Angular displacement is usv ;:erzwuk i79 t165okm 0wikhually express in units of

  Angular velocity is expressed in un1qkzm /x, uqpkf1n7:-78 /la:oba:pgzv yd xtits of

  Angular acceleration is expressed in uni4tn d)gwq noe8v 9)6qxts of

  A boy and a girl are ridhyh)n3 v1b;ilc a k ,n/6q,isqing 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 angnc ih sq6)1, ,lk/v nbh3ay;qiular displacement?

  A boy and a girl are riding on a merry-goss 0mbbt3 e1/rng(f/n ari7 0k3mf u)e-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 angular speenr(e3 fn t ub/sa)f/3meg0ir7m b 01skd?

  A boy and a girl are riding on a merryypig 7 c c69 *ua4/totkzl,hxu4fe-m0-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is 9hz4 f7xou*cy a6/ ,tgt ck0e4imlup-closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which i. b+t ,pz,z3vk,ffzey fu.ipf0w/ j3;sby:xm s turning at a constant rate. The b, :fuekyfz3;.msy3,bw /zpi xvb zft0,jpf.+ oy 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 riding a merry-go-round which is turning at a constx9zkw oa a0nbi 32.4uoant rate. The boy is 9biuxwo42a3n 0a o.zk near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that ihq+ kco k *29x6xlzezc6 j35em m-ckr+s rotating. Which of the following is an accurate statemenmco+3re qxz lx5+ck*hk9jc 6z62e-mk t?

  Rolling without slipping depends onw /sr,n-yv:tu*a -v fi

  Two equal forces are af j((0a4jjlr fpplied to a door. The first force is applied at the midpoint of t j(4ljr(jf0f ahe 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 door at ;b8 v.b*cd xiokbng+p5s2g( nthe 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 exei*k85 bx+no2ggs d;cb bvn.(prts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door.+n xot,s*wgmpx e)(a+ The first force is twice as large as the second force. The ratio o+)xe ,g otxnsm+p (*awf the torque of the first to the torque of the second is

  What is the quantity used t,ma3.*qf ogtz)cl6 26f j7yd8vrq y amo measure an object's resistance to changes in rotation?6a f.7*tz6 rm3,lyqc gmaq2)f8y vdjo

  Consider two uniform solid spheres where both ha/3 fqohf(o6nfqt;:r pve the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia ioq /t ff:q(n;hp6fr3os

  Two uniform solid spheres have the same m hmc6f pr5v:cl0i f5)nass, but one has twice the radius of the other. The rati :5)5lmpfcricv hf0n 6o of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where ons ,cm7ral)k.nn;x v0 we has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to t,canrsx n) .0kw;v m7lhat of the smaller moment of inertia is

  A uniform solid sphere has.ye*-jvr whh0 mass M and radius R. If these are increased to 2M and 3R.0vhwhy-e r j*, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wilzmns/ee)fc o1 er*im0( f e4v0l

  The moment of inertia of a solid cylina ey7 2fjlm(l0der 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 hasy/ yfs qts, u;0dm/ci1s,b6 sw a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotatio1f ,0 y,stisd/cusb;/6 sm ywqnal kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere ofs(y-7qjsyuu-j-xfr dy 64 o1y mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity o7j6-f -yo y(rydy-squ1sx4ujf the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping;l 0w kmgcdkki ;0y:6e down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends onck0y;k6;gkm:ile 0dw

  "The total angular mod9ed8gbb80sx u/o 3 wdmentum of a system of particles changes when a net external force acts on the system." This st08 bxo3sdu/98g ewd dbatement is

  In what circumstances can the angular velocity of system of particles ch :wx6ic l.a gfl0q8ev/ange without any change in the system's angular momewxcve 6f.q:l0 a/igl 8ntum?

  The Earth orbits the Sun in an elliptin3ae6t ktzm;md er +4(qz1*cacal orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about thet 3;+qazemmez64dc(n1a trk * Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth 7yp(mua.4 qzb9q7iy 7x zh)ggmoves close to the Sun, then which of the following best describes thebh.7qgy7) mzi x4a q9(gyu7zp orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretch+u9s(m(/y lkcl-9gwip3 yvt yed arms close to his body. What happens to his ang-upl ycws9(/m kiyg3lt +y (v9ular momentum about the axis of rotation?

  An ice skater performs az4o i j pq/ i9w*ass.ik:dx+a; pirouette (a fast spin) by pulling in his outstretched arms close t/q4s:iodpxazi wj;i *a9sk. +o his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) b i;1:l -wf:wf.dkhtl dy pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of rotatio:d.l wfkdw1li: ;- thfn?

State the law of consjfsbu,3vev. 5 +: mypuo bk6v5ervation of angular momentum.

  What arc length does the Earth tf n0;0sep;pl z g+-r(w (e/fz-y sjkohravel in a three month period in its nearly circular orbit about t0ze(pfrsjne/+0z;pfho (gw - s - ;lykhe 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 distancr1q,y,4 z3qw cu7b v (lwmif3oe does the tip of the second hand sweep through in 3 minutes and 45 seconds?,l,bfcow733 rmq41 yi (uvqwz

  How many rad/s is 25 revoluti i n-)jpk5.fdweu9x (gons per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolu0x h3z5gu(ari)a qyy.v i*h 5otions in 4.0 s. What is the g5a3v* xoyi (ra5q0hzi)y.u hfrequency of the wheel's rotation?

  A pulsar (a rotating neutfb-wg qz9pq/n); * axjron star) emits pulses at a frequency of 0.40 kHz. The period of itxjaqz)*gfpbw n9;/-q s rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turbv/pcx e.3-hp n in 0.20 vpcep b-3x /h.s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far wiljhdyd 13yxdtb5hkr6g5u7 l ( :l a point on the outer ri 5( b1kgdxh6yy:d3tjuldr75hm move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.wd f7 fseh6 cex6-xh +b e8valad4::i-0 revolutions in 4.0 s. What is the average angula+ e6d--lh w6: aecbf ei:78hd xf4xavsr speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. W v5gblz1:ea yfv42f0e:8ceg bhat is the linear speed of4c :vgeebe1l: b5 vf28yafg 0z a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a disto/ 8 sqrmtyfu-j)o5skjt13j9y0;y xe ance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pujjyuo j- s yysm1r9qxtf30; o5/tk8) elley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating wit9y;+q0- lca yl)zbs7j1 ncchy h a constant angular speed of 2.0 rad/s. What is the linear speed;qy)l-lbch0ay+s9 jy7cc n z1 of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m .m6cix 39 lhiain length. If the motor rotates at the rate of 20 rev/s, what is the approximate xh3ali6.cm9i linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating2ju1fdswo2ay0:b3k+.qu5 b z z:p hn z with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel+konbzs u.:1 ab wqu :5fd3zy0p2j2zh's rim?

  What is the centripetal acceleration of a point on the perimetdw)+l2 avr)3o/bgt*p 6vlr)g,br l jder of a bicycle wheel of diameter 70.0 cm when t wb+6lbo3 ) gajt/rpl)r2 vlr)g *dd,vhe bike is moving 8.00 m/s?

  How many revolutions per minute (t7qr8yyh7)ikrj4 :zm 9my- v grpm) must a circular, rotating space station (r = 1000 m) rotate to produce an y7- h9r )vzq yryg mtk7m48ij:artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular dmlj-4utj- y 7curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided -d-l7j4 tyjmu 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 6i);e/xp-m5 r zhfqz pm with a speed of 20 m/s. The maximum centripetal force (ppq5)f h eprx6m;/i-zzrovided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attachew /;lod46-2 pr athh( hp4ssktd to the end of 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 r ;w(sa4h6-4thklo /p t2sdhp the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slj;k6 fh5xb;ffhw3r 6jipping 10 m down 3fxrf5f6k;jj ;b h6wha lane 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 witi6*dlak it)9dh a constant 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 accei-bb1dp) gp 6bleration 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 tire rotate after starting fviwn1cs70)e1csc qgchg*( 0drom rest a c0g (g7dcccnw1 he)*v1qi0 ssnd accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and iufla lm+qj i (+6/1yehas 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 angpv-2vy1ael)o8 l dy4dular acceleration of ev lo812p4dvyly)-d a $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from r9xlg gwsf)cldc 3t(-c,h nuc :s. i.w+est and reaches an angular speed of 6.0 rad/s while turning through 9 -f(dx c:uccgthcw3sl.swi gn,.l+) 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slo: uc8er)c( amuws down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the whee:r(e 8ac)cumu l rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.58 *g1 becllvf40 m/s to rest over a distance of f851 vblle cg*115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to :lzm:zqlz: 0c;eij8j 6 of4 mbrest over a distance of 115 m. How long does :z:0fjm4j8me:ql o biczl z6;it take for the wheel to come to the stop?

  A centrifuge in a mej4s*86kp jobi,o5exm dical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at j 4o,kopemb ixs5*j68 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 torjd gqr5l, 9*qj:2fzpaque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when tgj5q2z :,j* lfdq9 raphe force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 j:n)b uzwo; z9cm long wrench is used, what is the magnitude of theuj:z)nw b9o z; force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerti gim/.v0xijjgf y tc ;-td011ea $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: cg8mkj5m) i)a mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the5jammc))k8 gi moment of inertia about the origin?

  A solid cylinder of muef.,n7 rt ig2s4jd:pass 10 kg is pivoted about a frictionless axis thought the center O.:sre.4n 2 ft ,ipujg7d 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted abojehy+c+we t2 o+gis::ut a frictionless axis thought the center O. A rope wrapped around the oej++ :2ogeyc:swh+i tuter 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 is initially he /dp 3e7pv+(sexbdb ;qld in the horizontal posiv(+;dd 3e 7 /pxqbepsbtion, 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 rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1 g;b oxa0da)p2msu+ z/.5 kg. Neglect the 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 d0sz gba 2;po+/a)mu xdoes the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a 2ne*msxm)wkkgdy0 )9frictionless disk pulley of mass 7mkk nw9d0gs )m)e 2x*y.07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on amrpj+l1 tpdu 3zl-h9 q+4nj- m rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accelej pj+dmh 3mp91n 4uq-t+l r-zlration of the mass?

  A rotating flywheel can be used to a57(sz1httejzk ja;,,*v(3 w tb2m yz 0xjqrc 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 yp- .fs-w+z yeinertia 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 f,;mh8w dq*sdxo0l h10.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What dl8h o;1fh 0mqx* s,wdis 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)0/nk x 6warue with a speed of 10 m/s. How high up an inclined plane can it climb beforea x6w/)knu 0re coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from regszc dml2q53 iljh 02ms4/f)e st and allowed to roll down an inclined plane. How fast0h3meic52l dzl s2j4 )g/ qsmf is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rollsg,w7k4 ugaah8y2fqkraen d ) o/ r:d2*ato0q - without slipping down a 35e incline that is 7.0 m long. Assume it started f8frka4nk r2 ad2a7 agdq:w0gq,t*/) o- y houerom 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 by+ x3l6n; 1grf trcx a5dpd4z5mgz )uk3 $20 \; kgm^{2}/s$ 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 momentlk64mrx54ons h 8 llj1 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 ar-yy8 fv .24drp1pwoxhms extended has a moment of inertia o 2 8o4rxyv1fppy-dw.h 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?