Angular displacement is usuallj/ jw56tjmmk),ubkosi)*v 3r y express in units of

  Angular velocity is exp*yyyqrh1rz, 9 ressed in units of

  Angular acceleration is expre9 cz0nfob-s w,ssed in units of

  A boy and a girl are ri +pc5obgo 6h 8n;vp)mmding 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 gre p6o8h+ocnmbp vg;)m5ater angular displacement?

  A boy and a girl are riding on a merry-go-round which xuba;:h), .msog7 aseh b5y c5is 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 hysg )ob7bhaexa;u 5.:ms ,5cspeed?

  A boy and a girl are riding on a merry-go-round which iio 2hxgl0 0k 3cv+7h0+:0ayhsj rssb bs turning at a constant rate. The boy is near the outer edge, and the girl is closer to the cenh02 h 0yxrl 00kssosva3 hji++cb:g 7bter. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is tez axb6q7/n ;ofgk02vd -.y)p :pny eturning at a constant rate. The boy is near the outetd.ko/xy nan26eb p)q:gfz7e p vy;0-r 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 9n sr+wct by**v73mpe4jb9qb at a constant rate. The boy is near the outer edge,3* cjn r*bsb49b7e wv9+qtmyp while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body th+g7 5 6nlnm;ijhc( ovwat is rotating. Which of the following is an accurate s clvni5+(7og6h ;jn wmtatement?

  Rolling without slipping depends oh1v u9pyg1pa/ n

  Two equal forces are applied to a door. T6/*xj) v;jx-osv 4xoh5ns owahe first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the dooavvj*nw/6ssooj;o 45- h) xxxr. Which force exerts the greater torque?

  Two equal forces are applied to au0s tl;me o)cw 7)awrh9,fgd- door at the doorknob. The first force is applied perpendicular to the door; the second0t, ug)h9 -wm d7 wo;escaf)lr force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The firs8lkjt;*7 t x2w 1umetxeo1u+ jt force is twice as large as thuxlo;+8 j7*ujxm t1etetkw12e second 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 changes in ed zbl9 ,,okol ,yj:6lp)w+bkrotatiojpl6,zwlydb: eo +lb,k9 )k,o n?

  Consider two uniform solid spheres where both have the same diameter, but onl,m;7jd 9aa0scl - ompe has twice the mass of the other. The ratio of the larger momen7 a m;sd-,cl9jlmoa0pt of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the /d(s(p mugdtc ,p; ru9same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smallgudcp ,up/(rs 9;mtd(er sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the yl q;b qu4 c5oy9 2fsnfarmf11: imu:mxd.9s2diameter of the other. The ratio of the larger moment of inertia to that of the smal5b91omfu9q :y1: mr fy 2 q.nfsu2msx d4;aciller moment of inertia is

  A uniform solid sphere has mass M and radius R. If 7 ichykilf72qc7 -41nikgw0v these are increased to 2M and 3R, what happens to thk-7iv1c7 c7il 0k4ygqifn 2h we sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object z 8in3j+c lu0otchmcr*t*: hjwts ( +(will

  The moment of inertia of a solid cylinder abouab ,ixgcb45o.sg4a5 q *fre v3t its axis is given by 0.5 MR2. If this cylinder rolls withoute3 bvcqxsfaib5g*5g.r44,oa slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, onec, szik4d8zd3, i(y .j0nvrgy wheel of which has a mass of 10 kg and a radius of 30 cm. What is the 4,n rk, vi (0jygic8.syzdd3zratio 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 witho+) zfgwh)f1jvut slipping down an inclined plane starting from reh j)gzwf+ )vf1st. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid spherepo:4jsko c, )e of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the inclisje,)c: okop 4ne depends on

  "The total angular momentum of a system oblyq,kom,b 7 -f particles changes when a net external force acts on the system." This statement ,m,oyq b-k7l bis

  In what circumstances can the angular velocity h)kd-emwzyp6 :kl53 z of system of particles change without any change in the system's anguzkk w3py65d)hz -mel:lar momentum?

  The Earth orbits the Sun in an ellipti ek ,:o.fa0cdjcal orbit. Ignore any friction which may be present. What happens over time tekd, c. o0jaf:o the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth m-o iuyfr26v kr e/.hk+oves close to the Sun, then which of the following best descrio/ u+2khf.kyver-6r ibes the orbiting speed of the Earth about the Sun?

  An ice skater performs a piroueer9 3q+f ywcegxhk7*gr+2 )dh tte (a fast spin) by pulling in his outstretched arms close to his body. What hdec wyrkr3h7 +9xg2h)q e* g+fappens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchsdh(c2 s .qz h(9wa5vmsh,b.hed arms close (s,95zhmdcsvqh.s ba. h2( h wto his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a piroue g*fmq/vy 5tt.tte (a fast spin) by pulling in his outstretched arms close to his body. What happens to .g t*/qyf v5mthis moment of inertia about the axis of rotation?

State the law of conservation of angular momutm -p6szx+hh7a x;- tentum.

  What arc length does the Earth travel in a three mspbo j r*pb/,bvs5aj r;f1a5 1zvce 76onth period in its nearly circular orbit about*pv6v aa1, f/5;ojbbesrzjcb75 1sp r 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 ktwf-ffu ve 9.nd1c5) does the tip of the second hand sweep through in 3 minutes and .5-)1ew dc tffu9nvfk45 seconds?

  How many rad/s is 25 re0fduz,y (y9q 8ka bxe2dss+ 0rvolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutionef2gr 82-y+ yfs,ze uys in 4.0 s. What is the frequency of the wheel's 28 syeufezyrg yf+2, -rotation?

  A pulsar (a rotating neutron shwwn7 bjn ru(8: 6;qtmtar) emits pulses at a frequency of 0.40 kHz. The period of its rwu;7: rnnq6w8( htb mjotation is

  A phonograph record rotates at 45 rw,v ( ;m:xt(gyh/vn wqpm. Through what angle does it turn in 0.20 s?vqmn,t(yw/:h; gxw (v

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a poiamue,zy3*vz vzvpt ;,br3:,xnt on the outer rim move in 2.1 yv3b r, ,u:* vz,ezpam3xz;vt s?

  A bicycle wheel rotates uniform0 nmicr8(iq klt /-3l y/p-vxlly through 2.0 revolutions in 4.0 s. What is the average angular speed of theiic 3 t y//lnm 0xlq8-k(-plvr wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.l99xz k98noss 0 s. What is the linear speed of a point 0.10 m from the center of the wheel?9xno9 s8zslk 9

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cabl3e (6jgyhg:6zwlt *gf e which moves the car is drivw3gzt6jy f* :ehg(l g6en 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 angu8/)qkcwyfo05w5 z ubklar speed of 2.0 rad/s. What is the linear speed of a point on the whek f8qwc0uyk)5 5b o/wzel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. 9 *psf lwc-yn:If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?y:c 9nf-slw*p

  A wheel of radius 1.0 m is rotating with a constant angular spee 5((zr26jzapnod v9l qeb;liaph683*re 8thp d of 2.0 rad/s. What is the centri8a5 hp bj86 aph9i6nqrt;( *2r(zdolzep l3 vepetal acceleration of a point on the wheel's rim?

  What is the centripetal ag+d6ct*em r2acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is mov6tre2dm+ac*g ing 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space 5q*z;ahx +tv w9p 1yypstation (r = 1000 m) rotate to prop+vz*qx91 a;th y5ypw duce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 mo;rj abygyc:f1/l -p ttr- :i3u 2pne- with a speed of 20 m/s. The maximum centripetig :etyr-al ru;jnpp:b1o2-f-3/cyt al 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 wit q)da3qd8 dz*4 w lfilc1g;:ush a speed of 20 m/s. The maximum centripetal foa 8 cfi)w; zus:qddlqgl*43d1rce (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached tq7 suhth)v4ksikf,5:j1va 4 yo 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 74,qhyuj)i4ks1 f av5v:h kstcan the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg andt,oy c. npfdz5r79si) radius 9.0 cm rolls without slipping 10 m down a lan.py,if 5sc 9otdn z)r7e 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 angular acv;r n9j0o ud. h(d,nuy u+-qu3( wgmteceleration 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 n05 -kn;abimi*ti q:me qi-9fgular 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 ryr95dc,,un skkib( wi3alarn6 .:;y5zt xz y9adius automobile tire rotate after starting from rest and accelerating a;zi (,9dr cr a.wi6 :9 xau5sy y3n5,tkbkzlnyt a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has zu ),m, mljvs: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 angularaq6q3aou:puqul i 1 7 kb:3kn6 acceleration of qa nu6:6ui7qpaobluk:q1 k 33 $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaxgtxp/fe.c *pz rx022 ches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average e .rc/2x z0f xxpptg*2angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly fr2 2-ao 75avol m3gje (1jiprhnom 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in com3vn2l aojjia2go 1 7h (5-emrping to rest?

  A wheel of diameter of 68.0 cm slows down uniaf9e/8zufrn ha 3z93tformly from 8.40 m/s to rest over a distanza9ta/ r83 nzu fhf93ece of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to restlx7e;.2 c nd/ ql7mi4o ff9z7bnbw3pn over a distance of 115 m. How long doesp x4b2l lwe7q/.9;n7n3 oz fcinmd7f b it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed ovsd+;b mt:6u ef 3600 rev/min. When switched off, it rotates 50.0 timem:+; d buvets6s 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 require5znm- la,3,ehbu x+1f (fh4lt esiwy 4 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 perpend4h5,l 1 bt,s-nffa4(hyxl+ezmuei3 w icular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nmcp9i )tcp,l4m. If a 30 cm long wrench is used, what is the magnitude of the force required when the forc4tpc ,)iplm c9e applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inmnvx(2lg50mjeyrs 1gp5 w7y1ertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mab;dw2x yxdp;o 84hk4iss m is at the origin, mass 2m is at x = a, and, mass 3m ;b4 8;4x2ikwxhdyp odis at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless a*unkajx2 rs dbz ;k0g:c06p3 xxis 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. (See Fig. 8-1.) What is the angularbapnck6sgx;3 k2 :00ur*j x dz acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought the yni3z6q*gzmn(6)r2 do+ wwtm(l rwh (center O. n6mglw6iw3r((no (wz+2*qmdz) yr ht 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 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially h2w g6prjp.e 9;3mow3lrh , dydeld in the horizontal position, and then released as the free end is allowed to fa2,933oerhlyd6;m.pw g r jwdp ll. 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 1.5 kg. Ne3( nsg6hju+(kv .sawbglect the mass of the axle and w(sjk3 bag+u6 .h(vs nsprocket. 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 it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictiozo 5;knetf 5m81 pnsp8nless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angulnks1 5nfz;p 8 em85potar acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapx bqyt0x4;pf 0ped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What ix0xp4 q0y; btfs the acceleration of the mass?

  A rotating flywheel can be ywn0ws zbiht 5 ba;lc542: .housed 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 + 4 /)zgrqkko,rnty;aqmpk-;inertia 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 starts fromh1u h7)ouv, ei rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of t 1hvi7uo,ehu )he sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and 4q7tzkvez5(eipo:e*wgp1h yr ,j45 jradius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to r5 oyv41 r5eitjgke *zjh wp(e7,z q:4pest?

  A hoop of radius 0.50 j t)w)mqgxtc bu0s/ xwp;649wm and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving aft xj9tg 4/q6pt cw);0mxbu)wswer dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls withouf9urf-f: d *kbt slipping down a 35e incline th: 9d-brff kuf*at 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 momentum changeswi ubc b+aw0iac,y )gpg((8gg7o4 q9q4yn 3b g 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 inertiag3i6v.y pclt)o - za:o 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 exten a0ue.q-hw k0gded has a moment of inertiaa0kuw- 0hgqe. 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?