Angular displacement is;lv4dp6d fae2 usually express in units of

  Angular velocity is expressedw 6m-vn ylbc+ e78p06b8ylvoj in units of

  Angular acceleration is expressmlql4p :l+8 hcbafp (),va *rred in units of

  A boy and a girl are riding on a merry-go-round which is turningwj7omgz/:q7 g at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater ag :jm7o/gw7zq ngular displacement?

  A boy and a girl are riding on azogk bf)-o;v;hn6d rkvupepi2, 41 u 4 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 angula 2 4u1bn hpf;pd-;ve6ok)z,ouk r4vigr speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constantbep i4* 5ojo;p ;,ztui rate. The boy is near the outer edge, and the girl is closer to the center. Who z*ij5,p;t ;oiu beo p4has the greater linear speed?

  A boy and a girl are riding a mer-hz4dmjb fp4,h(g( ccry-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 centrip,c g(-hdhpzb4(f mc4j etal acceleration?

  A boy and a girl arevbwp.+hw w4 ; u0yw0dq riding 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 has the greater tan+.0ph w;40qvy dwuwbwgential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurate (:ibs,bfliw mc.*47 i 5hilmjstatemi.w:fl,j*lbm5ihi b cs(74 iment?

  Rolling without slipping x7ki6geowe3:; 9pb sodepends on

  Two equal forces are applied to a dr.nmbi hgn8 +)nspq 4w4 8e)gw+e -wrvoor. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied pp b-wnwq84+ em))g.hriv gnw+8ern4serpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is appl/pu81iv. w nlhied perpendicular to the door; the second force is applied at 30e to the plane o.v/n l8uiw h1pf the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first forcgkg,, o:;nuf(bf;bi45p*wru5 w kngj e is twice as large as the second force. The ratio of the torque of the first to the torque of the second is jfgf k wnuig,;n*b5kg 5;rwp,b4(uo:

  What is the quantity used to measure an object's resistance to changes i dfc6;rd :/gfan rotatiodgrf d/ac f;6:n?

  Consider two uniform solid spheres where both have the same diameter, but,rquv(ov,l 9s,bw2 kr one has twice the mass of the other. The ratio of the larger,o (rl,q 2wv kr9u,sbv moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twic;rxxzk dn;,mfc fj 5.h5wl-v0e the radius of the other. The ratio of ,5vx kc0zx;5fl.rn-w d;mjh fthe larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has kaj3vdj f1n 7h/)x3njtwice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment odf hv j3n)7x/13jaknjf inertia is

  A uniform solid sphere has ma,eag/88 zp4 d5mhrnx3(xflec ss M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment ofea(c xg 4d883he z5rxnf, lpm/ inertia about a central axis?

  If a constant net torque is applied to an object, tfr g)er aa2ki8y5 u/0khat object will

  The moment of inertia of a solid cylinder about its agzgd*7j/ ddyzl(,n5 : 9rdscexis 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 oe1miz i3t 530k(m)liyxmwv2m x6ezv 7f mass 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotm y v e7iw1x5ki zztli)2m33x6ev(mm0ational 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 rolls without s:kbtqx+1uox bh4sd5ui;3n y 94z5 lhalipping down an inclined plane starting from rest. The linear velocdt9 hkx+ n;zx1 4 4uslib:ao3yuqh 55bity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R mt-6 jgv.ct0 4ik0vn7rck7 aw,rf3)l ar0 btnrolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the.aaktnf0 n-w7vrv4k)milt 7cr, cbj0g3 t6r0 bottom of the incline depends on

  "The total angular momentum of a s 2f0aak*yn(j (5lsklbub d 7)rjpls,*ystem of particles changes when a net external force acts on the system." This statempr7yjb(b 5lll,na(k0* aujs2kdf) * s ent is

  In what circumstances can the angular velocity of sy3z*bayq/8spl hn:n ibx*1pl 4stem of particles change without any change in the system's angulasq4ynab81h/ *lz3 lnxb:p p*ir momentum?

  The Earth orbits thee:7 wug(1pnw1ty d 30phnwqc6 Sun in an elliptical orbit. Ignore any friction which may be present. What h(1y 0uq hw1c p: 6pe7dwwngn3tappens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ell1*e7if v ct r89*kyi6xgtmd -eiptical orbit. As the Earth moves close to theemi1 ft 879dxkv-**y i6gr cte Sun, then 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 outstre-0hkg6 zu6vq,oul x lb5)g2brtched arms close to his body. Whag6h0ruz b6 lv2,ukbq -)xog5 lt happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast koba2+8mi9yp99nse+ xf q kh)spin) by pulling in his outstretched arms close to his body. What happens to his rotational kineti2b+qfm se9k 98n+yah )xiko9pc energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in ha) ,0y3yvk dvpopt8+ ais outstretched arms close to his bodya oy+ydp, )kv3 v8p0ta. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angulq4thcf/td6 , sar momentum.

  What arc length does the Earth travel in 5k0yysj 9e4m/3mp ev a;cu:qo a three month period in its nearly circular orbit about the Sjsv5mo0 :3y4cky / ;e9uqpame un with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a leng0y7/ l iqnwn8oth of 0.30 m. What distance does the tip of the second han0wnq/8l nyio 7d sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute+gro 6jgba+ro7/)o ws equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions i0 jh0z9-am)ilgml0 lr 9ipv0pn 4.0 s. What is the frequency o)lp00a rml i vz90h9p0gi-lmj f the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. epbf+5 xxw9 r;1zacdfdb,eiu+ , 4cc9fu6d4r The pa+9f c,ebzc4x+w uf,prc u e64dri1db5x fd ;9eriod of its rotation is

  A phonograph record rot/1yd1jol rvu7ates at 45 rpm. Through what angle does it turn in 0.20 jovrd/y1 l1u7s?

  A wheel of diameter 26 czj4 a ) 0cas;linzb*b3m turns at 1500 rpm. How far will a point on the outer rim movjzn*ac03b)ba; z isl4e in 2.1 s?

  A bicycle wheel rotates uniformly th ;cbj6tsw - 0o .;inyxcbgn9*9i +zororough 2.0 revolutions in 4.0 s. What is the averaxcn.z9by90wt o*+goc6 b;jisi; -r noge angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions iu4 w x egp:pb8epf.kb1+ 3lyh*n 4.0 s. What is the linear speed of a point 0.10 m from the center oe* xe4kf.gp18 bup:3by +lwhpf the wheel?

  A cable car at a ski resort carries skyjj z7i3h1 )ry sm-3rjiers a distance of 6.8 km. The cable which moves the car is driven byyy r7j -mzh3r)31ijsj 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 rotating with a constant angular speeday0g2 4gxi y/ vfqvh9f6q*i* g of 2.0 rad/s. What is the linearyfigx9v 02 h 6 ifg*/qy4a*gqv speed of a point on the wheel's rim?

  The cutting cord on a gas-poweo1c e0:hi z6d:ac)kdvred weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linhad:)dck oe01ciz v: 6ear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a consh4gw*zjg-m22p 7f thr ut7 6phtant angular speed of 2.0 rad/s. What is the centrig2 4h*t6m2wuppz -rt g7hhfj7petal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on 0irbcd;r97d7 .vwo dehu( 7mq the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 0 bdeud 9o(hrdqr.w77 i;vm7 cm/s?

  How many revolutions per minute (rpm) must a circular, rotati7up:xww72q iummd0snx2z3 t5 ng space station (r = xu2qm2wm :np7xzdi7wt u s5301000 m) rotate 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 / s5;ps6wku yrof 20 m/s. The maximum ce u/s56pkw;rsyntripetal 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 a speed oawby)oc3s5 rt fe)h.3/ x s8uoeq0sb) f 20 m/s. The maximum centripetal force (provided by static friction)8)0owssas5t 3)uocx)b hr eef./q 3y b 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 5ps- +u az4hypstring, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear spp+z -p4au yh5seed 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 slipping 10 m down,*4cbv xcxm2u a lane a ux2*cmcvb,x 4t 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 const)3shxvwz ,8x p d.6rgiant 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 angula8kq)+du buj +i hogc6;r 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 aues i.w8t)mx o1g.4dsctomobile tire rotate after starting from rest and accelerating at a constant angular accele4x)i.8tms wgcd1 os.eration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular a+hda+wztzb4p 5*hssf 4c1k / tv. hhk*cceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerapdn9g ,kw(kt( 0/hilgtes with a constant angular acceleratiog lgkktn( 9p ,ih/(d0wn of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from reso : 2acz3h*t*xr ulcgq5d.el*t and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration 3acdeh*x gt*qocr. l*zu:l52 of the wheel?

  A wheel of diameter of 68.0 cm slows down uniforz 7icq;ch)t.x mly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutiqh.)zx itc7; cons the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s tw h1;tolol1w)o rest over a distance of 115 m. What is the angular acceleration?l woth ow1l1);

  A wheel of diameter of 68.0 cm slows down uniformly razr 9.aii64pfrom 8.40 m/s to rest over a distance of 115 m. How lo69azrip .ra i4ng does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/m-d ept5h0n egso0 sk:bh41a0fz v0 q4qin. When switched off, it rotates 50.0 times at a constant angular acceleration before cqp0-zbqfed0 h4:4vn 01g sa0h to5ke soming 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 requin 2 p (7u9cjxb8i3nzrore 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 forcej9p(7b23n ou n x8zrci is perpendicular to the wrench?

  The bolts on a car wheel requimaq 3(irsr r39;dp -lbre tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is theira3lm r -;9bd3qp(s r magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia * )wq,t bv0a0orf(ej a$3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as fokvcwm6zm * n/fb(n64 sllows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the momemw4 fs/c6n*m(b 6n vzknt of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thol/- r qv50c)knq0pkcw ught the center O. A ro0 r0k)p w5-lqnccv/ kqpe 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 10 kg is pivoted abopryc d8:d2 tu2f)bu6sut a frictionless axis thought the cebyds pfr d28u)26uc t:nter O. 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) 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 b lf94sy.rw p.pnpg0 l2t61wbis initially held in the horizontal position, and then released as the f. w .06pl2 yrpstpflwg94bn1b ree 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 wheeld;o3 9*veej lsuh8tq7 to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axl3es9odvht;7 eqj u 8*le 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 disk pulley of ma ;co.r/ nk.;q02o0px kghc nnrss 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pugn kcpo.;20x;kc/.r hrnnqo0lley?

  A 1.53-kg mass hangs on w b0bw q,pgy-wq/0; v4d:qfqd3l2nln a rope wrapped around a frictionless disk pulley of mass 7.07 kg an 4ldq 2 vyl,qbgfn/ qdp -w0;bwqw0:n3d radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel ca 44 jqiphy+fj uh)64cvn 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 iny t7sk3k6-s09, : k guoewbiffertia 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(w3/t sbxith(.co*hmv e .t1g radius 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 the inclined p1h(t 3o tgwmhcs/*. (i.tx veblane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 e;ila6b;o1 aqp e(lv6m/s. How high up an inclined plane pi lel; 6veaqb1;6(oacan it climb before coming to rest?

  A hoop of radius 0.50 m fmzt or87(6an/p)fuz and a mass of 0.20 kg is released from rest and allowed to roll ( /pnf6ur oafz)7tz8m 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 radiuf sgs,;de2a b9s 15 cm rolls without slipping down a 35e incline that ib9; esds,2ag fs 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 momentum changes b( ugbxd g5ylh,l15y6yy $20 \; kgm^{2}/s$ 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 mop67 f2zdlpwk9/9 bugzment 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 rotat2*5rhcxc/bn8x;zk t d5en,jk ing at 5.00 rad/s with arms extended has a moment of inertia ojkd5rn8,xt * nhec5zc ;b k2/xf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?