60vzbpbs; c de-.dv2bl9, ls is rotating. Which of the following is an accurate statement?db l.;c2 z69e0lbbs -zs, pvdv

  Rolling without slipik e7wa42 *ahaping depends on

  Two equal forces are ypjw vr2( zp7.applied to a door. The first force is applied at the midpoint of the door; the second vrp7 jz(yp2w. force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are appliedq-b/;rmhk d*el:.i4 m r .xmov to a door at the doorknob. The first force is applied perpendicular to the door; the second rml .hxq mer;m4v:k/ d*.bo-iforce is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a5ywh6td 3qpvjc 5jf 04 doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torqu5jd0c v 5ht4yj6p3wqf e of the first to the torque of the second is

  What is the quantity used to mea .p,blw3m vzb+sure an object's resistance to changes in rotation l3bw vb.+,zmp?

  Consider two uniform solid spheres where both hav 3 (rak3d1f *t3p,a8ubekxeea e the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the sma a*bpe(kaatk eu1 3f ,x8e33rdller moment of inertia is

  Two uniform solid spheres have the same /.m:tm ny-z nomass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the small:motn z m./y-ner sphere is

  Consider two uniform solid spheres where one has tncx 3e aae0ft.:g20 wl;yudl,wice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smx0n:f2g0d ;3eectw uy,a. lalaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these n8sdijr /z3nbu k0zgolz( 3. :are increased to 2M and 3R, what happens to the sphere's momentzo. jkg(03 ns/8 3zzlb i:dnru of inertia about a central axis?

  If a constant net torque is applied to an object, that object wicg7r-w ,ls1 6j/t4oc mu hn;zpll

  The moment of inertia of a solid cylinder about its axis isg8yh3xhuz9q;qi i ,9u xp9 cb4 given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinet p c3xq 4ybg i,9xuzh9h;9i8quic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which he3i w edtq32b8as a mass of 10 kg and a radius of 30 cm. What is the ratio of the rot bq 3weetd8i23ational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere ogrnlvz31-tbdc6 7g7bf mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottov7- dnrcblg63tz7gb 1m of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withx :5i4i;m px6* ydm1vx9jugthk*1khz out slipping down an inclined plane starting from rest. Tk; zgx:95yvt6hm*h1dp4 mj*xx k 1 iiuhe angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes whx,*ma1zlax 7sj 6v)rcen a net external force acts on the system.s,1)x6 varal7jzm*xc " This statement is

  In what circumstances can the angular velocity of system of partaroht tz(x/m9x w0j c.sz ;/y+icles change without any change in the system's angulaxjh( +yc .;tz s/9x0/o azrwtmr momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictiu x4v(ucb/pi0,tc b0aon which may be present. What happens over time to the Earth's an/4 (cpt0u bvb,cx aiu0gular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. :-eho(/oghizAs the Earth moves close to the Sun, then which of the following best deg:oh(h /o eiz-scribes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outst vt; 8tjwn;z0nretched arms close to his body. What happens to his angun;w v;0ttj nz8lar momentum about the axis of rotation?

  An ice skater performs a pirouette (a fa6vwx0q8vmhy ,pg;9yg st spin) by pulling in his outstretched arms close to his body. What happens to his rotational kine0,pvvy ghy; 89 gmxwq6tic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast sxg g4 g6sar(;y r0uoa*pin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axaorg4 u;s0 x(ag r6y*gis of rotation?

State the law of conservation of angular vz f*j)x,kqd4hrx6i(: 6iwabmomentum.

  What arc length does j i*8 g8wt.ojmrj7kpm /b )ah*the Earth travel in a three month period in its nearly circular orbit abokb/a7*j8pgjj.o8 hm* w)i trmut 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 ytjym;17 .efjdistance does the tip of the second hand sweep through in 3 y jj.1myfe;t7 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent to?xfc7u-fi. -lw

  A bicycle wheel rotates uniformly through 2.0 revolutions in s(xw *,+oa6x lvy5rtm 4.0 s. What is the frequency of+o* r(xlxa6,wtysv5 m the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a fsa-,c u -.,04hloio j+eqg q cw,je-virequency of 0.40 kHz. Theiagu,v+q0ocis. l jq --w ,ehjeo4-,c period of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it t wh3l9ydh .lrydk5.cs2:ksf 7urn in 0.20 s?.dk h:clr3ys5sl2 w9f7ky d .h

  A wheel of diameter 26 cm turns-m2fv2vopoj0f0 s e ;p at 1500 rpm. How far will a point on the outer rim movovj0m20pfop s2 -v;fee in 2.1 s?

  A bicycle wheel rotatesku dy 0x9f/8hecle2m(c l5:m b uniformly through 2.0 revolutions in 4.0 s. What is the average angular sfe/lduhcxy:0mkl (5e 92 bm8 cpeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revoluv:h 7 ei6koydox1tc0r5xp x2g*.) eewtions in 4.0 s. What is the linear speed of a point 0.10 m f5ov:)xw76 x0 ekg.i e* p2 rdothxcey1rom the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8g q v0:q+q,tcd::nb gx km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fastqg b 0tnc ,xdv:qg::q+ 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.):x.zpqv:t du What is the linear speedq .ux:dpz)vt : of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0m k1oymq2z.6(.qcvof.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of fq o1mqc.6o .zkvym 2(the end of the cord?

  A wheel of radius 1.0 m is rotating with a cotj4tx sv,j5jd 1h,ir1nstant angular speed of 2.0 rad/s. What is the c4 t jxdrhjt15svji, 1,entripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bi u h)3fise4z ycxwf.96cycle wheel h 93uwz 4xscfi6ef) .yof diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (dgai6d //mn )x lur;/arpm) must a circular, rotating space station (r = 1000 m) ror/ai;mn a6g/ /xl du)dtate to produce 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 ys))iib xp m) r*ij.ag3(g+jem/s. The maximum centripetal forc)iaxjrgj*.e3 sym ( i))p+g bie (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 a speed of pew :ycljpk26az 4 g6)20 m/s. The maximum centripetaleykzw:p4 )c66 2 agjpl 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 whirled* cag96yjt i)-ee;bfj around in a smooth level table. If the maximum tension that the string can with-c;6f*)a tj9eibgye jstand is 250 N, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5p ut)sjp(qd,,8uyq 2 c kg and radius 9.0 cm rolls without slipping 10 m down a lane a,scyp2 qujq(,dt) u p8t 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 c e*dxr;f ljt--onstant 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 a constant angular 09 ,i4mpcqumgacceleration 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 does2empe hob/3l 2)5uqs j a 0.300-m radius automobile tire rotate after starting from rest and accelerating at a constant angular acceleration of 2q b2 s3hjeu)lm5ope /$2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, 8uq2w .cm3d;7ilzh(3b o cj yband 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 decelerates with a constant angular accelerpe96pcdt1 d7h(ghk.e atide9.pe76 kt1hhg(d pc on 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 rad/s while turning-37mqzdryol z 9r3vx 0 through 2.0 revolutions. What is the average anguz 9v3m rlozd ryq0x-73lar acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40pq347da ktiwm8- -rmi m/s to rest over a distance of 115 m. 4q38w-7imi -da ktmrp What 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 rest 0*r7-nxb:ztkqouw+d* 3:xi vel m9fk over a distance of 115 m. What is the angular accelerao:zt*fk m39+xlwrix 7 :n-e 0d*qu kvbtion?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s tcsc6;s2pf; ffkfc 8o 5o rest over a distansfcfcsc8;p6f2o fk; 5ce of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a mediccfu,*y hs1am/ al laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to restam/,fs*1 yhcu .
(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 x0ldoe )*nqypu:- m7 x -oqpy-u8eu; ia 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendiculalqp 80pnx*yu;ouu- me-x7o )qe-: idyr to the wrench?

  The bolts on a car wheel require tightening to a tomj 9ri; pnb*r2 bwq5,+e5zrtmrque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the fom2rn,5r9e*p q z+b;bjmr wt5irce applied at $53^{\circ}$ to the wrench?

  A wheel with moment w ib2 b/pm00ofof 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 myo9ty8- //ak-y 7tcv t0 qwpor is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is a 8tptqc//yo0-- row 79yytkvthe moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pi6ur13hyy3t ns tlb63zvoted about a frictionless axis thought the center O. A rope wrapped around the outer radiu1s6n3 bt36h y3zrlyuts 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 10 kg is pivoted about a fr z.ub,xmcui8sn9x 5 9hu 5poai, 8j4ssictionless 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 exertuo ha4s5bj5pis8. mux,ix8 uz99,cn s s 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 initially held in the)x4.k wo2 fn8 m23ysjazix-haf(g u)ed q;h4g horizontal position, and then released as the free end is allowed to fall. What is the angul4ghxw hzas ky;i8j )g -ouqad3f(m2 x.42fne)ar 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-hwwca6; q h/)(e cuvv 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 ;ehq /u()- vca6wchvwtangentially 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 frictionla0r03 wxrwx+ dess disk pulley of mass 7.07 kg drx3xw ar0 0w+and 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 disk pullfav-*ws,+3yu 1 :idfn,dlnii ey of mass 7.07 kg and radius 66.0 cm. i*n yisa:n-d1,ld,i 3wf f+uvWhat is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is reqhyaqfqf z 5g5;6n80xs uired 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 inu5mcgwv) hkn6z 31.v, mp*jfzertia 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 and0- 2 pb8 hsy2(lfndlih radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What inl8-ys dip2h2lhf 0(b s 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 ofzy- wi,n f*,4u dfxd+1nzb f3n 10 m/s. How high up an inclinf * fi1+zd d,nzfn b3,w-yn4uxed plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rw62gfd.4g9yyl4w u56 mbosx nest and allowed to roll down an inclined plane. How fast is it moving ab 9w o6fmg4 ynw4dsg5ly.ux 26fter dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping am:+f*bnf 5)r1,qgm, lynt l4fss i;g down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is sgn :llfft,my*m1n r, q ;fs5gi4ab)+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 9 moc8fpqoyw2( +kw2xd1n9vy 8dzyg0momentum 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 + 4ql6u n2nexk u0.nicl2yvev9sy7.eof 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 ofvg c.z.k:z3he inertia v.:.zek ch3gzof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?