Angular displacement is usually exoae0k j42gco8 press in units of

  Angular velocity is expressed in units o60 jec6hi7rn;fbn 7gindrntzj:8t4fun.+ m( f

  Angular acceleration is expressed in units of72v7rtd g(zmt

  A boy and a girl are riding on a merry-go-round which is turnin.1kued1vvg 8 mg at a constant rate. The boy is near the outer edge, and the girl is closer to 1umvgkvd8. e1 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 g*lp+eav4(wq1c 1mgqconstant rate. The boy is near the outer edge, and the girl is c1p lwc a*( mvgqg1q+e4loser to the center. Who has the greater angular speed?

  A boy and a girl are riding on a me)6 .w ai7 nwgt0smw-zfrry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the grea- .w6fz)7i gwwtsn0 mater linear speed?

  A boy and a girl are riding a merry-go-rounu2 *utnjd3(o3vzy/ zkd which is turning at a constant rate. The boy is near the outer edge,uz(dj3*y2 ovk/ nu3zt 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 coi sfo -gg47jx(6c ne;wnstant rate. The boy is near the outer edgw-e(c 6jo i ;nf7g4xsge, 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 accurarnq2 s 48evzq)jex+d 0te statjq8 de2qzv)x +0s enr4ement?

  Rolling without slipping dnn;qegxt i-xwpqh,9j1kyq):v z(.;repends on

  Two equal forces are applied to a door. The first force is appliem8 mqs0zo um9d/fuop+gxno(9 l +sp4- d at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force eo(u +9 n/ml s80 xf+9zodgummpsp-oq4xerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first foryb+l g0m:(keerm2b1aj cc4 t1ce is applied perpendicular to the door; the second force is applied at 30e to thcm(ecjmbl 2y10 t +beg4:ka1re plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The firs, )j/fk 4szmz,5 w-dfs:dthi ht force is twice as large as the second force. The ratio of the toj )fh:t4ms5w kdzhz,fd/- ,s irque of the first to the torque of the second is

  What is the quantity used to measure an o2k nhcp )).bjlxb5ildsy) 3 g2bject's resistance to changes in rotatiopky bnxdbl)gh2)ci5 3 . 2js)ln?

  Consider two uniform solid spheres where both have the same diameter, bzhisijs:. zw 80w2ykg396f gfut one has tw3ffj sg. wk9 s2h8 z:w0ygi6izice the mass of the other. 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, but one has twifj1wz3n w.n; 1caqmu+gc(drvcd *hmfm4* v5/ce the radius of the otq/ ;1h5+v w ndc*af1d4*mm3mr.c( fzj uncgwvher. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spher77ro- z6tc eodz*5bgt es where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller momc bt6z 5o r-o77zd*getent of inertia is

  A uniform solid sphere has man (9jmq6jdiyw1 t+ gbp5 3vd0lss M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia abou5mv g 3+ n(9yqtid j61pbdwj0lt a central axis?

  If a constant net torque is aojm7wd) m(wj5s a x:p1pplied to an object, that object will

  The moment of inertia of a solid cylinder abn9-t3kch.dej,o ha a1out its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its trao-.ka c1jn3 9dh,eh tanslational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 1ymn r2u,pif b8,kw/yug a4)2v0 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of t/nu p,4fb8 2u k, v)ymargwy2ihe wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slippgt/ sp2wx+hia l.g:2aing down an inclined plane sta2a.i2t/ xpg a+ :hslwgrting 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 slippingl;5u p)njnt* l down an inclined plane starting from rest. The angular velocity of the sphere at tt )l;5jn*npluhe bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a n.zs04 yw9 mnwxet external force acts on the system." This staw0xws 4m 9.ynztement is

  In what circumstances can the angular velocity of sysn ;yad4*3wx6lz 9aaxqtem of particles change wit3a9 y4axlx;z*n6aqwd hout any change in the system's angular momentum?

  The Earth orbits the Sun*a:c n+rl,ov/ eax 8u;nsrt1j in an elliptical orbit. Ignore any friction which may be present. What happavrrc;no+ * /s ,ux1l:tja ne8ens over time to the Earth's angular momentum about the Sun?

  The Earth moves about t (5 4izkru7r1)gvp 2t9xtr xunhe Sun 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 about the Su)i4(ugrn 2zupr19t7xxtv5krn?

  An ice skater performs a pirouette (a fast spin) by pulling ih,d h* ;*nahxpn his outstretched arms close to his body. What happens to his angular momennx ,a*p;hh d*htum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched 50b. szojn:7 b kqwzv6arms close to his body. What happens to his rotabk: z.ojz 670wv 5nbsqtional kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (oh6dsy s) ,k-ya fast spin) by pulling in his outstretched arms close to his body. What happens to his m sd-hy s6,o)kyoment of inertia about the axis of rotation?

State the law of conservation of angull 4p (k v7y6o0 tbpcix)lt/ia3ar momentum.

  What arc length does thk 7egtlba5 ;g.e Earth travel in a three month period in its nearly circular ok;5eglagb 7 t.rbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a cvayka n 4z133xlock has a length of 0.30 m. What distance does the tip ofa xzn4k3vy1 a3 the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent d9utx - /+ypefto?

  A bicycle wheel rotates uniformly through 2.0 revo lc5z3o,xutp 5lutions in 4.0 s. What is the frequency of cx,tlu5 oz3p5the wheel's rotation?

  A pulsar (a rotating neutron /z-vkyujz2 nu 5trqyj8 u p12,star) emits pulses at a frequency of 0.40 kHz. The period of its 2-ryz, 2nvzk/tp ju q juy58u1rotation is

  A phonograph record rotates at 45 rpm. Throut68 ,1rvvr6u sak uuhtmg(33cgh what angle does it turn in 0.20 s auct(,k3vvrst68 r136gmuuh ?

  A wheel of diameter 26 cm turns at 1500 rpm. How farr+(xo qz+8c lq will a point on the outer rim move ilxqrzqo + +8c(n 2.1 s?

  A bicycle wheel rotates u, n0 - ju1roq:4tiuhitniformly through 2.0 revolutions in 4.0 s. What is the qh-n,0otiuui :j4r1 taverage angular speed of the wheel?

  A bicycle wheel rotates uniformluc7dosqd2 oe2wm 0-3 wy through 2.0 revolutions in 4.0 s. What is the linear speed om woodu 022 3wqsed7-cf a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries sf,am,e9 ghuqy-:g cu* kiers 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 rotate for the cable car to make the trip-f,u9hcu *qyg :ae,m g in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of qx2- x t+,nyjbxi0nke2xgp l55u ,za: 2.0 rad/s. What is the linear speed of a point on the wheel'-52+, exnyuqlj, 2 k ax:t0pbi xngzx5s rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If theyqc r5l *y+)wd motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end o)y*qwrl 5 +ycdf the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s4 lsro*m-sys1 . 1*lrss ym-o4 s What is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a poijv3-e jl, gx)knt on the perimeter of a bicycle wheel of diameter 70.0 cm when the b x kjlv,j-g3e)ike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space svhec3yt* x ;/ltation (r = 1000 m) r/*htv;xl3 c eyotate 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;fh-;zft t;cn9t- p zpz8;k ws of 20 m/s. The maximum centripetal force (provided by static frictc;-hns z8 ;9zw-tt f;pzkfp t;ion) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a f8xv n m*ply,7m 4qxafvwq+b:(lat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fricta qb,mv:8 7w 4lmx py*nx(vfq+ion) 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 0.70:z1igab6;uvveivk)41kp; ka jk7cf50-m string, 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 h1aki6)v zg cap j40k:ku;ivkf1ev ;b 7ave if the string is not to break?

  A bowling ball of massr* of vu 5y7bf-o21jrh 7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane ay 5rr*1fjb7vf2ou h- ot 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 coqpmeu 2+ v;)ya7,gtdbsskgv6 /m+ ;nv nstant 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 acce9psvhww;5b y +z4jxq 8leration 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 0.3 fwpgws8p ah vi*;.b+,vu),/v hlzbs000-m radius automobile tire rotate after starting from . 0 g /ufbs+w,wv;vpah)pihs, *lvzb8 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 ha, i jb7qw1 wgk;lcyqs +0.jit;s an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating:.ln+r0 vkop nli(x( m at 20 rad/s decelerates with a constant angular acceleration (x:llnn0m.pr+k (i voof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 cw4* xavgejp3w a7 y3dtfp-9/rad/s while turning through 2.0 revolutions. What is the average angular accelerati w*cy a39vde g ax/3-tpp74wjfon of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to r(h t3a5;+ lw3e zxnlut(a bd1uest over a distance of 115 m. What is the total numbl5l1e;d wu(+u bt a zn3ht(a3xer of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s toexn g1 p5p0o4 dihz*;z rest over a distance of 115 m. What is the angular ppoeg45hxd zn 1zi*; 0acceleration?

  A wheel of diameter of 68.0 cm slow0nj6 r6mwfz/hs down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the f6hmnj/0z6 wrwheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotatioa,5uvr .zcc ad0(a:zunal speed of 3600 rev/min. When switched off, it rotates 50.0 u0c.ca,u5a(dvaz: zr 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 wh;a+vpcw h epe(sowdka87 g nmjv /837(eel require tightening 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 pe 8vps+kh;7 v(gwwe3/dcn 8 mp 7(oajaerpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 3 * i:1in+su7ds h+acj dvof :7qwug5v70 cm long wrench is used, what is the magnitude of the force required whhu1fg j+ aw*u7:c vds 7sn dviq5+i7o:en the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner0 cgzew3+*gfi s1dm 8ndxwx10tia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule 1f.rhv)j m q,*yq6pkp is modeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What*.q6m1jhyfr,vpk) qp is the moment of inertia about the origin?

  A solid cylinder of massoy x( iy*)xh3adnkcp5n(j6k9 10 kg is pivoted 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 second rope wrapped around another section of radius R2 = 0.50 m dp69n ij*o)cakxx5( nyh ky(3exerts 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 pivotedm+h d7+a dx16nl/w/c,u /h+jg bsr who 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 second rope wrapped around another section of rx a+,1hwbug+n hcdm/wd6 7lo/ /s+jhr adius 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 hi qf)oc))5bb9i1cjpak nged 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 as1)ojp 5qf)9a )bbc kic 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 b cxrp8loh3z 1wr5) **m hz/wmand mass 1.5 kg. 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 doel3cm8p hz 1*rwz r w5*h)/xbmos the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictikxxj,+ /plx*5t 4yw (s,o onpxonless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the a,lopjw 5/xn+y4xtxo (k, s*p xngular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a f7zxq3 a mu1hs 89uil.qrictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is th9msq1uixla3. 7hq u 8ze acceleration of the mass?

  A rotating flywheel can be used to stozg:gt ;iqjna 95j3 3mjre 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 iz wl*;h x1 4q9jrvcle0kr1l/hg0t 4yynertia 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 kg a11 f+ti/ x* gp)toudland radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of tho ali1 *g+f/tpdut 1)xe sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m r+b5o)av 0uyzc ,nwi 8jolls with a speed of 10 m/s. How high up an inclined plane can it climb vu5+, yb) oan0ijc w8zbefore coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fromwil xka+st2u j4la+17 rest and allowed to roll down an inclined plane. How fast is xu2+ s7 lka4+a1 wtijlit moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and r6ut6bme 3 u+lyadius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started fromtu l6+ y3eub6m 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 momentum changxxe;faab2pn. i*kzz5 (r9/v xes 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 momen l u70s5e/f5mivrw-f biz(znx /mz:z8t 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 rad/s wi)c0tfe0grkoez3 / wfpkoq54; tb+q2o th arms extended has a moment of inertia o 23 zce b0fr0q ;pok/t)ooe qk4g5w+ftf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?