Angular displacement i+ uof+j )m)3mam v758otislvrs usually express in units of

  Angular velocity is exprem5:5 d-iqx k27u4sn aw3 zipcfssed in units of

  Angular acceleration is exprejqlcwi -8 5-qk b5,szhssed in units of

  A boy and a girl are riding on fx 1 z,uph nj 728bbt:(f1o1xtfklu0da merry-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 lxbb2zfdjt1u08,u:( ftxh o 17k1n fphas the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constvjyawc7ik4) 2*su q(tant rate. The boy is near the outer edge, and the girl iswk)i7qc( *2 ujsatvy 4 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 at a con ma4:fi0g h0ubc6 l:;oft+gxmstant rate. The boy ihuog6ma ibgl+x:0tm4: f0;c fs near 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 whicv/m c+ym0 apgw;ce.e(annb0fji* 0 o5 h is turning at a constant rate. The boy is n n5f0vea+ awm(ci; pbe/. o0y cmg*j0near the outer 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 conshvv08 1t8k 1ua ier7tetant rate. The boy is near the outer edge,18uit87vk hvr0a1et e while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotatin.:2)c2ymi m )) sv b ixg9cady7us7dyog. Which of the following is an accurate stat db:9yiu)y c7x2mdyv2 ag)o s 7i)c.msement?

  Rolling without slipping depe; ykoy: .b 4xcrgc3s; lbz4gzd8k7ry8nds on

  Two equal forces are applied to a door.g /kmge1 9qmr6 The first force is applied at the midpoint of the do/m ge9rg1 qm6kor; 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 ay313wq5x vgtu t the doorknob. The first force is applied perpendicular to the door; tvtx3uqwg1 y53he second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doo+wrbkp 8 q77d1r h1hrprknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of th7 7qkrr+hh 8dwp1p rb1e torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes in rotati0,e if7u7ywvv 7w3q+ nwl.xeaon ni ,70uwv3f ey+7v.qxw lewa7?

  Consider two uniform soofylee l*,gn/c ( v2-+cvgw +hlid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to thafy *2w+ ,gvl/echv +on-lgec (t of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but on ytucjah7ib; hxce: w -*-)q(ge has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that ac;h gx*wchyi7ubj(-e )-qt: of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the ds.ovjyz+j, e*a+ 6qwkyl y -p n+d0x:+pdg8dxiametely6 pv-j8d++x.xjg , spay + ed+0y*dknzo:wq r of the other. The ratio 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 theseisb5 iy smt75* are increased to 2M and 3R, what happens to the sphere'sb5*ms s7i5i ty moment of inertia about a central axis?

  If a constant net torque is appl (ourq785 wmlwied to an object, that object will

  The moment of inertia of a soztr(6tjyn z8 o 5*zg:olid 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 motorcycley70+6 kpf 0jrjuao7ns of mass 150 kg, one wheel of which 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 yo0p 6rkan+0 f7 7sjujthe total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass1b:1pa e.j +pprwkc61j * zbrvq90fqx M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere abw*pb0jz a1 v+p re.q9 cp6qjx1:1krft the bottom of the incline depends on

  Suppose a solid sphere of mass M and radiuske 9i s5k*rwv+ R rolls without slipping down an inclined 9+*se irv5kw kplane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net externalpu)til e6w 0f7 force acts on the system.6f e) l0tuip7w" This statement is

  In what circumstances can the angular velocity of sys+ km b1 (nj;/g2inykx9y)ccrm tem of particles change without any change in tx( c 1i)b;gy2m kmcn kr/y+9jnhe system's angular momentum?

  The Earth orbits the Sun in an ell 5 fqk,2srr wng0xh.w.iptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentumrwnx,rwsh.2qg0fk 5. about the Sun?

  The Earth moves about the Sun in an elliptical orbit. od ,*,qhic2/cdwpct, As the Earth moves close to the Sun, then which of the following besw ,cdq*,cht2cpo ,/dit describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pull4/ d5 dyqg7jbd:0 vvw lv+s6mqing in his outstretched arms close to his body. What hdvd0ybl6 4qd/ q+mjs v75w v:gappens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullin j2.rmz 9y:whlxrj7(zg in his outstretched arms close to his body. What happens to his rotational kinetic energy abou:jxr7jwr( . m9zlyh2 zt the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his ou 1wkja;dv 8okovc3 j*qvn 5u*-tstretched arms close to his body. What happens to his moment owk5n8vod3ok-a * vq cj1j ;u*vf inertia about the axis of rotation?

State the law of conservation of angularjb9i-:81yj8g :i g i4vszsgtr momentum.

  What arc length does the Earth travel in a three month pept6i3 qi9wx /driod in its nearly circular orbit about the Sun with a rxwd9i36 qpi/tadius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the tie zh7/ 1c4r+ dxuk8 6ytqnxmr:p of the second hand sweep through in 3 minutes and 45 ser+rxu c x6ndht:q8km/ye 714zconds?

  How many rad/s is 25 revolutions per minqt/:nua atws33me3 6sute equivalent to?

  A bicycle wheel rotates unifo8lbkef(u+/6 j: hniktrmly through 2.0 revolutions in 4.0 s. What is the frequn8 klt6eb:jfk /hiu(+ ency of the wheel's rotation?

  A pulsar (a rotating neutron star) emit6jylrrkcwcqv0f5,07- j sqe oi-* -i ts pulses at a frequency of 0.40 kHz. The period of its rotation iyjqf7--0 l5jwv r*06ecir qc-ski,t o s

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.2j , m5)(losuor0 s?slm)5(uoo ,jr

  A wheel of diameter 26 cm turns at 1500 rpm. How.cot3i vn(n7amnq 4j7nuaaz748 m 2lg far will a point on the outer rim mong4nzqlan 7om ( 7va u27atn8. mj4c3ive in 2.1 s?

  A bicycle wheel rotates uniformly thrxu-93 jxcq,1v;51f ligy +g,plpeovpsny4s6ough 2.0 revolutions in 4.0 s. What is the average angular speed ofs 91l+iv6jqp;enp14l o3f 5g , ,pyxv cu-gysx the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 ;4d sz4vq-w gps. What is the linear speed of a point 0.d ;v-zqg 4s4wp10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a disep 9 jnuueoaqt5r.-d1mc/ l7xb 5 zos4km9-i1tance 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 pull9 ds umzo-97kne t1l u4ab.q5om-xi/5pjc1erey rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with t ux +jkcg7;e;d . 5ib2.cyinna constant angular speed of 2.0 rad/s. Wh7yc i5kj .;t.+gcn;bxe i2 nudat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-pvb(e 9b 3pb*lbowered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the *v3(bp beb9lb cord?

  A wheel of radius 1.0 m is rotating with a constant anglvdok -6k fqv)o*-;jh aq6bv3 ular speed of 2.0 rad/s. What is the centripet v3kb- fqo;)-a6kvoqj*l vdh6al acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycklvc,,g9qknfs.7n :9 edoa+ule wheel of diameter 70.0 cm whe qec+v 9,sndk.kg7 :ul fno,9an the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rog vez:0e5cfaxo whir bf9-)2(tating space station (r = 1000 m) rotate to produ9(5- i:xhoavwe)zf f0g2cbrece an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating e ejx60:4pnjoa flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by statie:ne 6opj04x jc friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat cill-h )(da;wpq;a *68kiz4rtzodl p5 zrcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) isi4 ;h d85wr pl;(-*dz ata6qz)olpl kz $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750-m string9a2/wtpa cqh 9lu36 nh, is whirled around in a smooth level table. If the m 3p9hl2h/antucqa9w6 aximum 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 7.5 kg and radius 9.0 cm rolls without slipping 1ov5nj ,lwz i5q2g:kao27acb00 m down a lane at 4.3 m/s5v27co,jokalzq5a 0gi2 b w :n.
(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 angular accelerationb(rr(i/d/eixz es ,j2) aiu-w;a ,poj 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 with7:lfe8+ s 2wna4kgfah 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 az tqb9p+f/x+4vxo 3q automobile tire rotate after starting fromqp9+4o+3 azqx fbxv/ t 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 a,zji kg/gehtf5g1 4.1l +puwpn 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 deceleqf 7tg;r;olq )rates with a constant angular acceleratt7;lr;f o) qgqion 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 speed of 9srsqln8 gsy2dp:(-x hkax396.0 rad/s while turning through 2.0 rev3-sq psnl2:d 9grah8k (yx9xsolutions. 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 to rest over yv3.qhet/tuf-1qn*a tl- mh 4a distance of 115 m. What is the total number of retq3 ntqh4ltv1uem.* -h/-ya fvolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.4*99r-*steh)yms dz8 y mty)wb87kd n h0 m/s to rest over a distance of 115 m. What is thyh9d8 )9e** -7tdr)s zmkwb8 tmysyhne angular acceleration?

  A wheel of diameter of 68.0 cm slows down un cwh:x krgr6**iformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheekh6g* rw:*xr cl to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotate9m5oet6tyk , ional speed of 3600 rev/min. Whm9y t,ee5 tk6oen switched off, it rotates 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 )zit53 ; ;,yoggn(2bjkoy yyw30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to yg;(bo,) 3kynjwyio25 zyg t ;the wrench?

  The bolts on a car wheel require tightening to a torque of 90 N14gaj:7 tcob8xuk 1u lm. If a 30 cm long wrench is used, what is the magnitude of the force requirt8ka7 cju4u1lx1 b:oged when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerepg51epsoe ks mc) 6*,tia $3.00 \; kgm^{2}$ 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, masshi5wucyz. h( s+3c 8yf 2m is at x = a, and, mass 3m is at x = 2a. What isc.i(hwfsh 8zcy5yu+3 the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frict-n r))n, cwrusionless axis thought the center -sc,nnrrw )u)O. A rope 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted y(wsdas -qt) -about a frictionless axis thought the center O. A rope wrapped)(ws d ayst-q- 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 b3daowy;e;(h yn: q ;finitially 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 dy; oqb;:h(fywn;a3e end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kgavi1ozbu3 0 iq) dq8fcb /10yy. 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 4afydy b8bz v)1iuo0q1q0 ic/3.1 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 d8n)mos jsq1 sjhlbz :)24otw)6)axg mass 7.07 kg and radius 66.0 cm. What is the xlgq dm)j z b js)14ao)wn8s:shot)26angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped ay+ l/ii8psfze-:8.5 euiuhjm round a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mf/8.ii z 8-mh +l:seji5euupyass?

  A rotating flywheel can - b(8-q* nzzxminhe0obe used 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 7f1 el sxib/emc//u5ovz9j x9of $5.00 \; kgm^{2}$ 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 0.010 mp5/s,2nnbe 8ba3a qcv starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed n 3c5bns8 q/a,ebp2va 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 roll 8yvrlo0b/p6 qs with a speed of 10 m/s. How high up an inclined plane ca/8yrl qp6vbo0n it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fro5f egrfs s63n9lbf9p5h2 kq9+ mvelbq xh:: t4m rest and allowed to roll down an inclined plane. How fast is it moving ae+vsfn kg :59rlxmq:bpb46q29th9es5lf h 3ffter dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls withov3dfrx ,gdims6j( -q: ut slipping down a 35e incline that is 7.0 m long. Assume it started from resm(fdd,3:- 6x gqjirvst. 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 chak gx+nqzz2 7tsdodc,3bsxk8ph. /:-r nges 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 inerl.iy7xg.0a d5ai 4ghitia 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/b hkd*d*-c u+8q8 b q*d-ikmw;jbc m:as with arms extended has a moment of inertia ofkc ju8qw:mqk*+d h b*mcdb *a8--;idb
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?