Angular displacement is usua(rt0i o2d gewjh(7ln 3lly express in units of

  Angular velocity is expressed in y,9e(k z1gim q;1y5bav p5snkunits of

  Angular acceleration is expressenv whg-v,*eb13nca: kd in units of

  A boy and a girl are riding on a merry-go-roundbqvojs:yajhoi 3v+9 lr8t7 ,6 which is turning at a constant rate. The boy is near the outerio6sv+ jar3 yot :vb8,9hlq7j edge, 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 is turni gytvw3df;9z9ug 8p :cng at a constant rate. The boy is near the outer edge, and the girl is closer to the cez9wvupg9;d8ft3 gcy: nter. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constantgyrll: 5sup.6 ras5.rgyulp l:6te. The boy is near 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 csu (ucca1 zjggni93sm6vf* +:onstant rate. f3 c z n gg*(msjcvis:ua61+u9The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riir9n+89nnact q1r:zpv9g/mm ding 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 tangential a9nr8n 9 1a+mgmqi r/z:9tn vpccceleration?

  Consider a rigid body that is rotating. Which ofmu;8 d:hb glpoa(+8j7qwvpzw bd02fg3d5 7gm the following is an accurate staomh7jw;a(p7zgd :5g p 30gu bwbl+288dfm qvd tement?

  Rolling without slipping depend sm66ma0q ugi(s on

  Two equal forces are applied to a door. The first s2fb1:9 s/h1;cz ad rhi zv aitttg6y;kll365force is applied at the midpoint of the door; the second force itbdivs arf:6 c951gzay 1 ;63htl;kslht/z2is 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 ny/bxbm5oh, //iwu, qk 4/net door 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 exertsh5,nmkt//4n y/ biwxob/ , que the greater torque?

  Two forces are applied to 8 ln4;dv4iv x g2gvazthy2:r0a doorknob, perpendicular to the door. The first force is twice as large as the second force. The i;xndv 42a4tg v2: vr80yglzhratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resis nj70wjg5)qbgo4jyf9r k 5 xk4zd1m(utance to changes in rotation?wn 0do45)zjkyjmub(95 fg 7 r4qx1jk g

  Consider two uniform solid spheres where both have the same drtf7e k11ea 8 dstu(;qiameter, but one has twice the mass of the ot sq 8ae rd(1k1u;t7efther. 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 radius of 3nr)i/a ibkykta,z0) th kt ) i,3b)kia/yrz0nae other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniformq- 6wm w26,3oj7q3n+ qfnxew cumi9kr solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smallerwf3ixn wurqo32wm 76 +,kqenm6qj-9 c moment of inertia is

  A uniform solid sphere has mass M b 3rt *gc57rdjenoy.ig+3ih4and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of in3nod *4r hgbje5igr+ y3ct7i .ertia about a central axis?

  If a constant net torque is applied to an object, tuo nmj fvt0 yo ,8ieu2dp,j-.t 1kk06vhat object will

  The moment of inertia of a solid cylinder f:9lfv k1xi 6tabout 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 hg;,p eiprv: nj,6lj(f as 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 kinetic energy of the bike? Assume the wheels are:jeir(,g,np fp; lj6v uniform disks.

  Suppose a solid sphere oflvzv)m vka-qxymeb2fp-8;6oo7v 7u 7 mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom ofuxz-7)flombpvam8q6 vyo2v77 ;vk - e the incline depends on

  Suppose a solid sphere of mass M and radycrcy;z93c9s (g , hlnius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bot z(ycclc9 ;g,h 9ny3srtom of the incline depends on

  "The total angular momentum of a system of particles r 8uy(2o8da7jrwh 0zrf m0x*w changes when a net external force acts on the system.0r20 8 8ajhufwmr(xd 7z yo*rw" This statement is

  In what circumstances ca/ibgrscktj(-( + 2ye: f6xcm mn the angular velocity of system of particles change without any change in the sys 2gimb/6( ecrjk:c+ (yfmts-xtem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any f7cuvdclg0pf (**8 fburiction which may be present. What happens over time to the Eart glbc*ufc 08u*df7( pvh's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As q gc hgp. ere8w(pg82*the Earth moves close to the Sun, then which of the following best describes the orbiting speedqpgpghw * r(g.c 2e88e of the Earth about the Sun?

  An ice skater performs a pirouette (a fast ln3m;y: p2c.ooye4rkspin) by pulling in his outstretched arms close to his body. What oy:.yo4mn ;2cep3kr l happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pghkjpbi*l /uvf. m(3)ulling in his outstretched arms close to his body.( /*3pj)ubhgmfvkil . What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirow -ft.)a z1udpuette (a fast spin) by pulling in his outstretched arms close to his body. Whu1)wfatp-. zd at happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentum.e3m2z1: h fjgr xpo01d

  What arc length does the Earth travel in a three month period in its near4pl0rsren++n6m ;usaa hww/h, 4 nva*ly circular orbit aboutn04hpn 4aew;sw/u v*lah,m6+r s +ran 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 distance does the ti;, uv( pd izih.ju-nf;uy)i23mgbi 4kp of the second hand sweep;ii.uub gmjy4i3vn;)z p(ufi , k2d-h through in 3 minutes and 45 seconds?

  How many rad/s is 25;4rxym xp ax)z60msfmdm-6 b9 revolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 jz(w5qwj.w ;3frk 3 ahrevolutions in 4.0 s. What is the fr3j3wa ;wz5jwrf .h(q kequency of the wheel's rotation?

  A pulsar (a rotating neutron3iaa2yf m.o*a star) emits pulses at a frequency of 0.40 kHz. The period of its rotation is.2 iyomaa 3a*f

  A phonograph record rotates at 45 rpm. Through what angle does it turn in / xj/rlmb vd*:0.20 s?ld*m/v x:/jbr

  A wheel of diameter 26 cm turns at 1o mri4 : m-bp.-o)ekez500 rpm. How far will a point on the outer rim:.pmz4eo-ekomb i r- ) move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is t6pg 86or.hskyhe average angular speed.h6orskp8 gy6 of the wheel?

  A bicycle wheel rotates uniformly through 2.45,rhhvb5ud uc lls/9aq/ ml40 revolutions in 4.0 s. What is the linear speed of a poih/mv,9lurbl4asd 5uh 4/cq l5nt 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skl7 iql5io/8u liers a distance of 6.8 km. The cable which moves the car is d liiqu5/llo87 riven 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 rotating with a constant angular speed incm76 u wy7cg8r 2cm62)zv h+tgwjn/of 2.0 rad/s. What is the linear speed of a pocg 2yu877c nh /mn )mz+6j6cvr2iwwgtint on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lengtr,t m1(kvflpirqq4 0)*9 zcpwh. If the motor rotate)vr(pf p0lt q9k 4iwq,cmr*1zs at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a ct*ve4,crqn.t/mew4wc p2m :lonstant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's rim.m4l*tw:q ,2e/nwet rmvc4p c?

  What is the centripetal acceleration of a poi701qo (k7tzcnlc* eonnt on the perimeter of a bicycle wheel of diameter 70.0 cm when the biceoozn*1l77 ( 0ckqtn ke is moving 8.00 m/s?

  How many revolutions per minute (rpm) m*g9enxswi 7k 1+ lqu3c ,d9tgkust a circular, rotating space station (r = 1000 m) rotate to produce an q1c9ket d kggu+sl 9n*7 iwx,3artificial 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 e57 i5efkq;8;wgqipa1g vip 7/s. T;gig 7vkpw p1857;iiqq5ae fe he 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 radl obw:h+yb8)w5ff ,ivius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static f:+fho bww,by 8lv5if) riction) 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, ip1 oo7)v kegmrctv*vx/has *. utt3-;s whirled around in a smooth levtgo*rvv;taet x)m 7u*3/pcohvk.1s- el table. If the maximum 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 9.0 cm rolls without slippingud sjfgsah6 2 kqq-/uel.9-9y 10 m down a l-eh ud9kj9 2qsygas/ -. ulf6qane 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 c s6kkmfqn2f- 8ilg(6 aonstant 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 accelbxxfb(enp4(59 (atou b whr,(eration 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 automobile m- 1gcksu0i:: lh-bxhht)9lw tire rotate after starting from rest and accelerating at a constant :lu)h- i1lkbw9xmh: -s thgc0angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an a:col3elztmuti p,mb r4(:cf+s+w52 y ngular 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 constarbs+)-4aftdn(o /nxzl(d x2int angular acceleratio bxz +oit42r-)fa /l(s(nnxddn of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and rp0ccn/u c/xy o2qeq9jcf 9 p;9eaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accelejp p/yx/909u neqc29ccf; ocqration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40o:j) s81 noce vr zqcp1t+tsq-v5+ df/ m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to res8vncq)+/t11oqs+f jd -5:voprz scett?

  A wheel of diameter of 68es1blk5jn6ze o4/0 7 cx2ai hm.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceleration? x zo157lhecbk0ms2i6ae/ nj4

  A wheel of diameter of 68.0 cm 3nz)u: -vupfa;fzh 7c slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel7; cuf:hz-azu)pfvn 3 to come to the stop?

  A centrifuge in a medical laboratory rotates at a ro)d8t 5: getzwgtational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleratiog :d8z)tg 5etwn 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 requ a*kyhnk+yw +.44erdfire 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 is perpendicular t+a.f+e *kr 4yn4hk wydo the wrench?

  The bolts on a car wheel require tigh sk *+1qpkz0ohtening 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 applied kphoq+sk*1 0z at $53^{\circ}$ to the wrench?

  A wheel with moment of ine kwik6vj wuy 3965gapzf)x7 e/rtia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as 2t h26j7 kjhiq(2.xndab3 lzg follows: mass m is at the origin, mass 2m is at x = a, and, mass 3.qa2xj2lih tz23gd(7jkb6 h nm is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frgfnxm*9 dt3 hlv)(ly2 ictionless axis thought the center O. A rope wral 3) 2hv*xf ny9lgd(mtpped 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 frictionless axis tho29 7gm(t0ld f0c gmurlught the center O. 0ct2 lrdmg (9ml7ug0f 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 o)28b oygtb 5rb4l-kv y4kd d0lne end. The rod is initially held in the horizontal position, and then released as the free end is allowed to f)dv k8boyldy lkb g2t405b-4rall. 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 wheel to be a ring of radius 30 cm and massnv:iszn6 vj8-xsg- p)tii4 -q 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sproc-ji8 sz-)4q:gv6p n-xnis i tvket 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 rszf hd/3, 1m p;yo+-q/n wonb2db1chhope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pull1y;/o2hbh-dswmo+n dh zq/f,c b31p ney?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of maam3yej j) 7ws/ss 7.07 kg and radius 66.0 cm. What is the accelerations3ye)w 7/maj j of the mass?

  A rotating flywheel can be usg9 g7vn0-qio 2aj7ldied 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 ineroh8m8p 6 mrrsgcj2 0y5tia 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 st4 7 4+wqyixnr1,ry0bez.c3s7 ylt lsiarts from rest and rolls without slipping 73yst4ry b i inzy. lsec1+4,r0wl7xqdown a 1.0-m high 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 59e.sk:*darj7t a g psof 10 m/s. Hsr d .:5ej 9sa*akpt7gow high up an inclined 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+1la*yg2zqps rest and allowed to roll down an inclined plane. How fast isq2* l+za gys1p 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 slippidw) kj5 n* cx0h.vflws;f4*x xng down a 35e incline that is 7.0 m long. Assume it started from rest. 54* w cshnwdfl.;xj x0)kx*fvThe 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 by 97yrq)jx qv pb ;o3r-q$20 \; kgm^{2}/s$ 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 ofy1n 1w8a;2xp)q yv.ot+x a izl 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 extw o8(clm:uud y t7 *lbhjd(m64ended has a moment of inerti6dlmcwby7 t:j uo( d*lmu(h84 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?