Angular displacement is usually expz it,6ncg+7 ehress in units of

  Angular velocity is expressed in units ofvvaq6 qcsj (k6-)- ftf

  Angular acceleration is expresmw3vc/qa mo-g-sz: m;sed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a con-v.(c7wia g uistant rate. The boy is near the outer edge, and thegu7acv.ii-( w girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-r gjdft5sh6bdro72c8, ound which is turning at a constant rate. The boy is near the ogc5ftrd678oj s 2 ,dhbuter edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on ( 6(igi p:xeelrijec/ (m mj0/a merry-go-round which is turning at a constant rate. The boy is near the o(:mixm/ije/6cj(( ip r 0 leeguter 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 0bpr9i k+),i o91 b3y vzasxqcm uux;+which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater ceciz1+km b9s 0i3x;9v,o)pabru y ux+qntripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant,u,b/5l kph8rfitw4gwlx p4 - rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tang/k,8 fbwrt5 lp lxi-pg,4u4 whential acceleration?

  Consider a rigid body that is wl* ;mli ejk(k7yvipe 9*g3 o5rbae: 2rotating. Which of the following is an accurate statem g:3me*bw akyip(e5 eo 2v97 ljrk;il*ent?

  Rolling without slippi 4m/hv vo; :dwjoho,)vng depends on

  Two equal forces are av9pfy ta9c5.5jq* +lvhq nmcn,v6 b h(pplied 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. * l nq.5+f,99 n tjvph6vbq5hcmy(cavWhich force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. T8 8- h/ge-k,dno /zzo,/pmfhwlekfc( he 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 fd/ozlh8oh(8wzm /kpgc- -,f k ,n ee/greater torque?

  Two forces are applied to a doorknob, perpendqcvf;8/ z+ureicular to the door. The first force is twi;efcv z8ur +/qce as large as the 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 resisp x-e32p 2xgjc(ixq o1tance to changes in rotatio(q 3 x2jxopixe-2c pg1n?

  Consider two uniform solid spheres where both havaz0r,5mycll7lso ; 9j4 7cs2n,al lqce the same diameter, but one has twice the mass of the othey 749ljq;al r l0lsm5a2sc7 ,,lzonccr. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same ma+ihbh ol4-2/xj3 cx()xd up lvss, but one has twice the radius of the other. The ratio of the larger sphere's mxoh b-x (cvdp/+hu l4i3l2j x)oment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twices so1f,*.bf bb p1b9il the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the sma9bpsfs,1bli1 *fobb . ller moment of inertia is

  A uniform solid sphere has mass ( jvikb fh;/rzr k.2y6M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of in.vkyh 6r(jz2; /r ibfkertia about a central axis?

  If a constant net torque is applied to an object, that objectgx-+u--o8 d. hea;vx(v u2bjxhx b8g s will

  The moment of inertia of a sol* o;lz 5bn(i2m1-jiuex yf- qwid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls witho-jyilw2xm(o5*fi-q ; u nzeb 1ut slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of whixbcu b 86.)ubzch 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 trans6. )zubx 8bcbulational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without sl qbe4xzgq s27cf,6u))0 tohdr:u no;dipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends e )gr)h:uxqt;suqbz 6, dn4c fo27do 0on

  Suppose a solid sphere of mass M and radius R rolls without slipping down /syjg7s;wu z:*o8bx8o qso j.an inc8ss*wb:8.ooj; q 7 ozug/sxj ylined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum b 0a,flfnbo 78of a system of particles changes when a net external force acts on the bf lo,b08a7 fnsystem." This statement is

  In what circumstances md;d clh60x9g1x5 hdrcan the angular velocity of system of particles change without any change inlm6;d0dxr gh h9xc d15 the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fri3z)2ecp5xj j iction which may be present. What happens over time to the zpj52) jeixc3Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbi9ylm zmv:.k; jt. As the Earth moves close to the Sun, then which of the followinvmkyl:9z jm.; g best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast b:vckw8 bsdrlg2d 8k2q zzr1;3 9iou-spin) by pulling in his outstretched arms close to his body. What happens 9 gd12;iov-8b u: wlz2q8kds 3krzcr bto his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) b drrxg (p,.wh9y pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotatio h,g xr.rpw(9dn?

  An ice skater performs a pirouette (a fasthlqr,411t vh -5l) erp7damj d spin) by pulling in his outstretched arms close to his body. W5jhldh rq7-4 er,1p)mlv d t1ahat happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentumdr o;25;hc2nk lmp0z,d wd59: dbyfk a.

  What arc length does the Earth travel in a three month period in its neq 5r+hd0: mmpxarly circular orbit abo 5hm:d0m pxq+rut 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 does thlt-z6ghqp7. q q)cl:,ksp 7i ge tip of the second hand sweep thro6p c .gqp-ql:)i tzgh7qls,7kugh in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutiopx;1 b +:,bf-qlk hojn5xzra4tm(d2+ ap2cay ns per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revoluti(s355 3.-e7xbhuwf6 iicfvcb bz- kxzons in 4.0 s. What is the frequency of t(wc5-zifxvk ci -hbs3 65b7exfu. b3zhe wheel's rotation?

  A pulsar (a rotating e* g.zkyzco/* neutron star) emits pulses at a frequency of 0.40 kHz. The period of its rotatio/z*.yoc* egz kn is

  A phonograph record rotates at 4*hs mulj5 n0-scug(6 y5 rpm. Through what angle does it turn in 0.20 s6syu*j- h0lsgc5(unm ?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will i3z /nx)wxt/j a point on the outer rim move in 3w) /x n/izjtx2.1 s?

  A bicycle wheel rotatef,rlka+i/pmz2aafvng dm 5 k9d1u4c is/-v+3s uniformly through 2.0 revolutions in 4.0 s. What is the average angular speed of the a,cd521np3i g m 9s/ kfzvvl+4ia-mfdrk+ua/wheel?

  A bicycle wheel rotak h x/ .b4snyql2ti*, j2:y9+mbvx toztes uniformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the wheels 2xji4ot mb*k/qz+92v. lyy ,htn:xb?

  A cable car at a ski resort carries skiers a distance of 6.8 x +2mktq5wqi/ ,smp.f km. The cable which moves the car is driven by a pulley with diameter 3x,t sq2f m kp+wi.5/qm.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 angq k::y).8d t3 epkqafaular speed of 2.0 rad/s. What is thed f 3qakyt.)a:kqp :e8 linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. x m9 )a0zv6/ mzzsfbh;If the motor rotates at the rate of 20 rev/s, v;sz0x 6z) 9bha/m zmfwhat is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotatix20-pqxx:dc tng with a constant angular speed of 2.0 rad/s. What is the centripetal acceleratd2 0c p-x:tqxxion of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimnzok rti;2g3wi(+ y 6teter of a bicycle wheel of toi +2(nkr ;3w6zygtidiameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotat jzxgba*s:ix 3l+(20 9ezd d:qzqc,zh ing space station (r = 1000 m) rotate tobe9xa h 0:q,cz dgslq3j2(xzi*z :zd + produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radiut wi4z,eq26em; 1ss*s+deeils 50 m with a speed of 20 m/s. The maximum centripetal force (provide+eqsm6;d 41seeitz wi l*, s2ed 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 with a speed ofn4 bk o9jak wb8*dq9dg 9sz8d; 20 m/s. The maximum centrip8zgskd ;obwbajqd 999 n *4kd8etal 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, p2eff r ipjcox80.0k8 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 can the mass have if the string is not 8 fr.8ke02p pxocf0ijto break?

  A bowling ball of mass 7.5 kg and rayjctqb;kse8ru b:1hhl.5h ); dius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/u r1kj . bey8:lt)5;;shcbq hhs.
(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 angular6rnjn: wvgj ppze( sw::a4r *0 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 acse 0nz 0u,t,6;)jlbhd/r fvqeceleration 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 startingzfwlu8y o x:iivfa 63 -.xkca3w 76f-m from rest and accelerating at a constant angulk8cx-fa zo-ffvx 6.wmu:yw3 a73ii6l ar acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleratju ;qd owagt*2 qyg8:5ion of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rv5;,lunf- c gii8-:fhk(a cleee1c4ead/s decelerates with a constant angular accelerationicn;e uakf4- :e vlfl (i8gch5- eec1, of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest a it/o c:the i(x1j58zdpn+z f*nd reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angulaeztti o8:(pnz*d/15 ifxc+h jr acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over aajc,1/c/gwh9rc5 u ja distance of 115 m. What is ,uja g5h/ c1aw/ 9cjcrthe total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter ofz-+ e.v fggy/2evz +ol 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular aoz2/fg+e +le.vzyvg-cceleration?

  A wheel of diameter of 68.0 cm slows down unifo 9-cxt 5sdnd-t6zsvj)rmly from 8.40 m/s to rest over a distance of 115 m. How l-65s -jvd stxn9)zctdong does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotatio sy,8**n-m )3nmcclmzt tzu2l4oavo 3nal speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration befory3,mvt*8 mn uo-ao2 4l3 ccz*zl)tnsme 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 a torque of 90 Nm. l c4vgc) -6pcw,2 6-pigl4ghemqo 0frIf a 30 cm long wrench is used, what is the magnitmr lvcf-c, w -4 6)6oi4hlg0qgcgp e2pude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightenl/ um4u6xjld3ybx;o jm4 3 qc7q+hh3a ing to a torque of 90 Nm. If a 30 cm long wrench is used, wha+uj3dmx3q qoa6jxcm4l3/; h hyul 74 bt is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiyznxo:0mc,n 1g l2 8aul/hfz5a $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mage1el+boq s2 2ss m is at the origin, mass 2m is at x = a, and, mass 3lb12o+eqs2eg m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivot:dh .(g vrlimsi 76 bu4t/8ejdh1s o6+rpk: nced about a frictionless 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 se7lr4. ur t(p1/hmdogk+ 6b:6h : i 8dcvisesnjcond 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 frictionless axis thought the . ly68-cqk ldhcenter O. A rope wrapped around the outer radi.dycl8l6 khq-us 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 neih s.y, k *w9cc;tsa6ppc6;is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular accelerat syh6t a;ne*.6p 9c,p;iwckcsion 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. n)89iutm5o ke*.h,b zzib6l s ,v7z ya 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,9 b yiokzb7*s6hn u. 8v)z,5ztaimle it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frif n de7-4 an2j 7avp ;oul;te;4:gooqqctionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accej; on-qld4;oa2 voq7f;7t4u g:epnae leration of the pulley?

  A 1.53-kg mass hangs on a 6*ry* po: zlb b(tvp6mrope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What i(m6l:b*zbv rpp6y o *ts the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requirr p) tebo3vphoa0r1s0 bbs n8j, je8sm,0w/ b:ed 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 of t hzce,40u5z fxv-rq 4$5.00 \; kgm^{2}$ 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 radius3;f-cfe2qz5 d (g+qq j4v63 ru lyvo*-fsz vbe 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined(zqyv332-e4zj -f;gec *b 5frq sovv6 qfl+ud 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 radiufx tr4yl 166qss 0.010 m rolls with a speed of 10 m/s. How high up an incq16ls fx6r 4tylined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a niqhbe r-8un9 k/.r myr(*vh;mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical q- bi/u9n.;e8( vr kyhrr*mh ndistance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls we4u 4po2 *ausxwf( mcx13 kd-nithout slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The momentmdsw a34c *k4-1 2 xfoup(xenu 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 ch rv/ro0de et:a wv(z b35yp1*hanges 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 qaha r4d22+pvpsnk0 ,moment of inertia 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 ra6x0,5+saik.n ocmfjrzqi4x 5 d/s with arms extended has a moment of inertiaa,zi4nxf+i c 5rm5 0 6s.xoqkj 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?