Angular displacement is usually express in units oa99a2gb..emi e7h8 b4bkbc f hf

  Angular velocity is ex5-qn e(tvx 1egf 4gj,ih2jl+epressed in units of

  Angular acceleration )pu *sf/k: 7krgvwvd-z g- z-lis expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a cons had* :onj: g cld63)xqr7*ygftant rate. The boy is near the outer edge, and the girl is closer to the center. ddnlxhfyo) *cga3* grq7:6:jWho has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round whic(:f:0 zt iina6d3o m5m-gcwb jh 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 swbn: 3iiagz 6dm5o:0 (jc-tfm peed?

  A boy and a girl are rid w8y bobq8fs2,ing on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the giys8b,f 2w qbo8rl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which cp42vucnpxv +d3a 5t.w; f uz8is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater cen+c3f. t854; u ncvdwvpp xz2uatripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant ratylwh :t4u)ul 6,w t6tee. The boy is near the outer edge, while tlu6ulwtt 6: 4h wy),ethe girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accuramk eg ,ack(5) wtd10lbte stataecklt50bm gd ) w,k(1ement?

  Rolling without slippm szjxtd5; 31d/zmue)ing depends on

  Two equal forces are applied to a door. The first force is applied at the midof u8zurm5tn8h:ewk(kg+(/ tpoint of the door; the second force is applied at the doorkh8 5+wtmn:ufeo/((k ztrg8 uknob. 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. kzr u-4r kew+x9u6/vrThe first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the doorxz-k9u4vewr +/ ruk6r. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The firstol+mgw 5 y4ys4.lvth4 force is twice as large as the secondv4yyo45l+t4s h . mwgl force. The ratio of the torque of the first to the torque of the second is

  What is the quantity usedilq d,)y f,-er to measure an object's resistance to changes in rotation,dif-rly,q e )?

  Consider two uniform solid spheres where both have the same diamet l) a hh*t+ri9hvy+0mxsv1b l/er, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of thyvx9rh/ sh ah ll+1+)m0vbt*ie smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius i ge,g24xk kgn8atx77 of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphagigkk4,tex27x g n87ere is

  Consider two uniformp3oudgyumx5w 8m cu fiz:p*,-3 vgo6; solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of iz63:v;m5u* 8pcpooy w3mdg uf-ux ,gthe smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these ar9/: an:-syr0m og tmyqe increased to 2M and 3R, what happens to the sphere's moment of inertia about a cent9a 0:g: r/yy notmq-msral axis?

  If a constant net torque is appliedg- i gov-,1 ekdg m wxc5a50//dftwl2o to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given bbze( x38bg., n3 hapouy 0.5 MR2. If this cylinder rolls(x8nbe.a3u,gp obzh3 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 which has a n bbdcs/dfm.tibw: e2.e b5 /vb8,5cqmass 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 energy of the bike? Assume tc /.tv. c2bb8,sdb5 /ifmdbb q5ew: nehe wheels are uniform disks.

  Suppose a solid sphere of mass M and radius-8f 6w7alsyyq l9s3;*q pbhkf R rolls without slipping down an inclined plane startingbyqhfys6klla;7 8f9pqs -*w3 from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an i 9s fz(0ex5(nmw7p)t csngy 8snclined plane starting froste xp5 c9g)znmn(( wf0 7ys8sm rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particlei(qo**:lbnpl.d ;q 3zq p tl5;xi4 lbrt3l0qts changes when a net external force acts on the system." This stat*lpt iqzxll; ttqnq0l* 5d:q3l 4o;b3p(i. brement is

  In what circumstances can the anu/1,9lw/y9a7el jeit5p h we xgular velocity of system of particles change without any change95w1 ejlwxlh9/,ute ie/ y7ap in the system's angular momentum?

  The Earth orbits the Sun in an ellipt-k:i -3t4p2kitvlku y ical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum ai-k pt3k4-v2kitlu : ybout the Sun?

  The Earth moves about the Sun in an elliptical orbit. Ad/jf3+f uqkl: vytuwx* w-t/r3( wn,ws the Earth moves close to the Sun, then which of the following best describes the o t(j wutx,kv/*nw+fdlw3r w:uq3/f-yrbiting speed of the Earth about the Sun?

  An ice skater performs a pirouettekid;u2e(f t+i (a fast spin) by pulling in his outstretched arms close to his body. Whatikf2et ;d(iu+ happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pun ry) dz1ucl-+qmt5 5nlling in his outstretched arms close to his body. Wzmu55dn )yl-c+q r1nthat happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a r.qn+sfwo 1,,6m qo cjfast spin) by pulling in his outstretched arms close to hijn ,s ,1fm+cqqwr o6.os body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentums a 6r8u6 s48jgf:ielm.

  What arc length does jh2xh xnowx 3 9sw24-z yjpcu0:5rax, the Earth travel in a three month period in its nearly circular orbit about the Sun with a raw5h:,p ycojx 2 jnx32rs xxwuah94 -z0dius of $1.5 \times 10^{11} \; m$?

  The second hand of a ir k2 0a0)gi:hi-wtfs clock has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minu h)2fk0 i s0tiai:rw-gtes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent t r,um3,hg44nyg.xurgyqdl c08i nv:(o?

  A bicycle wheel rotates uniformly through 2.8 b qkaedq0w:9(p*1h5 tyg zoe0 revolutions in 4.0 s. What is the frequencgkbz* 1(a0d8qeeq p: 5ty o9why of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.et))rt8- ai/mkmv 8in)k2 gfk40 kHz. The periodkm2v 8m a8/ti-e) f iknkg))rt of its rotation is

  A phonograph record rotates at 45 rpm. Thro b-tm -h2 :oh nw(k;-dl mi81 *mz7kk;awiztiuugh what angle does it turn in 0.20 s?d ;w kkkm(8wu- 2oi -t7-hhi1mzi *zabmt;l:n

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a pogpk* ig;eoznpp0tzh0: o: 6 t;int on the outer rim move inpg :*n phg;t;6:pik0zo 0eotz 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is vnt3;/ cdhr -bqv hic65* p5wgthe h g*v-c6;b inwqr5t5vdpc/ 3haverage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What*bzq ) dp 95k5zf pbg.,gsaa7m is the linear speed of a point 0.10 m from the center of the wheel? 9sa,d.g5p)bg b mq7za*fkz5p

  A cable car at a ski resort carries sk*jc1ap vv6f k+ql6w2riers 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 tv wkvj +p*a 6f26l1rqche 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 ang wtasi89y )cj,yz 0go7ular speed of 2.0 rad/s. What is the linear speed of a point on the wheel' s8,o y9g7ya 0zcj)itws rim?

  The cutting cord on a gas-powered weed cutter ae sk obszsz4re*f3p* n ) lmnf35)0w*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 end of th*e*snf)e5bar zon 0)*m3 wpslszf34 ke cord?

  A wheel of radius 1.0 m is rotating with a chvj: ,im6ztmla8p/yk -ppy* zd+-t0 uonstant angular speed of 2.0 rad/s. What is the centripetal accelerat ,z -vj td6-aph*t80mzply/up+iym:kion of a point on the wheel's rim?

  What is the centripetal acceleration kh9tc 1f1cds, .s6lzfof a point on the perimeter of a bicycle wheel of diameter 70.0lt. scz916 dkh1f,cfs cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spac,bb1, -ix/ssd hwx l/ae station (r = 1000 m) rotat1,a hx/,b/ sbsiwld x-e 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 * 0bonsu*ekc .of 20 m/s. The maximum centripetal force (provided by static*k*n cu. sbe0o 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/aqy/uz f6/oml lj9*ru+7hxf2 9 vux-qs. The m7-v* 6z/u9q 9al/2ohqluyuxx rm+ ffjaximum 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:9lp1) ;)gu/ zrhiydm7zupfi , is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what m)giz /)7 p9flhprmdyuu;z :1iaximum 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 slip z)hubxy)l*f.+d 1liuping 10 m down b+1h udlu). yxif)l*za lane 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 const.tm(w nunb3 *tfk-c )5 ewqk.kant 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 wi+nauynkr7 q .:z+unyu1/j t. lth a constant 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 radiush4c9/i 6 4mi0 o,9cysilehe db automobile tire rotate after starting from resh4c9ci/d m eh e6,4iybl9is0ot and accelerating 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 acchj 0vp,/9+vf y /q qzozps2-aqeleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating;yhr(v e iadd0 l07:op at 20 rad/s decelerates with a constant angular acceleration of 00d(:vi;7o ardyleh p $-5.0 \; rad/s^2$. 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 while tuzj 8mcxbu9lh xe8c+mc f4 +/fu(a0u 9vrning through 2.0 revolutions. What is the averagehmux9xcfl0z ec9vbf8 4j8u +/ac m+ (u angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uni 9yyopcnq-ib h2bn 8)kc3h)f( 6fk3zke4f0g zformly from 8.40 m/s to rest over a distance of 115 m. c 3hn09i)b(e zb3q 6yh2pg8 4-kffyfcno k) kz 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 8.3o 21w 2iftnk 8ipd- *,vl te5q1zulgk40 m/s to rest over a distance of 115 m. What is the angular accelerav5p eikwqndo ltutgl kz32181i-f2 *, tion?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to res3k.r-c1p z.mnwnu i r;ye*.5gtt) znht over a distance of 115 m. z.n*)y. hk m nrnpgt5eiw.r -u1c3zt; How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laborator(zo k)-wnlw; ly rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angnw-(lw;)lk zo ular 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 ac)w6r9+hg4,u 3izv.f door me torque of 90 Nm. If a 30 cm long wrench is used, what i. omwruohf)6gz ce4i,3vr9+ds 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 90 Nm. jaw+k)d9r.c m h7 lajg7 20b43zgssm f If a 30 cm long wrench is used, what is the magnitude of the force requir0b w s797s+ aad)jjcr4lmfm hz.ggk32ed when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner idicz aqq6mx 7cr7-6/tia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is model dn 9-si;q3qnued as follows: mass m is at the origin, mass 2m is at x = a, and, m-qd;3 n u9nqisass 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 a/)fu u3rf fqn m/:g*sgxis 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 aroungurm*gf// fu:)qs3 nfd 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 p,mhbyk0 ed*,c )ekzu*5u gb 6mivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force Fmk65uz,dbhe*ymc b,*g )0ke u1 = 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 mg3xth o7ridq ;ijoxz 9,h8q837ri k7 held in the horizontal position, and then released as the free enqhj9,orizmgq o33k7x7hitxr 8i 7 8; dd 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 a ring of radius 30 cm and maswnthwkl2 u-78s 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of rw8k7nltw- u2hadius 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 )sjd +,0j dbf kjivbm,qm ff(1nd/i*2frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration dm,1,j/f*ivmb) 20j fj+dnq( sf bki dof the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictioxde*zq +f:els07q;e f af7:xunless disk pulley of mass 7.07 kg and rads:e: zdqx xfelu+7 q0fef7 a*;ius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requiredk g*k3h(v)zcw)1y mb-5c dqmd 6wzje* 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 oq )wan8kf.9ekf $5.00 \; kgm^{2}$ 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 hkm 4i,s.vo1brolls without slipping down a 1.0-m high inclined plane. What is the speed of ob.skvim14h, the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radiusjgc+ww 0d u6sch2uv4 f fb3g71 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before com fc vw2wgu4uj+6scg d07f1hb3ing to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg isuou9tsd iyl-p- p3m3 af-x7 9:k v,t2is+acwj released from rest and allowed to roll downsais y, x-mv2djip 93ck+ lutw:a-9t-puf37o an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mas. m,l- sqh:wkjs 1.5 kg and radius 15 cm rolls without slipping down a 35e q :mhjs ,wl-k.incline 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 mai:p y1 )w/rktu( y0vpomentum 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 inered 62 bvm5pwvlg,:glp3; -dvp tia 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 extended has a moment of inerti2++l gpb8bz mssmp g+8b+2zbla 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?