Angular displacement i*gb;p xanua5+s usually express in units of

  Angular velocity is expressspd9 o+i4t 5m (/)bthhj1menhed in units of

  Angular accelerationt3my 1;mbb,q88yzh + t,doitb is expressed in units of

  A boy and a girl are riding on a merry-go-round wh11h,m ousts9wblwmxb sct- t9 )/- 0xlich 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 d)wwxm-lm9b9lbtuoss-ts0 t/1 ,1 xh cisplacement?

  A boy and a girl are riding on a merry-go-round which isi9tzj, tt94otc 13pbf turning at a constant rate. The boy is near the ou4b jtz 9c,tfp1o3ti9tter edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a co 3qh q/llvl+-i, i3ut:hfi5 gznstant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear speed?il:q3lt-hli 3,ghqu v+5/iz f

  A boy and a girl are riding a merry-go-round which is turnda/ua-4 la),uvbtz,h6e0 cqming at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetd,h t/-a),0cazm ael4b6 q uvual acceleration?

  A boy and a girl are rid8 i cn e/)mvwf,7pu+cling 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 acceleratuf )wv8p+ ,e7mcclni/ion?

  Consider a rigid body that is rotatoqac r*vg3uiu .q7 6/ voizngd-p(n- lj+89hving. Which of the following is an accurate stlq*g-+dg/h.n67vpn( ciq vrzao3 8- 9uvouj iatement?

  Rolling without slipping depends hcv3owk; r;c.cjvu1tt1ni*: ,ir g-yon

  Two equal forces are applied to a door. The first force is apdk(0i7-bnmd *,yjqsrb.w g( pplied at the midpoint of the door; the second force is applied at the dooddg(-rb,7m iq n* byw(j.p sk0rknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first fors9 i1e5b*kqn3tzvm6u u r 2sx1ce is applied perpendicular to the door; the secon*3 9sme2z tr51 ukusb nx16qivd force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a docupy b/jm)( 9 +ctff-(putd l3so/u:e orknob, perpendicular to the door. The first force is twicefps:f -uy+9( ump) ecudc ob(/t3/l jt as large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity usedxwts f9mgy:bc5,k7m 3yl/lp 7 to measure an object's resistance to changes in rotation?fml/lm 97pk,:573tgw yyxc sb

  Consider two uniform solid spheres where both have the same diameter, but ono (c0jqqr.q* oe has twice the mass of the other. The ratio of the larger moment of inertia to that ofjo rqq(.*c0 qo the smaller moment of inertia is

  Two uniform solid spheres have the same mass, bu *4uhqh7*ks iqt one has twice the radius of the other. The ratio of the larger sphere's moment of ine*k*quhsq h7i4 rtia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twiyt uou82y,t 2 pc;qv s9hh. tag*7cmy4ce the mass and twice the diameter of the other. The ratio of the larger moment of inertia to u y qvh78mcs ,9u apgth*o4yy2tt2c.; that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are in8*o6cm0cq yfh creased to 2M and 3R, what happens to the smh6*ycoq0 f 8cphere's moment of inertia about a central axis?

  If a constant net torque is applied tq6;xv sg(pki9who0ml9awli 9o; jt i0e6vf( (o an object, that object will

  The moment of inertia of a solid cybaewvs;e:4-hy3h v r* linder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translat -hv;es3evybahr* w 4:ional kinetic energy is

  Consider a motorcycle 48hbbr5s2vyr s 3c+hsw*rfh/ of mass 150 kg, one wheel of which has a mass of 10 kg andh vy/5hr bh+swsc 8r2 3f4rbs* 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 uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping downeo.t 8plt7matng.;m, an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends onm,m. ;ape 8.gttlto 7n

  Suppose a solid sphere of mass M and radius R rolls without slipping down an ta )yo,s3qqx6 qqmx+m j:1i-linclined plane starting from rest. The angular velocity of the s,3i):61j q q aqlsxxtoy-q+mmphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changebf7e4dpey0ztzz : 92r rhy *5fs when a net external*9p5y: r zh2r0ye7zed tzfbf4 force acts on the system." This statement is

  In what circumstances can the angular velocity of system of p id;*a e e0linub,1n5varticles change without any change n5ia,1 in0 bevde; l*uin the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fr:+ tu-kw2.hd/vv kwwpgn si ;*iction which may be present. What happens over time tkdwkg ;- whns :2 /iu+twvvp*.o the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbszx4ag4um 3hd 2zj9c8it. As the Earth moves closecm2d8ua g 9jhx3s4 z4z to 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 his outstlir z-.o v/k aroan2ox9 up151tkxd*-retched arms close to his body. What happens to his angular momentum about *ak 9rxlr/d 5xtniv 1k1o.-o -2auzop the axis of rotation?

  An ice skater performs a pirouette (a v a 4rdkaj:us7amxc.wal.;wvih: 9.7fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the ax7ia;:mw a7d v4ucx wha:9k js.rla.. vis of rotation?

  An ice skater performs a pir2kduc bllb1m9w *9x,5,ayrp kouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his mo 5uxk2b9dpbky ml*r9cw,a, l 1ment of inertia about the axis of rotation?

State the law of conservation of ana-w :ir 7t 3emci knro0-9ho8dgular momentum.

  What arc length does the Earth travel in a three month periuk;* pjn rq 155vjgs,mod in its nearly circular orbit ab uj5*n5;g1ksqm, rvjp out 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 dista1fyf hnu2r9o3dlhd ,:nce does the tip of3uhd r :h, 1floyd2nf9 the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per 3ehyx+ f gif9k3a0+z)h4a;sg9oj w o pminute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutio5) nwl(( /y, zpeipexrns in 4.0 s. What is the frequency of the wheel's rotation wl/ n5 ()piyzre(x,ep?

  A pulsar (a rotating neutron star) emits pulses at a frequea,skcrib5 ( rxfts5h8)n (q4vncy of 0.40 kHz. The period of its rotativcir q,kssfa(hb x)r5(5n 4t 8on is

  A phonograph record rotates at 45 rpm. Through what angle dzqxcbul ,l3n ;t ccm*tib4*9q h3(vy/oes it turn in 0.20 tlbz9ccih/3 x4 * q3qbnuv*(;y,mtcls?

  A wheel of diameter xp; u8o tg d,go:qk2l-26 cm turns at 1500 rpm. How far will a point on the outer rim move in 2.1 tg,g2ldoxqpo-u; :k8 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What gypwry.d-m/-o0oc, p h;mk *d is the average angular speed of the wheel?p- wcokmrypmgo0h-,ddy *;/ .

  A bicycle wheel rotates u7c1ejll.v hf0 niformly through 2.0 revolutions in 4.0 s. What is the linearejv 7.l h1cl0f speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The can,xlp89dxe d) +4xo 3oz.nysh9 5mrea ble which moves the car is driven 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 l+5and9r, ex8h o4 s x9zp)ox3y.nmde12 minutes?

  A wheel of radius 1.0 m is rotating with a constant axbt pk( q(awk.3o w/uo-m2qa0s gv:i7ngular speed of 2.0 rad/s. What is bk7u-((sa0v tqwqgkoxw p .m3a:o/ i 2the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powe frp0jiysy 4*4red weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the *fij44 0yryspend of the cord?

  A wheel of radius 1.0 m is rotating with a cous bbo *0lrpi(2m-nul zer+0 (nstant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point om+rz0o * siu2rlu pbbnl-((0en the wheel's rim?

  What is the centripetal acceleration of a point on the perimeteizf dy 2 ve:1jqod.k b.iqv*p3k2bf1)r of a bicycle wheel of diameter 70.0.bkd*3dq.kff1: iqbep2 vv12 jiz) yo cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must 6uyl87 hj mkg:c3nx0ny xhs87 a circular, rotating space station (r = 1000 m) ro7jsny6 07gxmh3y 8 u8: lnkxhctate 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 of 2u41 bfi; z7 ):vuxtbwv0 m/s. The maximum centripx: 4 b)vtwvb17uu;fizetal 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 20 m/s gkx/e)chh*i/ )k/ih/ce hgx* . The maximum centripetal force (provided by static friction) 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 s6mo yfv*;kn ;ttring, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, 6n; ;ktyfmo*vthen 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 slippingcty u 8 c evwre*v+bt/2r5sj;- 10 m down a lane / v8tebv;tjr 2r-y5ew u*c+ scat 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 accelerax ug ls2w2cbhd63sj1/ y ;rq/ttion 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 2vm9k ncy)s+u)hn7nkacceleration 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 i9t f0xxtytb1hk/y- .tire rotate after starting from rest and accelerating at a constxty0k t f.1h /-9txybiant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an a5/h 2: cwz;z sh*lvjkfngular 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 ,c gce /*rq2nf t6ja*gwith a constant angular acceleration /c,fn*egq2 a6cgjt *rof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest anduy h-uq u,2t9dc+xur6 reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular a+qx urt 2yd,uu-c u9h6cceleration of the wheel?

  A wheel of diameter of 68.0 cm slowsl;+ o r9 i:dqi01c ,k:utzac:6wtdkad down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions ic+u d9ak: w :ra,1dzq lo06tdi;t: kcthe wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest oqb5ymay4if )8ji)q (j ver a distance of 11i)qfq(y4y 5i)jj 8bma5 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly fro +9 ili74aulkcm 8.40 m/s to rest over a distance of 115 m. How long does it take for the ulc7k94a+i li wheel to come to the stop?

  A centrifuge in a medical laboratory (5aid5xmx s5onnuz)c9ti kr f 4s;6g4rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accxc 69uikonaz(4int)5 r5f ; xs5mg4dseleration 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 ro 2cf., 5-lsis6n q2k-m jsmxzequire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is t2i,2jsnclqk m5x.sf-o- 6mszhe 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.:m/f xtt6cjen .l; zi8i(jk(n y:(lxr If a 30 cm long wrench is used, what is the magnitude of the force ;nil.t: yxjxjc(6(:lm te (n rk/i8zfrequired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of m1;4k 0n xwvrw d6b1lsinertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mi9dmm7i x u(s+ass m is at the origin, mass 2m is at x = a, and,us9+mimix7( d mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a fricti io f;4p,8cwtzonless axis thought the center O. A rope wratfc;z84io ,p wpped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section 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 a; v45m7vumbj uxis 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 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 secob5;mjv4 vm7 uunds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held in thepbphntg,t./0 horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is releasenp.t/thg 0, bpd? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle whe/v31mo- /atedfp 0ci wel to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. Ifovf0 i3ead/m1 p/-ctw 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 wrap1s: hbbj/s8f cped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. :bfb8hc j ss1/What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulle u jq; yqx6ydc1+w85ugy of mass 7.07 kg and radius x6u8;+qwyc5 g u1jd qy66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be usedq++wdu5fp17ps a6kiz 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 inertia ofmnv )+t,7 vgz*7 enozx $5.00 \; kgm^{2}$ 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 rolls fc) ezf 2j:o*my81xqwm 6p+pn without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of zqn cp:f 6m+ex8wp2jo1* f)y mthe inclined plane?

  A solid sphere of mass 1.0 kg and68i4 lqyx1( yoqsed7 e sf4bq1 radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined p8lyyfb4qqisd x61q(1oees 47 lane 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 anf,5 uu0y mwcaa1j sju 04hc q+8k.3hhbd allowed to roll down an inclined plane. How fast is it moving after dropping a verti4q8f 0huhhy+ac, 5busu1j 0k3jmw c. acal distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 1m ;xthmt q3uu1 xyqvk+j*y0,* /c/jho5 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it s h j,u0xv;tqo//3*kh1ytj*ym+ uc m qxtarted 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 changjssz042bi w3yj1+ *pv-nw hrxes 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 inexp xivw/6z6+x .9 vri aqy kq44n7*jdnrtia 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.z x7gpa8(b* zc00 rad/s with arms extended has a moment of inertia oag pz7c*(zx b8f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?