Angular displacement is usually expresn4 nodpg:w jez:.0f 9ps in units of

  Angular velocity is expressed ws( d6+/w2l 4pfm buuxin units of

  Angular acceleration is expressed in hbc5cxz (t4g//v +t4xbzqi9y units of

  A boy and a girl are riding on a merry-go-round whichkis.4.t 9lf/d pd ou7bp*3qp*emp5c j;b wp v) is turning at a constant rate. The boy is near the outer edge, and the girl is closer to d5* f)l.ip.wp*bdsq t ppkp u/jbe;3mcv47o9 the center. Who has the greater angular displacement?

  A boy and a girl are riding on a mbxkdd6 ,zpc*mn3xvt kj6 0+c1erry-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 greak j6dk0zdv3 m*1nb, t+p 6xcxcter angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a consta j3lt l k3f3d-/tabzpjr4-.ghnt rate. The boy is near the outer edge, and the girl is closer to the center. Who has t3khl j / -lf a3p.d4z3g-jttrbhe greater linear speed?

  A boy and a girl are riding a merry-go-round whi)kfltuh+d(m -:y 6+s:b d ss.ydh.fep 2jgl f-ch is turning at a constant rate. The boy is near the outer edge, while the girl issb:-u dht (l.+f.+d-y2mhyf 6j :gkfesd lp)s closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are rz8hpfhd; 2c re;,drpb)f n0v 8iding a merry-go-round which is turning at a constant rate. The boy fdzp h0nrv;h8dref2p) c,b 8;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 rotating. k(sll;fde1o)c ; ucr . Which of the following is an accurate statodsc fl(clrk;)1 .; ueement?

  Rolling without slipping depend2 9ypj ya-o3rts on

  Two equal forces are apirpxgab6 a(a04if0q c;r*2d u plied to a door. The 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 door. Whicg(dqi*p r2aarai0f;b0u4x 6 ch force exerts the greater torque?

  Two equal forces are applied to a door at b35 gkwbt po2mw74 q7pthe doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which fg37 mbpwko24 w 5pt7qborce exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The firsvbg 7k 94xv7yzt force is twice as large as the second force. The ratio of the torque of the 7xg94z v k7vbyfirst to the torque of the second is

  What is the quantity used to measure an object's resistance to changt,tu81 ew6 k um+.udwxes in rotati16u,.dt+xme 8wutw ukon?

  Consider two uniform solid spheres where both have the same diameter, aa+bu +0xb sojewf5qk-m8,t :but one has twice the mass of the other. The ratio of the larger m+8bmek xfjq0tuw+b:as a5 o-, oment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the r2c3o xc 68x8 mdnvgjf. vrx01ladius of the other. The ratio of the larger sphere's moment of inerxl0883 xxv61dmcf o2cj.r g nvtia to that of the smaller sphere is

  Consider two uniform solid spheres where one ha5u(b6-h+a+yyj,lg 5zw mhh rus twice the mass and twice the diameter of the other. The ratio of the larger moment of inert6ag u,5+zr +bjyhy5lmu(hw-hia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M an/pv.tjr jq8w3zu-; p kd radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of ine;jrjpuq8/twk z -v .3prtia about a central axis?

  If a constant net torque is applied to an object,,-su6z wd vk6naab7j/ that object will

  The moment of inertia of a solid cylinder about i 4e+c8*yewi sg+dtb 6j,n:lwvts 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 wh dbg 538o+hi6apu lv8x6g(catich has 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 3p+xatg( ha 5dcl6o8gu8ibv6 energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and6 e5j;kh5 ps2.nytyf e radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends oy52 .n 6j t;eyfpseh5kn

  Suppose a solid sphere of mass M and radius R ru9;tvspj5+e- jpeb ,9 7rw odlolls without slipping down an inclined plane starting from rest. The,w-d jvs7 +rj pblpeu;9to5e 9 angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of paz*k-qm gug;kx t 74payj)y- v;rticles changes when a net external force gqpavy4uj*; x-7gmy -;)tk zkacts on the system." This statement is

  In what circumstances can the :. 6ypuazb(u zangular velocity of system of particles change witho(:a 6zubyzp .uut any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which mg0a9nu6*cgzz - .xa(yxqad * nay be present. What happens over time to the Eann x( c*g6u9a-x* .gzqzy0 daarth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit.m2 v*0 )s-d sbed 0*xhki)jyifres*:e As the Earth moves close to the Sun, then whxs*i)e)* jfes d0 imkse0* 2yv: hb-drich of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast ;g9,k :ykggo kspin) by pulling in his outstretched arms close to his bodykg: g,k ;k9ygo. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pul2cl s,l: wyr7yling in his outstretched arms close to his b7l2l y:y w,srcody. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling ;jypv t./h+ke in his outstretched arms close to his body. What htp v;.hk+yje /appens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentumf+4-xpd ja/x j.

  What arc length does tvl. sol(gm 50lt; zslx+(s4blhe Earth travel in a three month period in its nearly circvs4lslltb(zgl (0sxl 5mo+.;ular orbit about 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. itd0lk4vx3(l / g9gzb What distance does the tip of the second hand sweep through in 3 minutes and 45 seconds?dz l3(/4tgkbig0l9 vx

  How many rad/s is 25 revolutions per minute equivalente8w5tx (xw m v4khj.;-id9n az to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What i14nnu/ bzj7-f 6yr u+coxboa6 s the frequency of the whee+our 1bb-zn74c6u/ xy nj6fo al's rotation?

  A pulsar (a rotating neutron star) emits pulse jz/uq:zp.yv,3j z .fybng-v6sxx ;v ,s at a frequency of 0.40 kHz. The period of its rotatio jy-,z,.vfnbuv.qxz / v x6z;gy:pjs3n is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.27xffz:nnwa 1+ 0 awzf1x+: f7nns?

  A wheel of diameter 26 cm tf.1xu.q z,:viw(hy hi urns at 1500 rpm. How far will a point on the outer rim move in w.,uiv yqxhfh( i. z1:2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutpt)r/gx 9e* m nqt8qc:ions in 4.0 s. What is the average angular speed)n* 9cet/ gx:mp tq8rq of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutionseq-7 2vg2 fo/)yln(v c7tnhsz in 4.0 s. What is the linear speed of a zy sv vt/q hl7gn7)2o(f-ecn2point 0.10 m from the center of the wheel?

  A cable car at a ski resoy:gu,b6z 3klj rt carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.l u,6:b zyj3kg0 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 constan*oh42 exjit.7rhm eg. t angular speed of 2.0 rad/s. What is7hoh ex ert..i2*4g mj the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is zo75 ;ibbqf-c0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the-f 75qc;i bozb end of the cord?

  A wheel of radius 1.0 m is rotatibx:bf-zrl 4q 0ng with a constant angular speed of 2.0 rad/s. What is the centripeta0zr4b-:fx qb ll acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter84lnw4imn7 o5vyosky *o5ze 3 of a bicycle wheel of diameter 70.0 cm when the bike is moving 8. snz5*mwyol3vy5 k8 o44i7 one00 m/s?

  How many revolutions per minu3k4( ufb+hxjsrp ;0 xkte (rpm) must a circular, rotating space station (r = 1000 m) r +xj sbu3f rk0;x(p4hkotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating qpwe;t*o-678 gg kqb na flat circular curve of radius 50 m with a speed of 20 m/s. The maximum cenq- gbp87;*ko w getq6ntripetal 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 flatm7p2qu 6l or:z g:i1ff circular curve of radius 50 m with a speed of 20 m/s. The magizo 26f 7p1lqf:u:m rximum 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 string, is whirled aro;(igfv34q 5riexij;gquf 53 i und in a smooth level table. If the maximum tension that the string can withst(uie;fi;v53 f 4g5qqr3jixi g and 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 cm rolls.t d04a2(yc u b/+ond;f2qtbozmn(x u zlr s+( without slipping 10 m down a la/dzu2l20+ tbms.d o uqn((ocz 4yf(tn;x abr+ne 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 witl ugeo1t/qh 2:an +14wd7wh sjh 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 acceleration o0b8 w bm1n:ob3p xl,vqzz;ra9f $4.5 rad/s^2$. 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 stkc9zdd- h9z c1 r/az snl83a+darting from rest and accelerating at a constant angular acceleratio9zl8kc/d9dd c z ahrn1+a3 zs-n of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and ha y/lk .mfpuq 39zl1u;ys 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 ty7;xq ,dya)mwith a constant angular acceleratx;m7q) y tad,yion 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 2 xty;2dd(yo8;e+v*ha ifbzc while turning through 2.0 revolutions. What is 2f (vyy +ebtz2dx;hdio;a*8cthe average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slowch d.)wd7 s 8mhq;k 5ts,bnly38kf ,ots down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revo3nsd ,758o8t mb; tkkw)lh dc,h.sfqylutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over adr pj da lg-roo-rqei;s65051 2q0pgh distance of 115 m. What is the angua0di qs e1d;5o62-rrlg5h -or pqjpg0lar acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.4adz9tho6, ::g myg c(-hh*qq:kgd(ml0 m/s to rest over a distance of 115 m. coh(*t ggm:q: (y:,zmdh6 khlgq9-ad How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotatga b pzc7d.atztp-.+/ es at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a cons.z+-7 d aatp z/t.bpcgtant 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 tighteyl gj1*2z.k tining to a torque of 90 Nm. If a 30 cm long wrench is used, what isjzglk*12 .tyi 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 (7 xz 1j2l++kkhmztft 90 Nm. If a 30 cm long wrench is used, what is the magnitude of t tmk 1t kx++72jzfh(zlhe force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiahmvl v5i+jk+6u3t3 mq $3.00 \; kgm^{2}$ 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 o erm))mj;*kp6ph: qne rigin, mass 2m is at x = a, and, mass 3m is at x = 2ae jek)pq)hm rp6m :;*n. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictijwqce /5kc3-g onless axis thought the center O. A rope wrapw5qkgejc/ 3 -cped 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 about a frictionless axis though+ )s ooi1kml+7 kln:nit the center O. A rope wrapped around thl1s7 nn+kkli: )+ooime 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) 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 held in the hore7cg :n s(yd6bizontal position, and then released as the free end is allowb ydgn7e s6:(ced 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 mg(9 )sczq6n r h3er,srass 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 qre6sc3r(r )szn ,h9gdoes the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on 2 c8twp(zt:+4oqh 3wh8 zzcsla rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accz c(plhwtc3 8 sh 2o84zwqz+t:eleration of the pulley?

  A 1.53-kg mass hangs on a rovm-gqli7v6 zge+ :hth9 k4x ,qpe wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of tq4iv khg 6el ,xm h7g:-q+tv9zhe mass?

  A rotating flywheel can be used to store energy. If it is required to store kjc7e1ht9 3p:ym1w6pd;jdb h$1.00 \times 10^{6} \; J$ 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 iner 7gtof)pq 3n35omy gt)rb, 1hkhe,s;qtia 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 from rest and rolls w,e: z709lxck9h5u ;oixvdgf a9 sy. yuithout slipping down a 1.0-m high inclined plane. What ycfh ulzg7dxxa;sko 5:v,u0i 99. 9 eyis 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 4isl94m* rtcw+ xf8-5bxh9psxv1 oh nrolls with a speed of 10 m/s. l+hvb x9hx4-rf1* 5wtc soi4 smp9 xn8How high up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass o8 iow0j9*,k98p j1cdo crclo cf 0.20 kg is released from rest and allowed to j9cocr8p 1*oic9jk d,0oc8lw roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and rady6g)fk(j a z/s6g (itpius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sp(6ji tya/sz ggfk() 6phere 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 momenp)zz. gfp2e k0 z sfie73zt3.ttum 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 3 onbsy*j o3v0of $5.0 \; kgm^{2}$ 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 rotating0ut93t9l hudd at 5.00 rad/s with arms extended has a moment of inertia lu0u39t dtdh9of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?