Angular displacement is usually express0l h)ck: so pjvvnf:bi,-)br5 in units of

  Angular velocity is expressed in u4+ey l8zmv w- )4ywrfky+oq+inits of

  Angular acceleration is expressed in units2-g/twyp yuu, of

  A boy and a girl are riding on a merry-go-round which is turning at jfls )og.3 st,8nq,dn a constant rate. The boy is near the outer edge, and the girl is closer to the cenfn3,8tgo.)s q jnl s,dter. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a con( f8-qhlz*w qxstant rate. The boy is near the ohx wq-*z( l8fquter edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are qmb( ynvbu kur8v e-u7s8-z(i y*m7d 1riding 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 d umq-z-ksvnib y muy7vur8b(18(*e7 center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turn90a a 3tcwltl7ing at a constant rate. The boy is near the at3cl0t79al wouter edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ridingp g/wtg eh+*m2 a merry-go-round which is turning at a constant rate.2h t*emg/pw+ g The 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 rotating. Which of the n8x*ux hf2j /ghs.r+w following is an accurate statxfu/+x8hwhg.jn* 2rs ement?

  Rolling without slipping depenp/1a2/g7idf (iritrdgn 7m :o ds on

  Two equal forces are applied to a door. The first force is applied a(ke +v.hl2ugi wcq+e* tc)e6rt the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which foree+)ur hwgtl*q c+.cvk2ei6( ce exerts the greater torque?

  Two equal forces are applied t jjl;mae e/-gg-24fi no a door at the doorknob. The first force is applied perp-gie2;lg ejnm f- ja4/endicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doork;),: n znjscvdx6 dlszi 28ad9nob, 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 tnzj d8lnscdais9x2:d v,)6 ; zorque of the second is

  What is the quantity used to measure an uuy ic5v5gsmmpb+ +3 3object's resistance to changes in rotation?3+iug+5cb53s vp umy m

  Consider two uniform solidbanstbwsf7 iq4q, .81 spheres where both have the same diameter, but one has twice the mass.q47bb,ast8si f w1n q of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius of th5i7ye . m d1xqmxw(z yc3s;dk,e other. my5y7wm(qx.d1kxzdecs;3,i 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 twil8jo b* t-0yfhce the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment-h*oy0b8 l tjf of inertia is

  A uniform solid sphere has mass M and radius Rzoq sdmp*0 mtr8(ra;8 . If these are increased to 2M and 3R, what happens to the sphere's moment of inertia abs m 8 8(z*0;rqromdptaout a central axis?

  If a constant net torque is applied to an oy-exwj *s8kc* bject, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2. Imr41 7ivtcmp(djl, 4nf this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy dn (7m,r4ltvcm4 1pjiis

  Consider a motorcycle of mass 150 kg, one wheel of whi*/oso;nceiwc+k 4 d .xch has a mass of 10 kg and ;oo*4 nwscx.c +/idke 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 R6 m gv 6t4;dh.itxx; w1nfgi v:leey2/ rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline di6ne/;m eixt14y2t :vvlhfg d ;wx6.gepends on

  Suppose a solid sphere of mass M and radius R rollsb cze ds1: il)brpw;5o2cf3 0z without slipping down an incl fl5brcs3 z:ocw21b; ie)0dpzined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes whe9j/;8;x yc o vz5h7 -wjjlswakn a net external force acts onw 9zlj5;j / syok vwhx;7j8ac- the system." This statement is

  In what circumstances can the angular vh7udg2d duo l8ad-+2relocity of system of particles change without anyglhd7 d-2u dd8 rou2a+ change in the system's angular momentum?

  The Earth orbits the Sun ineg +c;e 1)prf,. wva p:lxho ;8t)n4jkjin b9d an elliptical orbit. Ignore any friction which may be present. What happens over time to ttjf1eakj8o c;gd)9l:e, pi;x+ )vhnp4 b.w nrhe Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth ku ipj36che5 : j0jh+jmoves close to the Sun, then which of the following best describes thehjj:35k6 c epj ijh0+u orbiting speed of the Earth about the Sun?

  An ice skater performs a piroueu 3x e gp(j*ssd4qz6p/tte (a fast spin) by pulling in his outstretched arms close t4sguq /s 63*jpz x(pdeo his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouettef3xs,1,wk)pwlo rc, er 2 r1bezm5ut/ (a fast spin) by pulling in his outstretched arms close to his body. What happe 15kzxr 2m1ebe,opcfls)3,w,urt/r w ns to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his o+slxe/(nvck s8c-ass m0* q1dutstretched arms close to his body. What happens tcne-a1 q8sm/vl sd +kscx0*( so his moment of inertia about the axis of rotation?

State the law of conservation rx2dn/cciu/k ; /,gbqof angular momentum.

  What arc length does t l:rb8 vmsv1.wy-d,yr 6g bd;phe Earth travel in a three month period in its nearly circular orbit about the Sunb8;yr.v vdly6mwd1sg- ,b:rp with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What dist ioi t2umuq1/(vh5 kv*ance does the tip of the second hand sweep through init* 1vh/m 2i(uuk5 vqo 3 minutes and 45 seconds?

  How many rad/s is 25 revol3 bgx: ciz0z0vutions per minute equivalent to?

  A bicycle wheel rotates uniformly th+f.8 e 7xbaizerough 2.0 revolutions in 4.0 s. What is the frequencyf8+eaz7.i be x of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses atw1lx2 y 9cyue* a frequency of 0.40 kHz. The period of its r2x y1ly9wu c*eotation is

  A phonograph record rotates at 45 rpm. Through what angle doesi1t,z kte nsmz,u f1+) it turn in 0.20 s?ut+k esztfzi,)n,1 1m

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on tw1 n4-ler5 jed-2a1lugqtt( p7m7fla he outer rim ap7qlwueemjl nfa1 (r51g7-tl2-td4 move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.h7j: : 6fzcus(:s:8j n bbzuik What is the average angular speed of the wh6:c:7bzku us(jinf:8z hbjs:eel?

  A bicycle wheel rotates uniformly through p, usd00 gg1gx7j jcm32.0 revolutions in 4.0 s. What is the linear sggjmc1 dsg03 j0pxu7, peed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carrii7e;1eo.smu 1ru v x)sa8fp)ies 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 rotate for the cable s oru m1sef1ep) .vai8;7 ui)xcar to make the trip in 12 minutes?

  A wheel of radius 1.0 m is ol. gc )zlyr/)ob.k5erotating with a constant angular speed of 2.0 rad/s. Wh.bzo l ok5/gcery l).)at is the linear speed of a point on the wheel's rim?

  The cutting cord on a g+yo(.5 m h+r hjv)qppaas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 a 5p .vrp(hq)+hyo jm+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 o lic z+q4csd;i4+lil, f 2.0 rad/s. What is the centripetal acceleration of a point on the lsc q;i z,4 li+il+cd4wheel's rim?

  What is the centripe v3ajrs3b/09qdzw*9 wzro u6jtal acceleration of a point on the perimeter of a bicycle wheel of diam9u6rqjw3d/* s oj0wa z93zbrv eter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circ qfhedwkpqp06s 3+z) (ular, rotating space station (r = 1000 m) rotate to produce an arti3s6k +qf dwqp(z)hpe 0ficial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of rag. tvkqm/tqzn- can jox,)+jn19wz); dius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fric+x /q-jwn)vz9 ;qc mg na)ztoj1. ,tkntion) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flaaoyh5bst 4p75 m2nx.dt circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided b5m hyx 47ands5pb.2toy 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 fn8d6vu,ck fjz;hp 94 a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string cank vpz8j ;f4f6,9ud chn 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 cm o,5e,yyb7 pv+ta3o9su .wm xm rolls without slipping 10 m down a lane at 4.3 m/se 5ym+b,wyov 9uaos, p.txm 37.
(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 angulat 3 j,bnr*,hav-llq j5r 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 corvz0e ;s1+ d (flt7dq0l js6konstant angular 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 automobile tire rotate after s+6fhdmtj:d , mtarting from rest and accelem mj,fdh t6+d:rating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has ky7wr( 6 bria3an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotati7ug v);jfygt5t -w zk5ng at 20 rad/s decelerates with a constant angular acceleration of k -5t z;yfgwt 5g)7juv$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed o xo+n;z u*mmu*f 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of thzm xun+*mu;*o e wheel?

  A wheel of diameter of 68.0 cm slows down uniformly brir 5r 91,ig6cec2z4 evg tq1from 8.40 m/s to rest over a di41 gcrbq5i egc6 t1z rie2,r9vstance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s5stvq0 8spiu0 to rest over a distance of 115 m. What is the angular accel0stuq p5iv8 s0eration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8. 9(iu 9u+bvuli40 m/s to rest over a distance of 115 mi+lu 9(ivub u9. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotationfp+prht makph 0/ 5:mir( ev.;al speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accel;t/ae+pr i mh 0fmv prp5(.h:keration 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 koqa bo6 p*tnbx2pb4j3p(n 98tightening 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 perpendicuo p9babn4 3j8xq6p(opntk*b2lar to the wrench?

  The bolts on a car wheel require tightenindff.rm3ki-6 ydzc,9 qg to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when fz,idr9d 3qm.ky6-cf the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ip -nuz*olx unjr+ 224qnertia $3.00 \; kgm^{2}$ 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 egrkiw3xwuf6t l /g8l-s2or9b63tf 0origin, mass 2m is at2/g9-lr gl6bwk6t ewr3 x i su3fo8f0t x = a, and, 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 frictionless axis thought the zcyv,b.t ruqq )s2 r4+6m 4zqdli1l 1ecenter 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 q,lmvyq 1bz)2u4lq+1rs tcre 4zid6. is the angular acceleration of the cylinder?

  A solid cylinder of maoypc nq5-7 oy.ss 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radiuo-5o cpn7yqy.s 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 init.vo 5a6u)koacs r1m (sially held in the horizontal position, and then released as the free end is allowed to fall. What is tcvku1s)o5o( s. r6aamhe 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 radigql/3l:fv qs6+4gaz xus 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 it :l3/zvx4s g lf a6+gqqrolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a friction;fbca aj 7ra740z1r mfless disk pulley of mass 7.07 kg and radius 66cz; 10a7rf 7fb maj4ar.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on ape30 /rs o j,sildeqrcl4t;57 rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of tr sir t,e;04c7 qlj3plso5ed /he mass?

  A rotating flywheel can be used to store energy. If it is required to stor rnjoz g8y4(n1e $1.00 \times 10^{6} \; J$ 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 1(9 g2 pvj*o3e-alo wlqc9kwaof $5.00 \; kgm^{2}$ 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 andpnn (s4q,ooe. p*t3b f rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of t(obp .onqen4*p 3s t,fhe inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of l41,zv a2 2ov ju3dmek10 m/s. How high up an inclined plane can it climb before comi4 v22eudzmvjoa k13 l,ng to rest?

  A hoop of radius 0.5vd5sj yrk(- c:0 m and a mass of 0.20 kg is released from rest and allowed to roly (c:-5drk jsvl 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 radius 1 bdo3 r+viok8zo* 9el1(aj jt75 cm rolls without slipping down a 35e inclioj1b37o( iz v re8k*olj+9adt ne that 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 momentumiqhej 6d4gwiz 5,kz 0).vvz.t 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 o6li7i 8ymomb,6x -+k 5w hthaqf $5.0 \; kgm^{2}$ 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 rotating02( pdnlv qmf1 at 5.00 rad/s with arms extended has a moment of inertia 0m1l nfqpv d(2of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?