Angular displacement is usually express imu)s:5nzwx *vweks .,n units of

  Angular velocity is expressed in l8z(zrg+/en j units of

  Angular acceleration is expressed ijhmaab-t0 )/ tewppz4(yo+iw*.k )r jn units of

  A boy and a girl are riding on a merry-go 6lx h61ars+ff8fvxh4-round which is turning at a constant rate. The boy is near the outer edge,4xxha166vs h+rfffl 8 and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a c6)bp1ay 4 sbyy/zke 9lonstant rate. The boy is near the outer edge, and the girl is closer to the center. Who pyl1eabsy)z469yk b /has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constant ka i;fp h+q7 e)22cqesrate. The boy is near the outer edge, and the girl is clpcsiq2qe 72)fa;+ke h oser to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round whceag278mjf9 qqzgp* *ich is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greatezqmgj a*8pce 2fg*7q9 r centripetal acceleration?

  A boy and a girl are zxr)*v3dtm zqam,/; t riding a merry-go-round which is turning at a constant rate. The boy is near the o)3zrm*d tmv, ;ta/q zxuter 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 following is an)d5g)/g, v xis8ji hvv(ccz2w accurate statemjzv w,vdsh /vg5 i cxgic)82()ent?

  Rolling without slipping depends onlrpy):ef m6 e(

  Two equal forces are applied to a door. The first force is appliedryuukxeqo 7,; 9u.g+d at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied pkuou d,rx u;y 9e+.q7gerpendicular to the door. Which force exerts the greater torque?

  Two equal forces are appliemv- f;jcih*gz6d- i.lcs(( eed to a door at the doorknob. The first force is applied perpendicular to the door; the se ;li(evg zchd-ecsi*6m (-.fjcond force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door.y c.r22jxwvl o95x0 gh The first force is twic9gl.c x2 2rvwyhxo05j e 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 resistance to changes1tg(moehs;m6r-h 5 ze : wfi.m in rotation?;:6fzt.ihehs5re o(mg 1m- w m

  Consider two uniform slmbn-n0i tfp6l gn8r2e(-gt 0j/ ltm6olid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia tmplitn -62elt0gj l(n6nm/ 8brg0f-to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but (3jfa(y57adhf :t fmmone has twice the radius of thea: aj mmfdyfth75(( f3 other. 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 twice the mass and twice the dvp x 34(* n1vptd(qpbcaq:ri9iameter of the other. The ratio of the libp3q1qvavr 4:c(p * 9xdpt( narger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these areke -u+ -ct+c5k2-swmm6 4u mjy8iaai j increased to 2M and 3R, what happens to thei8+ -c6u5esi - mwcuk+ta-kjy42 jmam sphere's moment of inertia about a central axis?

  If a constant net torqsra,xh p9c r3/ue is applied to an object, that object will

  The moment of inertia of a soh;zz:5n,r-gdu okcl/ 7 qp4px lid cylinder about its 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 wm (myl z2ne, k-ymesp( vy1.kp+n: tv9hich 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 energy of the bike? Assume the wheels are 21nm-ypy e+k ptm,l: 9vkm(v(sey.n zuniform disks.

  Suppose a solid sphere of mass M and f79ks8ccnm w-n o,+6sqgz+)v1ylcweradius R rolls without slipping down an inclined plane starting from rest. The linear velosn6w9yos c7 fzw-+cg) nvq ekmc +l1,8city of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M andxgweguk 2emf08-en l185 v6vq radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incli1508 8k egwqnexuemvf- v g2l6ne depends on

  "The total angular momentum of a system of particles changes when a net extl1s(w gu(rrk3 ernal force acts on the systekgl(( s r1ru3wm." This statement is

  In what circumstances can the angular sw;5g 8;mowp9rpfd6 m3pve u, velocity of system of particles change without anygwom p9;5p3srdpvu6m e;fw 8 , change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whzm2 /u,x 2ext0/ 7c0hjrccntr ich may be present. What happens over time trc/ 0 x2ert cjuhcz t2/nx7m0,o the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the (o; g8du : ju b(oh2ivi(rxot )de-v-mEarth moves close to the Sun, then which of the following best describes the ovor8h di(g(ev 2 dxmu;-io)o:- but(jrbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hn3n/xpm5b5fb qer6s 5is outstretched arms close to his body. What happens to his angular momentum abp35 qr5/5ne bbs xfm6nout the axis of rotation?

  An ice skater performs a pirouette (a fast spin) yh1mfypv/ o.m6xbv. ) by pulling in his outstretched arms close to his body. What happens to his )hvfyyvmmp ./x6.o b1rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette s c/enc--pbnz-c :id1 (a fast spin) by pulling in his outstretched arms close to his b bndsc /:1cp-cin-ze -ody. What happens to his moment of inertia about the axis of rotation?

State the law of conse i1 -yi 6dt((*bzjorwhrvation of angular momentum.

  What arc length does thu 8v:qyq:(, dyqenb8e e Earth travel in a three month period in its nearly circular orbit about the Sun 8bey::q y (dq8 envu,qwith a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lengthf-t ajc* u0f)p -jntf5 of 0.30 m. What distance does the tip of the second hand sweet) ja-jf*t0-f pc un5fp through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minu; up/)wu e4nnzm7z4k gte equivalent to?

  A bicycle wheel rotates un i+oy 736por*t qapr(03ujob niformly through 2.0 revolutions in 4.0 s. What is the frequeb 0(nyp+ ouaoq3ti rrp 7*o3j6ncy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 k58+r8qv ycdp rHz. The period of its rotati8c vpy8 q+r5rdon is

  A phonograph record rotates at 45 rpm. Through what angle does *1swmu ch , 5f gfy+)j)hdp2zzit turn in 0.20 sgf jsfmz+5hy) z)wh*1ud2 pc,?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point ogvzcdzo 5e :yz ;s xr2u5)k;sm.go:g,n the outer rim move in 2.1 scuez :g2so ,g5; 5 ymg;r odzsx.z:k)v?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wh7q:k du0ggwl;p)i. gl at is the average anguld l.70gp qi)kgug;w :lar speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolution:dn*su lkd .a,u hk3h8+* hdqns in 4.0 s. What is the linear speed of a point 0.10 m from the cendnn 8shq:u,ud*.d* k3alk+hh ter of the wheel?

  A cable car at a ski resort carr0lp2w ;1niua- y k5q * )poereloy9d,dies skiers a distance of 6.8 km. The cable which moves the caq0oddnr-lo, akeuwp;9y i)e1py2 5l*r is driven by a pulley with diameter 3.0 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 rota q-k03 hm .zhx1gyz/h-jcf.mc y;ni8sting with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the whejkyhzcm0h .3 cyf.mng/-8q-i1;xszh el's rim?

  The cutting cord on a gas-powered weed cutter is 0 ylg pg, bsa,/rv+4:(hov-wt n.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear spwr(-v :gb4g svn y+l,oat,p h/eed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant t2:6zytq ip.w angular speed of 2.0 rad/s. 2qtp tiyw.: 6z What is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the peri85u qxks9:wj2 b t ,oofuu .,)t7kxluxmeter of a bicycle wheel of diameter 70.0 c o:f s)qwbjk9u8utt7.xx ,5ku2xo lu,m when the bike is moving 8.00 m/s?

  How many revolutions pe9 fuxctq+chf :d3 ol5-r minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an 3qo uxfhc5l cd-t9+ f:artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat vz;ym gx0+rh1circular curve of radius 50 m with a speed of 20 m/s. The maximum centripeta+ghrx0yz v 1m;l 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 0+ l6(xc; :f dct-mvyle2 5mqqk4lgy9bd+sqccurve of radius 50 m with a speed of 20 m/s. The maximuly c-tq96ycf:v0 l52b sdlg+(qk;+emx 4qcd mm 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 ofx ;k)u0tl ewz; a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand txel)w;; kz u0is 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 rolls2tasmh-v ;.2 2py rca::hcc tw without slipping 10 m down a lane at 4.3 m/rac2h:pcs2htm;y-wtva c:. 2 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 constaf 7h p3m8fzyt)nt 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 olcq(.x7kwr m7fz5. xp-ib e g jt7g1h2f $4.5 rad/s^2$. 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 afterc7uw bh5jqft6n (lp30 starting fro5j (u6fp70q bl3 hnctwm rest 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/ dc/hxxd m r:g*,zwg5 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 with a constant angvns a 8)xn2lp8ular acceleration8 sanpln 2vx8) 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 sm mfxrakvj3g; w qd9 b260xaf3;if)x.peed of 6.0 rad/s while turning through 2.0 2xmxv0da3x qmjk b9 )f;i6ff 3w.rg; arevolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s tsr kuia3h;9isx6 knf (t )(e;uo rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to)e f ts6huxik(i;k(;rsa39 nu rest?

  A wheel of diameter of 68.0 cm slows down uniformlk)z7 ia+n2 fycy from 8.40 m/s to rest over a distance of 115 m. What is tz)kayfcn i+27 he angular acceleration?

  A wheel of diameter of 68.0 cm slu2qz 38gnaz8 eows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the8guz 8 qza23ne wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotatiovxojmlr)3w8 - nal speed of 3600 rev/min. When switched off, it rotates mvr8o )x -3jlw50.0 times at a constant 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 tightening to a torque of q1 8xkqfl)p/b 90 Nm. If a 30 cm long wrench is used, what is thex) k/qp81blq f 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. : m++uh .ktgl0o*ha 3mris yvx/f)-fjIf a 30 cm long wrench is used, what is the magnitude of the force required when the force applied a.xm-/ h0ty+ u)ifj +kgmsro :f *la3hvt $53^{\circ}$ to the wrench?

  A wheel with moment ofu.k3(v vvcl 9 ekt,h;l 2h-uxn inertia $3.00 \; kgm^{2}$ 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, mnj /pc07is- gpass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of i/pg nji7 ps0c-nertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless a x)ez ( y4;+hvtyaqfm/xis thought the center O. A rope wrapped around the outer rady )hem ;4vx(f+zqaty/ius $R_1$ = 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 thought;jo rdql5p 0(amnjkm,p fxq9v9 -)iq/ the center O. A rope wrappe 5k)j/qpvmornjp(9,0lq-qai d m;9 xfd 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) 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 hinax.,r- eu;y whged at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (The mo, ;he.- xwrayument of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius d1h eo8e u(eupc609yb30 cm and mass 1.5 kg. Neglect the mass of to d1 ye08ucp6ebe9hu(he 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 ropez,7a7v,zxrx . wyscx ( wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the zywvcx7x(s,,xr.a 7z pulley?

  A 1.53-kg mass hangs on a rdp,4t :f f3sp:ho1wozope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.3szwp:,pho: 14dotff 0 cm. What is the acceleration of the mass?

  A rotating flywheel can be usedyxqu*ldo2fwz4 p (d: ; to store energy. If it is required 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 oe r91aru, r3tsf $5.00 \; kgm^{2}$ 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 dfkrdj,)v32yh :ey8e (9 ghs qradius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphereg8 :qsehyy),e drhv 3 k9j(2fd when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg plc*q,kk+4/q0yv)elt) jxgu)m vw 8mxo 5o3sand radius 0.010 m rolls with a speed of 10 m/s. ylxxqkk * jmv,38oo )4e)lwp+v5)tc0u / q sgmHow high up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a md9id a; mqz63(sez ,elass 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 distancemqzs36a(;ed9 l edzi , of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slmmg,bi fwx -5 5z+j-etipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia ofewmz b5 , fj+m-tgix5- 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 m lrq*. agx;20rfgo ds-omentum 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 m4 8-uhcwbqu r*oment 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 5.00g a1b8owmmiy/1n 7tlti+ ls.0p et7+00 xjfsb rad/s with arms extended has a moment of inertiay bn+0s.m11 w 0 i+07el mtxptgfslij ab/7t8o 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?