Angular displacement i d ak02*cq;mzks usually express in units of

  Angular velocity is expressed in :z s-9e;ner:m3hcsb0fd tci8 units of

  Angular acceleration is exprw-p)w pa*7w rwessed in units of

  A boy and a girl are riding on a merry-go-round which is turning a)k(*ih a.o+jh, rjvnht a constant rat) j* h.hk ijhv+noar,(e. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are rid/x3y,j4tz0- ymqa gtz6i r8peing 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 greay4/- 03giq,yextmtz jr zp8a6ter angular speed?

  A boy and a girl are r:kcge l+ v*,ztiding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is cel+zc *gk, :vtloser to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a63j:k8 o wlktywfkicw: 1q;* o constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the :jo8ok qy:*3c ;w6kw lwtifk 1greater centripetal acceleration?

  A boy and a girl are ridingg0viy9d y( 3mk 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 taniygky3vmd0 9(gential acceleration?

  Consider a rigid body that is rotating. Which of the following is pjyayh*i* lxe)q 1 3c3tolc9dl t069i an accurate stateme9 *tocj3ey*3x09i 6pcqltl 1 )hyl idant?

  Rolling without slipping depends on+q-3vv exe/h j

  Two equal forces are applied to a door. The first force hy5tz4be2sum : w k4v/is applied at the midpoint of the door; the second force is applied at the doorknob. Both feu4:/s2 y wz4tk5mhbvorces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. Thecaqh 9llcrq. iv: 1y cufh1624 first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the grc 29lh6:q4.i1 ruychv1 cqf laeater torque?

  Two forces are applieia.(h4 lg+baz d to a doorknob, perpendicular to the door. The first force is twice as large as the si a.b z4+a(lghecond force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to-rj vz3(9rm:o(g mxsjj27ly y changes in rotation- ( 9yr27j:ozmx(mygslv rjj3?

  Consider two uniform solid spheres (h6 f ,atc9db+yhmd /0uhdp0jwhere both have the same diameter, but one has twice the mass of the othd9t hfmpy+ /0,hja60c(dbu hder. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the s 7+fvt9 izpak5kd/f,e ame mass, but one has twice the radius of the other. The ratio of the larger sphere's9fa ed+/ip, 5kvfk7zt moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice thi8hfl q6 bo2l6e mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of i2l 6of6bhq8lthe smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased /n.x ktou;ml) to 2M and 3R, what happens to the spher.mxkt;nlou) /e's moment of inertia about a central axis?

  If a constant net torque is applied to an obf/ uotz9t(ls7q rmd :,ject, that object will

  The moment of inertia of a solid cylinder aboutenp g,cw mqn+;*6.otl its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to iqe+lwg.n6cpno* t; m,ts translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which hm bnni;:wqt +nos7ibqs-3r+884 tz nuas 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 aw -ii q qt8 ;un b+7b+8mznssnrnot4:3re uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping down an in+7 f7wsgc s 2xf42hxwao xi61m;,xfew cli 4 w12 fmixa77wow,f gefsc;6x2+hx xsned plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid spher ( z)5)n;qdr3hxt;nce a ncyw)e of mass M and radius R rolls without slipping down an inclined plane starting from rest. T;c(); ntxeadz3nw)yh5c)n q rhe angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles chang li -tuk 6zve3gg/3i*ves when a net external fo-e iuvlk3 3/*v6ggtzi rce acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles change wdb 0uet.488qc5e l g /gmwjz/without any chan wce4g8mgz0w8/ .5/ b ujlqdetge in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictioqv+wy5g /ls:rn which may be present. What happens over time to th/rqlwv ys+5: ge Earth's angular momentum about the Sun?

  The Earth moves about5sy hz:g4guuc2 g /n 3bmd-cw0 the Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the c gz05dsh gm:/bug 3 c-4wnu2yfollowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretche*j:5o :f i( ;gmtz sy+wie3fjfd arj5yg+ iio3ztws;fme:(j: ff*ms close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performsbjx)qxbv2+ /9 xbx8r6dc;izm a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rob)db x6 x/2i+jx9mv ;bcrq8zxtational kinetic energy about the axis of rotation?

  An ice skater performs a piroy9 s2a/sed.tm uette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about th/. dtems92asy e axis of rotation?

State the law of consero.il +dg 6kin0wx9g f0vation of angular momentum.

  What arc length does the Earth travel in a three month period in its nexa5 /8c. vgkxkarly circular orbit about the k vgacx58x. /kSun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.3 y8d7jv+phist xq.3 u78wcb.j 0 m. What distance does the tip o+u7t x8.iqpj3bhwys7j .8dcv f the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revol 0;n,l1)(d/ i u8 p*0jffge4i bdcx5mmmdjyaqutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 r84j (1x ex:gzyi3vc 0lbwuy+mevolutions in 4.0 s. What is the frequency of the wheel's ru iym80cy 4lvz :gxw+x (3je1botation?

  A pulsar (a rotating neutron staibioy; kqa2) -stto,u;(il 8yr) emits pulses at a frequency of 0.40 kHz. The period of its rotati8 )oo;istyy bqiita-;l2k,(uon is

  A phonograph record rotates at 45 rpm. Through what angle does(vmo(..u/ fl4pwa gm s it turn in 0.20 swmu .m4.v /g o(lpaf(s?

  A wheel of diameter 26 cm turns at 1)e/;v;h pdn-ha+ ; h;auhxmag 500 rpm. How far will a point on the outer rim move in 2.1ax mdep unh/+;h g)aav;h ;-h; s?

  A bicycle wheel rotates uniforwz sc3iitv(/ix6+ns w d8c43n mly through 2.0 revolutions in 4.0 s. What is the average ang 34 ( n 8ws3nxiwvdzs/+ic6ticular speed of the wheel?

  A bicycle wheel rota*cf;eok4qcl4w4 cd4ltes uniformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center ol 4kcw eodq;4*c4 4clff the wheel?

  A cable car at a ski resort zx j.yqi7o 5t, (i5 vfn6iu-sccarries skiers a distance 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 pulley rotat su5 , ixjo6fi zvt-yn5(7ic.qe 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.c0q8yi:wcq4j ,+ cylmdfc .;h0 rad/s. Wwq y hc0di.q84jy;c,l cc:f m+hat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the motocfgl 5 sm188efr rotatecffl8s8e 5gm 1s 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 constant angular speed of 2 ktnwvmf 01.b 0w1o4mh.0 rad/s. Whk m0n1.h4 0fvb w1omwtat is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a b .v9/9hno j8s sluav;picycle wheel of diameter 70.0 cmsh 9o;spvjv8. ua/9nl when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) 6qbd/ ( tak08-qo*lqhelni9umust a circular, rotating space station (r = ( 9tl6o- lq0in8e*adqubkh /q 1000 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 x0 pw.ih k8+pjwith a speed of 20 m/s. The maximum ceni0 kwp8px jh.+tripetal 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 curv +obuhi)mvn :t *i1cu(e of radius 50 m with a speed of 20 m/s. The maximum centripe(u*:tu+b1imc )i h ovntal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, att5,sbjhgjfj m3wty.j )h648uj ached to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that thb5hjj.8ht ufsm6g3 y) jjj4, we 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 cmyl rra gb +c:mh9v81rzd5lmb3 v (8fg9 rolls without slipping 10 m down a l 8r:9 9v8 ( ra+d3b5mgzclrbyvhgmf1lane 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 ah m.0o 6 1wve2ocp4*xmnssz0fngular 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 accelerationt;:ub d bd f 0fxn)svay;)d*w: 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 t r)wi 0eidqm+,ire rotate after starting from rest and accelerating at a cons qd,ew)i 0m+irtant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelerat q 5iwkwpv:c:j *ai.2bion 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 dq(mujk7b5nq7c fu00 angular accelera(f cd5kq7n qb700mjuution 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 whm6s1lr pwu* :b3 xl8 hkbiou62ile turning through 2.0 revolutions. What is the average angular kuli612r3s*:o lxpub wmb 8 6hacceleration of the wheel?

  A wheel of diameter of 68.0 cm slhewkld4uw6 xmctw d1r c5:,*o w6-u3 l qwd/*tows down uniformly from 8.40 m/s to rest over a distance of 115 m. What xwe/,wq ttwh*6d 1:o 3kw ucl65mcwr4dd-u l*is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly fromq :qb4/b 6nvw7k1lqnll 2r k 7vpkm8(a 8.40 m/s to rest over a distance of 115 m. What is the 4( bkn7lk/mwq :a 7qvlnr8lbk216v qp angular acceleration?

  A wheel of diameter of 68. mt:n-gpkr;.fcagcx w u9 99l10 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come tmlkc g:.99t 9ucrx n1awfgp-; o the stop?

  A centrifuge in a medicz(imvf 3e+p7 /g6tp ji52maxbal laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a con 627+z ami5xftbp (mp /ievg3jstant 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 90s+5 xn,3r*xof7:ebpxoku, k a Nm. If a 30 cm long wrench is asuoxr7 3e x,*+5 nfpko:x k,bused, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. nh+,xy;5iero16 *gj.wvt(hvibn fzkt/ j4 y 5 If a 30 cm long wrench is used, what is the magnitude of the force required when the fnfb zi1vxe,ht yg h+5twr65i;. j( 4/yvjno *korce applied at $53^{\circ}$ to the wrench?

  A wheel with moment of lz8lr45ebzc q , o8i0einertia $3.00 \; kgm^{2}$ 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 m is at the origin, mass 2mbm wob4mx0a*oc19r 8z is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origicm4 9 wx zbbom8o0*ra1n?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis z8h85lznq c sed-8z+r;*we,u 0tg sby 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 sectiol t cd- qs5b+nsgy8hurz zee880*;,w zn 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 frictionless axis thought th tpj+v2n8/kzs1lgr; re center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A secl vjrrgnpt1k82;+z /sond rope wrapped around another section of radius R2 = 0.50 m exerts 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 endlze br0*i xl2a9f,4j k4i2epd. The rod is initially held in the horizontal position, and then releas2*eike r 4l,2z9dbxlj a 4ip0fed 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 ,)ockxqe* vp4be a ring 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 tangentially to a sproo*e,4 k )vpxcqcket 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 dis6i i -urzsw7s wb94kcejn,x4 ,y9s hz+k pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration oen,4 9ssb- z 4,u+j wz6s9xywh7ckirif the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pullemsi7/tfrf:;9twsbnn.w 80gn y of mass 7.07 kg and radius 66;7n8fbsn r t wf/ws:0mnit9g. .0 cm. What is the acceleration of the mass?

  A rotating flywheel can crhxe9(:b: yinx0 ip)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 ine) 6p8.ne6hp)tzzc vyrrtia 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 0kab s7ou30q7 :59 mzy qp5m8yqpxnf9g .010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the spee n x5kzq:qomq p3gps09 7y y5b97m8fuad 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 of5 ks-rusiy+xni 2c 49-0ertp p 10 m/s. How high up an inclined plane can it climb before c tx5ce -ips2n+ri-s0 9k pru4yoming to rest?

  A hoop of radius 0.50 m and a majez/f /xu0 ex/ 7+wpasss of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving aftes7j e 0pu/z xfxe/+aw/r dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 3j ,2qf (b60lm3nlvlxz5e incline tnvf2 l lbq6mlxz3,0j(hat is 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 mvy:j2fqer x(5 omentum 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 of inertia of kwb-o 6n hywea0ild89vtq,13$5.0 \; kgm^{2}$ 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 extepcdbp (fw + ggop9k.9cr(* e+gnded has a moment of inertia ggbgkw( pcpe.++p(*r9f9o dcof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?