Angular displacement is usually expr08 dqja3b,:tkbkd1l/pg t2 ej3 0pb guess in units of

  Angular velocity is expressed in uni5ljkmtgr.w0:kw 8/ 5 vv l7ftgts of

  Angular acceleration is expressed in unitsregj*b*uz. v,tx44 cr of

  A boy and a girl are riding on a merry-go-round which is turning at a constank4 /k72vy jxyn:t m6pat rate. x:n4k jp27ky/yam6v t 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 riding on a m: 5leg9h7z 3pej5u(xu lxltq*erry-go-round which is turning at a constant ratel7(juelg 3uexp :thz5q5l9x* . The boy is near the outer 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 x. /x *hct*(fak3 w p-xz3vk1m+dydih is turning at a constant rate. The boy is near the outer edc*px3tf.( w vmaddkz1-/kh* hx+yi x3ge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merr wz -v3bdet: p;:k6lzcy-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 centrilv k z:dbct6z:; 3pe-wpetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constao-*3m ira- )ncv:7qvfezh (ddnt rate. The:a-v zfdq*vd n ()hr73cie- om boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rot)o z9jwqh*zjb-;xhw; ating. Which of the following is an accurate statement?whh)j;zbz-q*9 x o ;wj

  Rolling without slipping dsxwrp);*;b rbyv:p0q:fg 5p z epends on

  Two equal forces are applied to a door. The first force is apu8pr/ae9hvr8xsqrs9u 94s j ) plied at the midpoint of the door; the second force is applied at the doorknob. Both sasjrq/u8r9hsve) x 9 rp84u9 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 forc)wypky )cz1 -so,ys e4e is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which forc,wse -y 4yko) ypzc)1se exerts the greater torque?

  Two forces are applied tr.)v06-jpsask5pd vc o a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of50 dk6- aprj sv).svcp the second is

  What is the quantity used to measure an object's resistance to changes in rotaehc1ci/he h-w1l+zx4 tion?4whc h1iex /e+c-zlh1

  Consider two uniform solid spheres where )f3 d 0lizsr zzg,8we9both have 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 isw0lrd z)9,z 3egif8znertia is

  Two uniform solid spheres ufc*l,p. x7kl ya0eq- have the same mass, but one has twice the radius of the otheea,yu.k f l 7cxlq*-0pr. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twicebt n)gzue0i6 qkc/8p yi,p9 8m the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that okmqpp9 )i uc ,y/0gne i6bz8t8f the smaller moment of inertia is

  A uniform solid sphere has mass Mwsl7m ;)dsey-g 0ewg+ and radius R. If these are increased to 2M and 3R, whlgewwd 7s)- ;e m+0gysat happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is app(flc ywjsf/c ff) 8/wmree,-, lied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is giv/ag fut iut3q98x n3;b-mdl0 oen by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kineti3tu u3i9 oa0l-/bfdtqxg8 nm;c energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 1w; :uu6b2bi9 u(4 zjowpbd3 wx0 kg and a 639(;o2 xp :uwwubdzbiu bj4w 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 radiusscu 8 j81ul7,o * hxozi:foxj* R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depen*hx8:o zj 1cux8*fl ,ojo ui7sds on

  Suppose a solid sphere of mass M and radius R rolls without slipping down a.xw*idid0i, dn xld :z14q4zk n inclined plane starting from rest. The angular velocity of the sphere at the bottom of the inciqzin1l xd.,id4:d xwd*zk 04line depends on

  "The total angular momentum of a system of particles changes when a net ey4 :x+zroe ssy 49v:twxternal force acts on trvzo 44t9yewx+: s:sy he system." This statement is

  In what circumstances can txm- l4bq odsx87t wsi5 b/i90rhe angular velocity of system of particles change without any chbx 4 o 7stq d8-/5ib0lsix9wrmange in the system's angular momentum?

  The Earth orbits the 09yt,:y)b;wjnvagdra9 hkj+xg ) rq2Sun in an elliptical orbit. Ignore any friction which may bh0gb9yn r)dw:r; ,j)vkt 92x + yqaagje present. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ez1-re jlppygw (paz-x4s,4( plliptical orbit. As the Earth moves close to the Sun, then which of the following best descr-p(4gr 1 (az-, pepsyx zlwp4jibes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hislv j pznep1i5a3 (n.e. outstretched arms close to his bo (3ea .ieplvnzn 5p1.jdy. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirn vl*qn:jb1)j ouette (a fast spin) by pulling in his outstretched arnnq*j bl:v j)1ms close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouettrc2k2t ua 77+nbb ;z iv(3jelhmqi7g 6e (a fast spin) by pulling in his outstretched arms close m k+ zl7a (i72i;cebtg6n hu qj3rv27bto his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angulrp;g (d(a8yj34mz3atkh ej pxa7vv87ar momentum.

  What arc length does the Earg b2eho cht4;bt n3u:1 s4qkp*th travel in a three month period in its nearly circular orbit about the Su3b oqtt;*4sb hp e u:1gchk4n2n with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clocinfdm dws:m-9 *5 a) .co,ottfk has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 sec-sw) datmocd9o *tf ,. f5m:nionds?

  How many rad/s is 25 revolutions per minute equivaleo qtk/i4jak0nzbafo;gsc s, 3dq1 56. i1d :nvnt to?

  A bicycle wheel rotates52vwnjy xh kj2g2*9slzob74 j uniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotatio x4l2bv yjs *2ohwjnzj7925gk n?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. The0ud0sr*zgh2 * dap1pl period of its rl a0*rpdd u*zp0h s12gotation is

  A phonograph record rotates at 45 rpm. Through5 9y h;)l st3rhn0hfsd what angle does it turn in 0.20 s 9lhdf)stnsy05 ;r hh3?

  A wheel of diameter 26) eowwul,izejl7u( 4.6 ,ip tk cm turns at 1500 rpm. How far will a point on the outer rim moew.u l 6u i,)(j4pz twkolie7,ve in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 re bm; x*tehz:qbzj1ht3bop 87/volutions in 4.0 s. What is the average angularh/tjz3bh8te q 7xbb1; :*ozpm speed of the wheel?

  A bicycle wheel rotates uniformly thv mp01r8lv6flrough 2.0 revolutions in 4.0 s. What is the linear6vv lf r18m0lp 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 cabws: hy,o y)-ssle which moves the y,:w)h y-ssos 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 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular; ei9 j2rxlvxn k;ddt6 ;f(ba7 speed of 2.0 rad/s. What is the linear speed ofxdk;f9l a;e;2vxnj 6 dit 7b(r a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.152 l w)vs5(t prqub-wy6 m in length. If the motor rotates at th2-)rslqwwp55ytvb(u e 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 2.0 rad/sal026 6jywqjd0:cxk/ t)kt:fn z- uxq. What is the centripetay txknwcd:2z: -/ qf)j0j6la t6qk ux0l acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a poaz i:b8 r db(v)zrh;u8int on the perimeter of a bicycle wheel of diameter 7r vbd)z8iz8aurh(b;: 0.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must axfl 93b,j sc6i. -gu-v upzd,r circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity ofd,u-gr3jx.izc- , vbs6l9puf $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50;;-/ubqfk5wmizzop 5 +r i 4pd m with a speed of 20 m/s. The maximum centripetaioz/ikqpfu4bp d5z5r;+-;w m l 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 spe1b mb5 mtlidamw0; w71ed of 20 m/s. The maximum centripetal force (provided by static friction) 1;idw 0t bml51b7awmm 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, is whirled around 6jwz/dnqfya:zn:1t o c:z5c: 9.dy ikin a smooth level table. If the maximum tension ziow5d9y :d q:n cjtk.n1ac/:zz6:fythat 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 y9 l vfbw,qun9y0x0+a;up t5y9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s.xu v990pya ;b5,l+qfy tu0ynw
(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 constaxpfu,v6,o g: znt 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 an:; x *.lu3moxppqjvs /gular acceleration 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 automob0xlz x4a46 7yenqkdru6v 2m.d ile tire rotate after starting from rest and accelerankxz2y 4drx66 u. ledaq04mv 7ting 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 angular acceleratdy /r.r tz 9zl7ty5y/jion of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates wi41l:vgc n yw(wth a constant angular acceleration of cg n:4yv w1(lw$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an9exua+ 9:ja jl angular speed of 6.0 rad/s while turning through 2.0 revolutions. ua9 +j jealx9:What is the average angular acceleration of the wheel?

  A wheel of diameter of 2w otzg2 2;bst68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotatg2twt o2;z2 sbes in coming to rest?

  A wheel of diameter of 68.0 cm slows down kpzz/pln 4ta5zru0d m 9e:pq7t( 02qw uniformly from 8.40 m/s to rest over a distance of 115 m. What is the27zzw0 5ua:pm4rkl /pd(ntpq0q t9z e angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s xm/1j a(9u;zgp zjo 8rto rest over a distance of 115 m. How long does it take for the wheel to come to( / 19;8zojxgjruapm z the stop?

  A centrifuge in a medical laborat*gv.p 3;n3 nyvlm hi--q, itczory rotates at a rotational speed of 3600 rev/min. When switched off, it ro-i *. z3ln;mvqpi3hv ,cgy-t ntates 50.0 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 90 Nm. If a 30 c1l sbci1*ahh+ o1k:uom long wrench is used, what is the magnitude of the force required when the force is perpenk* 1+a oo1:lsb1hh ucidicular to the wrench?

  The bolts on a car wheel require h6 j2qmp pe9a6tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force rp2am6e 6j 9hqpequired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iol. mm)t f,l+wnertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modele g4oigpxbn udg))f5 2 mslrzj+,)8 h,bd as follows: mass m is at the origin, mass 2m is at x = a, and, mas 8r j glu)pbghg,2d)+oni45 mzb)sf,xs 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg 4b cxvn+:xcd3is pivoted about a frictionless axis thought the center O +nxvcbcdx4 3:. 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. (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 tmn nhdr;ptl7t7,n8le72d8 905cf qyyy p9l ab he 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 9nn7d9tp a78pc0ymlte 7 5 ,bdfhqy2r n;8lylexerts 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 hinged5o2q6pj)j urzu ,o: rf at one end. The rod is initially held in the horizontal positij ):j ,oroz uqr6u5fp2on, 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 82f. 2nln f sj gc0 olgogdw9-se/o1g-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 sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, assuming sgfoo g20wcdj o fn1eg2/lg.l-n9- s8 it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrap(4p p2 lna/z make3 ryws+5;ahped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratio a sharl4z/pp(y3 nmk5+2; waen of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pu vfy84 uk(qjoi7 8n;hcqgp61g. l-mfylley of mass 7.07 kg and radius 66.0 cm. What is the acc4nck y (7pg.1-6fuqfoy8 8qljg imvh; eleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to storepr0k11 *oe)dyyaa e2m $1.00 \times 10^{6} \; J$ 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 inhqg(1 :bbw 1ktertia 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 st qj3tu /to-kq9arts from rest and rolls without sliu ttqqjo9k-/ 3pping down 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./-3okuy/cjutm 1hj ,2y gsb l:0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an i-o ug myb kys: /3ltu2/j1j,chnclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fro)uw3ln 8-ia0sel twz6m rest and allowed to roll down an inclined plane. How fas)a3-zntwli 8e0wu ls6t is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg *d8qc. pfv,qyand radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertiafq dc,py *q.8v 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 ch w,iwi4o31dqqanges 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 -v 842aunmsowna ,nh:$5.0 \; kgm^{2}$ 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 armk/2) nndw+k vls extended has a moment of inertia nvknd + l2)w/kof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?