Angular displacement is usually express in units of njpvtp4i b468iqdgu le+9e--

  Angular velocity is expressld ay cm;x ( c1..rkr7hjr,mu3ed in units of

  Angular acceleration is expressed in units o xystahu//y97f

  A boy and a girl are riding on apa,i p)5rh wg.iu.l dj)o3y a* merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer.p lig3odayaw ,)*ipuj )5h.r to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is twm9khk ;ro( n;urning at a constant rate. The boy is near the outer edge, and the girl is clo;9 mn(r hkw;okser to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go- (8a nz(y)dzdyround which is turning at a constant rate. The boy is n )dz (naz8y(dyear the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a conlg q ,l1mz7u:7irbg7m(w7q vqstant rate. The boy is near the outer edge, while the girl is closer to the center77m1 m g qiuq7zvlrg7bl,(: qw. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merrk4mw7sg)yw9 l55w)ncg ykp l8y-go-round which is turning at a constant rate. The boy is near the outer edge, lk m59w)5)4 gwcy7g8w knpy slwhile the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rs///cdbz v(j jotating. Which of the following is an accurate sz/ /j (v/cdjsbtatement?

  Rolling without slipping:d93v,a u quzvj-flw0 9m8cby depends on

  Two equal forces are applied to a door. The firstzo:ceirdlhf (4 hd5l40k*1c b force is applied at the midpointeo* 4 lcdcl 0k4(f1hzdh:r 5ib of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the qcm)* azc,;5e y :tzzqx.-hegdoorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?5qgh;xzz am-e )q* ccte:yz.,

  Two forces are applied to a doorknob, perpendicular to the door. T0 op (fb., re;5yf9pn1oojg9ma(jqyuhe first force is twice as large as the second force. The ratio of tou y((f jramf9 nppj. 10yogoq,5e ;b9he torque of the first to the torque of the second is

  What is the quantity used to measure an o/di7l* rm0jcj bject's resistance to changes in rotatiod 0*r7/ilj jcmn?

  Consider two uniform sm)gi r/qy wffg-s1x/d ,p-.t polid spheres where both have the same diameter, but one has twice the mass of the oth-r ,/q sw/.- ftx)py1igf dgpmer. 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)msedqz*+ gs7 hyh, +qa7,tdp, but one has twice the radius of the other. The ratio of the larger sphere tm azd +7)qedh7*g,s hy+psq,'s moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice thej f1 l;sddqnubf )56c7 mass and twice the diameter of the other. The ratio of the larger moment of inertid ju1fq5f;6lcnbs) 7da to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If6t7-.cz *r* ch gg5elbodu/xr these are increased to 2M and 3R, what happens to the sphere's moment of inertia a-o ugrb.6c gt/ xl5rz* 7cde*hbout a central axis?

  If a constant net torque is appls-v4p *p* q nr29hgasaied to an object, that object will

  The moment of inertiasb0jpes2kr5 fg,f 2c 0 of a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratiofrb,efjs02 kc20g 5sp of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 k (ehvd cexy73jm293-e9rmsprleb(( vg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio2-le mseerdxbvp3 9cev( 97(jmh 3 ry( 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 masstksala(sach z6e/ cnui1e -17 54l,nx M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sph/ 5n c,klistxaz1 7u es 4(e6anlc-a1here at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls witr3 2ihqm,b* +to)lqglf5 zrt-z v1j6bhout slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends5 zb qr3t zlt)o*l6mf+b-i ,q vj2g1hr on

  "The total angular momentum of a system of pck;ct *;sji m)articles changes when a net external force acts on the system." *k)c m;ctij s; This statement is

  In what circumstances can the angular velocity of system of particles change witss 6qv qab(ra 9t2,l lhyme+pj06-9 r ur1fzq0hout any change in the syste9 suhya-sq aq1 m2lt+err0b(r06 jfvpql, 6 9zm's angular momentum?

  The Earth orbits the Sun in an ellippla,ad(f*r9 eg x45 .kmne)nw tical orbit. Ignore any friction which may be present. What haafa( nredg4ke .*x)lwp5n9, mppens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Su 24qnlumpiy+(e34go a n in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth ep24ynula4 om3iqg+( about the Sun?

  An ice skater performs 7g1 k-ua i)dtha pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angulatg7 1d)uh ik-ar momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spi fp 8 dlp.24/qtf5sswbn) by pulling in his outstretched arms close to his body. What happens to his rotational kineti8wbq 2p./4sfps5tfdl c energy about the axis of rotation?

  An ice skater performs a pirouett+.nf/o tjvwhe9wx + -ze (a fast spin) by pulling in his outstretched arms close to his body. What happens to his m-/ o+hxw. j+ ntew9vfzoment of inertia about the axis of rotation?

State the law of conser28dty4t:c m h3 se3ajsvation of angular momentum.

  What arc length does the Earth travel in a th38epz nu8;wpg: ky6j ayd-l 1kree month period in its nearly circular orb w n;ug3p y8kdj18:z-lyapke6it about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length ofj;e c0uut07x ; xurtii:*/mcr 0.30 m. What distance does the tip of the second hand sweep through i cxx0eu/i*7tutu r :;m;r0 cijn 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per min*zker;e+lmr 91e ye +qute equivalent to?

  A bicycle wheel rotatent4) eyo bqj,:s uniformly through 2.0 revolutions in 4.0 s. What is the fy,b q4jo):nt erequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. oimte; hn7em.mru4 33 The period of its roteor;n4e m mm 3it3.hu7ation is

  A phonograph record rotates at 45 rpm.g 1g 7b2yhgxdq )3ptg) Through what angle does it turn in 0.20 s?g)gdhq7g13p tyb g2x)

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on z;z/fw)ycm4 oy1k hw+ the outer rim move in 2.1 sf)hww y zzkm;o/1+cy4 ?

  A bicycle wheel rotates uniformly through 2.0 revoy( n )kjng 5tso/l,e,wlutions in 4.0 s. What is the average angular speed of the whegoe jyn k/(5s,w nl)t,el?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4b7jdcvze /p 5j.imh +*.0 s. What is the linear speed of a point 0.10hjm5i cbd.+j /z *ve7p m from the center of the wheel?

  A cable car at a ski resort carrien-*/ueeo4 :xfcs2hvq qc:ve0t3 8 e aqs 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 pulleyqqhcetv qe oeacn-f4 :*:s8/e32uv x0 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 speed of 2.0 r aac7/ w*e7nv piciwka(1k)+pr-8)mxw - b taoad/s. What is the linear speed i)-)kxcar1iw wtvpb+nao a8kca pe77(*w m-/of a point on the wheel's rim?

  The cutting cord on a gas-powei7,0zxgfh0ld lso-/(yq tan e307 n svred weed cutter is 0.16 m in length. If the motor rotates at the rate o,v xnfl( solgy s7d/730iz-t a0n0 qehf 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/s.0 ll:i2irom3 m What is the centripetal accelerrmi:0io l 23lmation of a point on the wheel's rim?

  What is the centripetv5cng*ctdc-8b,-k f yal acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is v5nc8,*fcd- c y t-kgbmoving 8.00 m/s?

  How many revolutions perfvds ec)zh:g 9bb 44e- minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artfb4z ev9bec :)sd-hg4ificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a j15 ww1tpnl 5xspeed of 20 m/s. The maximum 11wlxt5pwjn 5 centripetal 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 radiud 4f;s4;zfg1r ng1eo7x rhqd8s 50 m with a speed of 20 m/s. The maximum centripeta14o gn f;xdg1;4hzrq rf se87dl 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 aroctd6w /k9e8 )tg2e xhlw2p3 6evttg/ iund in a smooth level table. If the t /6vi pcte 2degle)326w gt/hk9txw8maximum tension that 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 7.5t oom u* +shkh 14ui1bgte/3j5 kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s jhg /okthstuu1iom51e+*b4 3.
(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 constx5xoy;ml k-/x*i:jhiant 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 const/qergt9 -bqu+e5j5 y cant 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 ti.9vdhl5p8p kv re rotate after starting from rest and accelerating at a constv l.pkh58p9 dvant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, a jsq3+ .e/d.9 gqd2tq+girjfond has 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 wi9kpnuxwgln:kscdc e6 u 0off25,93 ijn:e8) t th a constant angular acceleration odi2up:wfu8xn ee cs) jc,k90ngftno l3k6 :95f $-5.0 \; rad/s^2$. 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 4idrc lm+u)pz+f+af6;f 9 uo s-igxf/ while turning through 2.0 revolutions. What is the average angular acceleration of + i6 -94;firg muzs/fp+dxu+)affl oc the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over nh6f7 qvaa/dt9t*hk4tb;3twf y+ e /la distance of 115 m. What is the total number of revolutions the wheel rotates in comwv7/befn64+ ty;qf l thda*th/a3 9tk ing to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to vltpfh (6difa7of8f( v900 9my pa 0phrest over a distance of 115 m. What is t(aap tv0fh9vd0flo6iy9 p 0 fp8 h7f(mhe angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over 7f s0 v0fgc4nta distance of 115 m. H4fsv f00 ngtc7ow long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 36k/b4lhm1k2.nxin.r+ 3bqb 7 tpyck 2p 00 rev/min. When switched off, it rotates 50.0 times at a constant angular a/mb41prtnyh 7clbk3n. qp+b xk2ki2.cceleration 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 tighteningkl 6 + axvcvyh3q+.d6g 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 perpendicl6.a c+q vkvdgh3x6+y ular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nkp8xlce 1 m*axlwr6+-m. If a 30 cm long wrench is used, what is the magnitude of tr wl8p-*xk 16cxa+m lehe force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of cb1- op)4 antgf2jhp/ k.+srqinertia $3.00 \; kgm^{2}$ 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 origin, massxqluj 1qv)s4/ 2m is at x = a, and, mass 3m is at x = 2a. What is th1/l qvuxq)s4j e moment of inertia about the origin?

  A solid cylinder of 7 mqx8)mbdr,pv l 83bmmass 10 kg is pivoted about a frictionless axis thought the cendbxvm,7 q p8b)3lmmr8ter 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 angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionllc090;6 ,jcxnloiho sv/kl) vess axis 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 anotherxk l6nlocj0c; i)svhv ,l /09o 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 +x+g l0vx;yr+umvt0uu ( re1i rod is initially held in the horizontal position, and then released as the free end is allowed to fall. 0 ui rtveu+xlu;(1v0 y+r +mxg 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 gp*z)r 0buna -to be a ring of radius 30 cm and mass 1.5 kg. Neglect the m* bz-pnu)g a0rass 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 rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frict)*xxjxezi)/pvlq //9a *r6-etv r fgfionless disk pulley of mass 7.07 * vg 9t-jxl)re/ivxz f*p6qr /)fxa/ekg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of 7odam: +q xl6jmass 7.07 kmla6jq +x:7 odg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to stosnc5j, ju8h;,4u yhdq/y c:tyre $1.00 \times 10^{6} \; J$ 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 off wrreea*c1 1d8c *gjgn5l j 3xbs/v3; $5.00 \; kgm^{2}$ 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 (td 1 ggf1(placm: 0ly0.010 m starts from rest and rolls without slippingay gc:1pf(gm0tl(l d1 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 1.0 kg and radiu:8sc6je2 woiro:ry +s s 0.010 m rolls with a speed of 10 m/s. How high up an inclined pl+ewr:y6 ioojs2 s:c8r ane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is release iwrod98x4y ;c. zcsp);ys 1kzvpo36x d from rest and allowed to roll down an in.dkpxo8vy3y zo s;9zsiw prx6c1c4;)clined 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,rc c**i6 h5ih y5gw cs5h,o2uc 7jmtz 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The migm6rz5h, c,5h ic2w j c5hcous t*7*yoment 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 changesyhso*v pjqb0 w*966lp 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 inertia9 1h4.qqool)h:kvimix20ny s 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 inery szu f;x2o 65/wsx1jrtia oss w y/;65xuor1z2fjxf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?