Angular displacement is usually express in units off4c,cu-mus 1l

  Angular velocity is expressed in privx.xm r fcc s:17 5(ypt2(:+bx kxpunits of

  Angular acceleration is expressed in unit;7f r5 /yyxwoa01woeys of

  A boy and a girl are riding on a merb. u:(j2 b sn tz6u 8nbs*oi5vl)g6llqry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to t56 j gbq2 n:ul sul)stb(vbil*8o6 n.zhe center. Who has the greater angular displacement?

  A boy and a girl are riding o zf-778cx )p6foygyjp*l tk 6ncka(p(n a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl istzy()n fflo(6p7*7-6ka yppkc gxcj8 closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning *yf1j gogi.f /at a constant rate. The boy is near the outer edge, and the gi/fji. yggof1 *rl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merr*csqz r xmzt4tx;z+;+ y-go-round which is turning at a constant rate. The boy is near the ouz;r qm4*++xttzzx sc ;ter edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a cof:8plan6lt )sx- 4nvonstant rate. The boy is near the outer edge, whilfp6a-lsnlvt8o: 4) nxe the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the ;cu52wu xclj :,/w dhr;rk0 ezfollowing is an accurate stateme,: ku2jurlhwc e;r5d0;c/ x zwnt?

  Rolling without slipping depends on *t ,e7vq)mq 8.tdt3sl lfn:vq

  Two equal forces are applied to a door. The first .fauy)4opt8 w force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpe pw4u)o.a8ytf ndicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door atdvtez+*cutuyfw9 va 4-12 0 hp the doorknob. The first force is applied perpev hwezc+u09 * fdtvt a1-4yu2pndicular 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 doorkno:,. ot*p/j7mg ;chmvy3:5 lk mbtai gvb, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of t3hg5gtvbkt:poy .mm7l :j m* vc,ai/;he first to the torque of the second is

  What is the quantity used to measure af,1 k9,in +wl3 yubwwqn object's resistance to changes in rotationi,w,wq+bywk n l31u9 f?

  Consider two uniform solid spheres where both have the s)g9uj53y ptx qame diameter, but one has twice the mass of the other. The jx3)gy uq59 ptratio 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 radh*wkkb zobh;i594oo2 4f;n isius of the other. The ratio of the la*52n;ofb oz9okibih; skh 44w rger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twqwd m:d(oqk2 * 2tpe5kice the diameter of the other. The rat2do d:qmq wk 2t(5k*peio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2M frnrg( 4l ot+e)p 8-nyand 3R, what happens to the sphere's momen fp n-)tg(8 4r+nryleot of inertia about a central axis?

  If a constant net torque is applied to aj,hpt )f:tg9s n object, that object will

  The moment of inertia of a solid cylinded mnix+ekc.z(gi .5 3gr 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 which has a mass of 10 k a5d 5gkkjjmq 2;.tfi 33.zgsgg and a radius of 30 cm. What is the ratio of the rotational kinetic ene;tmgj5sf.j qdigg5ak3. k 3z2rgy 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 radiucez1 87fklzw*h ih c-k1dq,u4 s R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the inc cq* ku8edkhzl1- iczw4h,7f 1line depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping 101t60nbz8o-a- k fzop hepfi down an inclined plane starting from rest. The angular velocity of the sphere at thp-tb6hf 8 a1z0p1 iz0oe okn-fe bottom of the incline depends on

  "The total angular momentuebc-,u+rj rleih 8xh,9z/s k6m of a system of particles changes when a net external force acts on the system." This zhr9ul+, jh rxkiee 8c s6,b/-statement is

  In what circumstances can the angular velocity of w)*jjb5qf4 za03le zwf e oa9;system of particles change without any change in the system's aboj5fw)aelja 9fwz* 0q3e z;4ngular momentum?

  The Earth orbits the Sun in an elliptical orbit.trq)pm/yyd ydy*z- zhfmw )054vk8h2 Ignore any friction which may be present. What happens over time to the Earth's angular momentu4 yw2dfr0 hdv y 8zt-pq)/hm )kmyy*z5m about the Sun?

  The Earth moves about the Sun in an elliptical orbxdeislp u7 d*is 0*(4fit. As the Earth moves close to the Sun, then which of t e*0ds4fli*xdu(7 spi he following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hivtjgwl0mvd 1uzsyct ,a0.uh u(:1 -d,s outstretched arms close to his body. What happens to his angular momentum about the axtl0h z cv1,u-m:,u vsy.udadtw 10(jgis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in oejmxcrr. 3 (-, lcl(zhis outstretched arms close to hi( z jl(ex.,mc-l crr3os body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs e(5w0stkhk c i j-n-w.a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis ow- jk swi-ce 5.0(khtnf rotation?

State the law of conservat);.kw len6bj:pztg h; ion of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly cirnv,nx /9jd.qe cular orbit about the Sun with a rad v,qnej/.nd x9ius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 6hp:jqu pxneg; .y5tl(.y- ikm. What distance does the tip of the secy.tnep q: ; gl(ijx6.kh-5ypu ond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalenth1lwrye; ls ,/,jxwghrt,/ h 9 to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What*zt:t x7p5g) uwh7tn,pvwz5+o ni5 u q is the f7zix)ttnwtup,qw *p5gz7vh +un : 55orequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulsemkeh snue+,6 xth6,v*s at a frequency of 0.40 kHz. The pe,k6 , *hxne+uhv6t esmriod of its rotation is

  A phonograph record rotates at 45 rpm.w6b0a6 c cje-jw 8q)tb Through what angle does it turn in 0.20 s?qet awcc 0wj6-86bjb )

  A wheel of diameter 26 cm turns at 1500 rpm. How faryhza( r9n-me14u4 l sc will a point on the outer rim move in 2.14- 4 zrm1cay9euhl( ns s?

  A bicycle wheel rotates uniforjey24 lzox7 r6mly through 2.0 revolutions in 4.0 s. What is the average anoerl64zx 2j y7gular speed of the wheel?

  A bicycle wheel rotates uniformly through 2yc5j5*v zq g*.n)lv.1aa pxpp.0 revolutions in 4.0 s. What is the linea*yacqnp vg 5pvpl 5.)1*.j zxar speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort c4t ,k dj: u5bhbi-tn(varries 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 rotah5u b(d-ttjn4 ibvk,:te for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular s 3 jz)+z7kvob3syq;ptpeed of 2.0 rad/s. What is the lis3z3jvqk +p o7y; ztb)near speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lec6. a7mcnh lbx(mk ,lp:p .wy;ngth. If the motor rotates at the rate of 20 rev/s, what islp;ma(hn x c y6 mk.,:blw7.pc the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a con(fq6,; meiz f k+fq5tvstant angular speed of 2.0 rad/s. What is the centripetal accelerationv +kmf;(,i fqq6f5tze of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle slfx- mu2kf)b65 ttf: wheel of diaxt2:bfu f) lk6t-ms5fmeter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station ,u-jxl2ck 4ggir,bo(2 m cu*w(r = 1000 m) rotate to produce ,4g(*-r2w,oc2 uu ijx lkbg mcan artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m wiriul)6h/ f( vl+st04s cr1zov th a speed of 20 m/s. The maximum centripetal forct/ zv h60l(l)rsc4os fi1urv+ e (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 radius 50 m 8/fri: 1lcxok with a speed of 20 m/s. T fc8:o1l xk/rihe maximum 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 stringa . :+lq +4xt; ltgt*h p;xndra)brb)p, is whirled around in a smooth level table. If the maximum tension that the string can withtqx)t*nartp4. bg;r)l ld:ph++xab; stand 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 9qr8 csv5r z27f.0 cm rolls without slipping 10 m down a l7q2 8vsrfrc z5ane 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 wibv) .o2q3ou jkth a constant 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 witj0-03gfaym;sudp -th 6du 5 xhh 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 radius automobile tire rotate after starting v yu 4ws-d;w ,+j dy2mjg.gn;rfrom rest and accelerating at a constant angular accelerati,jdj gd wy2snv;mwu.y+; 4- gron of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, an 9d:rae g:idd*be+: cfd 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 with a constant angul iua0kh*o vs((ar acceleration of * a0(k(vio shu$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of jzi6rwc* y92eb o gwq56zq 00ecg2/dp1x u6 ri6.0 rad/s while turning through 2.0 g2uejc* z6 q0o r6eiwdgybz/r 5 c6i x1wp09q2revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down5;t+5q+bq7 uuw) ylaq;uh;o fc j 2cig uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in cominqia ;o;t+ u7hw cyjfqc52) ;bgq u+u5lg to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s t;f9hef. de.vo o rest over a distance of 115 m. What is the angular h evef9odf..; acceleration?

  A wheel of diameter of 68.0 cm slows down unifo wl, d5 qf1knbon;(e)krmly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to the stqdn5lfb o1wk ;n,) (ekop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 369yjnbws l, jgs.s:x c: 2w,qx;00 rev/min. When switched off, it rota ,syxg snwx9:w,c ;s.j2:ljbqtes 50.0 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 90 Nm. If a 30 cm lotx bkop ,).0yqng wrench is used, what is the magnitude of the force rek ).px0qtbyo ,quired when the force is perpendicular to the wrench?

  The bolts on a car wheel require tigt a;9 /nk3ptlr,lt m;chtening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the forcamp9t,; nl; kt r/lct3e required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ik-pn c9ufpfx5chi 182q3g zs+ nertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as folljiq ows(0j, ln -e/zlk o,zd1+ows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is a/ -,d+o0,kz z (lno ijes1jqlwt x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted4vm +cjnix7eh* yn1q 0 about a frictionless axis thought the center O. A rope wrapped around the outer ihe*0 mj7xvyc+qn4 n1 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pif cm6ga:,)ywb ry9r).ev5h dbvoted about a frictionless axis thought the center O. A rope h bey.v9c5 bwdry6m)af: rg, )wrapped 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 hinged at one end. The rod is initial1w x* 7dj 2mip/2qofuw a0xay6ly 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 moment of inertia of a rod about one end is Mx1 y afw2u qpai /62*w0djoxm7L2/3.)

  Consider a bicycle wheel to be a ringnz/yoys 2um.wa hh49i h6) y9r of radius 30 cm and mass 1.5 kg. Neglect thm ).hsywunhoy92zr4y / 6ia9he 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 rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mass3ddi/k xn0 af- 7.07 kg and radius 66.0 cm. What is the angular accelernk-i/3 afd0x dation of the pulley?

  A 1.53-kg mass hangs on a rop mkc)mtnu n8277;au wce wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of thuntk w82a);uc m7mnc 7e mass?

  A rotating flywheel can be used to store energy. Iy deu y s5z8nh+fe7*;af 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 inertiam d4q)r; dqxh4 of $5.00 \; kgm^{2}$ 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 3y1tu33r0axt sx;jr0cbg ay , kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m higxb3ysca3ug1ra3tr y x 0jt;,0h 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 radius 0.010 m rolls with a speed of 10 m/smx1m r ;waujcv-, g65:0vinpo. How high up an inclined plane can itji p;:vcvgmn r,m5w- 06u oa1x climb before coming to rest?

  A hoop of radius 0.50 m and a n3y,n osg+w99 sn (hgzmass of 0.20 kg is released from rest and allowed to roll dow3(99 hsn+nwzgog, nysn 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 ancw lmjt65vr716gc j .xd radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given vjl jwr7.1c6x5 tgc6m 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 bd/2u wim g0itq.8lp, 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 inj kj5,c/bq38 wyt/oa rertia 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 )6pk2 l)3ce /l6op mfdjg)vgohas a moment of inerti jglld) 6)/gecp2o3m6 ok fv)pa 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?