Angular displacement is usually express in-3mo1n-pay ytt 0z-uj units of

  Angular velocity is expressed in units o*,hg*t ,sxo4 g*qbzw of

  Angular acceleration is expressed in uniebxxe 5. .d hb0ipv4q6ts of

  A boy and a girl are riding on a merry-gonx3kz q 71o-lur3lt xzi43io+-round which is turning at a constant rate. The boy is near titrz3noxl 7q1 zo3lkui4-+x 3 he outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are ridingrlp i83l. yy 8dda1e.s on a 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 angulad ar8.dyilpy1e .l s38r speed?

  A boy and a girl are riding on-uvshknp:eyh-+ ( ub dc 9edpo63j10q a merry-go-round which is turning at a constant rate. The boy is nea bh qvpu+69p1yhs-c dedjo30- (kneu:r the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a cons.lql0nr;s+n ;nu. f;lknf:lptant rate. The boy is near tk+nf;p n;0nrl n sf;.l.u:llqhe outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant l3k1ak cwqiq3 ;0ksyeo 4l*o/rate. The boy is near the outer edge, while the girlq*i kw0y s/c 1l34q3ka;lokoe is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body *x*ts/yt80pgb *bwlpthat is rotating. Which of the following is an accurate statemeny tl 0* pb/*8bstx*gpwt?

  Rolling without slipping depenqa aj lm qr(vw2+6f*f-ds on

  Two equal forces are applied to a door. The first force is 0 inxyi6 5ul 5d.:s v4y55c tgimyu,zjapplied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the gre6,tg5sl.y4ux 55yiijn 0i: yd5zumcvater torque?

  Two equal forces are applied to a door at zl jxbyc2-a7 qg7 bzi;db- ::en2ge. fthe 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 thb: ybx;i.n2zd: gac-g7 b -7zlf eqe2je greater torque?

  Two forces are applied to a doorknob, pernsf0wz(h7/rp58 nwxc; 6yt hjpendicular to the door. The first force is twice as large as the se8x7 hw(z6ch j tr /n5swnp;y0fcond force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to m,(9xtl e saiz b(v*ob)easure an object's resistance to changes in rotationes*lbvozx ( ,t9ia(b)?

  Consider two uniform solid j (5sdqzyj;fu) 4q6r cspheres where both have the same diameter, but one has tqr)4q( zjd ;cfjuys65wice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the rap w +/xqv/*tioos)mo(dius of the other. The ratio //ooo*ti ( pm)v +xqswof the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twic (qraykbw;dtc 4oelnn 85cob: jp1/ f1h:e7g 9e the mass and twice the diameter of the other. The ra1o5 ;l9n yhbpj74fgo( wtdn :krae/e8bc :1c qtio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M aq5d2rjtez*d.. i nw c(nd radius R. If these are increased to 2M and 3R, what ha w*i.jr5d cn2z(d.e qtppens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an obt;zr/+w 442 gqc kgcxts0v jps.yy:5yject, that object will

  The moment of inertia -)n;gmrq f sre-lx4 ;ps fn85uof a solid cylinder about its axis 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 of mass 150 kg, one wheel of which ha mtvn 5k5h.gl1s 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 kntgvk15 lm5.h inetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without m3kd: l3a0dq. e a8mdb,zpca/ slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline de0l:dbeammz ., qapd/3cd 3a8kpends on

  Suppose a solid sphere of mass M and radius R rolls without slipj3nm.r;a s 1yqping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends o1.a r3mjqns y;n

  "The total angular momentyfl3,1),u 1gx:y) j x g lwczqrrvz;,hum of a system of particles changes when a net external force acts oy1ycz h )g ,ljr1, xwu)f3vl,z:xrq g;n the system." This statement is

  In what circumstances can the angular velocity 09lmck3sas 3a4mep9 6iu, tfxof system of particles change without any change in the system's angular momenkc9a li9 pms,f63u 04sxa3 temtum?

  The Earth orbits the Sun in an elliptical orbit. Igno *htkv)h-s5x fre any friction which may be present. What happens over time to the Earth's angular momentum about the Sun*h )-h vxtk5sf?

  The Earth moves about thev0cho14h 7qq)-5rz)yuqtxv p )np f+e Sun in an elliptical orbit. As the Earth moves close top z)+qx57yur4t) h1opc q 0 )n-vfqveh the 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 w)wku6wsdl 06his outstretched arms close to his bw6wu0ks6d)lw ody. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast sg.b(0mis rt w gz.78a7p5p )kokkw(isb+pw l; pin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotas kwi.7kkl )wbp0(tog7ab+(g 5rip8. pzm;swtion?

  An ice skater performs ck10xv8iu-w t mtb b;96ukua0 a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of rwt6i 0; -tx 1bbkv0mukcuu89aotation?

State the law of con8zqzt8b y, az5servation of angular momentum.

  What arc length does the Earth trav,f nkv r+szmgqe/jz3 3,e-im4 el in a three month period in its nearly circular orbit about the Sun ,qr4k-fj3 ni,me sv3+mz/z gewith a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lengtw5:dfipxex, ,(d up7b h of 0.30 m. What distance does the tip of the seconbifp,7u5 e,wxdpx:(d d hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 ref zbp/xvu y8*,xwhv kpr )i,a0t9 .e:evolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thege 7 yn,/8tdoslb, ju7a t;4em frequency of the wheel's rotnjm7yal;/b 4se87,gt dte, uoation?

  A pulsar (a rotating neutron star) emits *e1)u ap0 jziqpulses at a frequency of 0.40 kHz. The period of its rotaij z1u q*pe0a)tion is

  A phonograph record rotates at 45 rpm. Through what angle does it tur ak dcdc5 q-wu38p4ogg h*7 s,2up0wbkn in 0.20 p gsu o*,27-uq50d g348wwdcakhckp b s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a4vr d)e,j t+nb03xb+fqh. iw l point on the outer rim move in 2.1+xrj)en0b,qf .dh t 3i+ wvlb4 s?

  A bicycle wheel rotates uniformly through 2.0 revolutionsbu0;9je. el zq in 4.0 s. What is the average angulz e.q9le; bj0uar speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in tr;(hyh m86nw 4.0 s. What is the linear speed of a po8 ht;nrw y6mh(int 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. .w 21nowwkke(hm13bjlb78bxxi/ )o m The cable which moves the car is driven by a pulley with diame13m i.w 1/w 72)(khobelwk bjmonxx b8ter 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 speed of 2.0 rad/s. *i1ww hz: i+3jocp;uh What is the lpwu;z i+hhio*:cj 31w inear speed of a point on the wheel's rim?

  The cutting cord on a gas-pyamz5 +vjzjp7t/lp oy * k/e)6owered weed cutter is 0.16 m in length. If the motor rotat/v7jo6*y m t)jzz+k5 ppa /leyes at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0q+-ea;w 3pgv g m is rotating with a constant angular speed of 2.0 rad/s. What is thepv;ag-e qg3w+ centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a poij(r gm 913furpw4v:qknt on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 mm krf39v ujq(pgr:41w/s?

  How many revolutions per minute (rpm) sy2tj z-yhrubc1v1 +, must a circular, rotating space station (r = 1000 m) rotate to produce an art jz1rs-2+1 t,uhybcvyificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circ8(/osfh bumzu(5w fxij (ku(q.9 .:r-fvlmq oular curve of radius 50 m with a speed of 20 m/s. fhowx zm- . ri:fu.9b/(8o(lus( mvuj(5fkqqThe 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 a speed of 2w*jqn6y /; 4bl ll*dxv0 m/s. The maximum centripetal force (provided by static friction4 xnyv6dll;jqb** w/ l) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end oyo2 gi d3am osc379n*qf a 0.750-m string, is 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 odom aqg*ny2cs3379i the string is not to break?

  A bowling ball of mass 7.5 p )+ty9y1uqj*yo ,anw kg and radius 9.0 cm rolls without slipping 10 m down a lane nw ypo1 jy*y,qtu+9a )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 accelerak lphfg/w1s8w+zb r5i0)hsp9 tion 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 accelen1,hbll s;h m,face+gm7c /q 3ration 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 y 1h.rrmzw4fs2l ,2k hradius automobile tire rotate after starting from rest and accelera h2hkrr1l.,z msy4wf 2ting 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 an-i(7noh;b d yf -ugsy6d)3nj jgular 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 wi-a. qodj5; bteq;9 ig6dj svp7th a constant angular acceleratio7;d9tj-vd g a s.o5ip6eb;qj qn of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angul-ou*yv*gdx qc9lus: li 2 m13zar speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accl*392oxsvcgyu : 1 mdlu *qiz-eleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to q rpry zx.1fs7-sg00orest over a disysg rxrozq0pf 1-7s.0tance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter . lgaj; 5yx)ybof 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance ofg xb yjy5.;al) 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows downe kwny, cs;vv**,- 2kr n-igbk uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to the sto*icnky-bwgrk*,- k; s 2v vne,p?

  A centrifuge in a medical laboratory rotates at a rotational speeda-l4q) v1 rin ybbhq;. of 3600 rev/min. When switched off, it rotates 50. lqqbnr4;.)-hi v y1ab0 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.u qzu i4vbe-i*u u 2,6aa7snu 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular t24u 6b *,inz vuaau7 qsu-i.euo the wrench?

  The bolts on a car whj)j1gn.s; b( p qmmxd2eel 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 appliedjdnm2m .jbxq ) 1s;(pg at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia-pd dot,6tta17hamk 1/eoa dmti11(b $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modelediy abz(21/zg dn0z;dn as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is z (zy01i ng/;d2z nbadthe moment of inertia about the origin?

  A solid cylinder of myz/toj8 v5ec2z8mrkn2d o m25 ass 10 kg is pivoted about a frictionless axis thought the center O. Ad528jmoc k/8y zevrn2 o tz5m2 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a flxyr2xvn (k,k)x +k- grictionless axis thought the center O. A ropykv(r+ -gxln,kx)2x ke 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 n5+2eatfu )l(h8f gf xend. The rod is initially 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 f)hfxlt8+ ne5ua2fg(inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mas) q(rh:ciq 0mms 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a m)ir (qm :q0hcsprocket 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 frictionlolkess4b e3 w,,+-wse u7 lix8 t+lm7bess disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pulm8,4s7xl,i t+ 3uk+e w eo7ebwll -sbsley?

  A 1.53-kg mass hangs on a rope (qr*7ytr tt9ajw1 kb8 wrapped around a frictionless disk pulley of mass qyrtk jtrw 18ba*7(9t 7.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. Iy+e .ci b.ku7y6ma* f*uqs6g(ltp s ;qf 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 ofti5qmd q*t4 u* $5.00 \; kgm^{2}$ 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 rest and ro x )z4ojge8gsga 4pha)):5igills without slipping down a 1.0-m high inclined plane. What is )j)i5x44gzhe iagp:) os8gagthe speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.cg :*5ca y+sbrf kumx1vv5x8q;k0w 7a0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plang0*7 m ayvsqrkv:kc 815+xfw x5;uca be can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest azg,a bmqe3+ /pnd allowed to roll down anpz m/qb,+ 3ega 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 cm rolls without sx uad38* ax9ikgn:ofb7 +iln0lipping down a 35e incline that i7b3:9ugix*x aildn0k+a on8 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 cha cte )l1l5x;uxtesr1 balb 653sk1vk c +/u.menges 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 ind3ns-o:h i7d.+8 1uv6cu *dku r :y 2akswbldrertia 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,g3itus* xd:wc qis37 rad/s with arms extended has a moment of inertii*3c ,utisg 7q3xdw s:a 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?