Angular displacement is usually express q3+9cp h c2bykin units of

  Angular velocity is expressed in u6lsuq66udjkh3 vg t vo90f +l*nits of

  Angular acceleration is expressed in units hxnw33. buz ecx1y1 q:;odyp- of

  A boy and a girl are riding on a merry-go-round which is turning at a cobq l)*gxh2j d/r5rq.fnstant rate. The boy is near the outer edge, an2. b)rdrx/*qq jh5lgfd the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on dz v(mpne v2+-vx.nz. a 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 has thev2dp.n. vvzz+x( -mne greater angular speed?

  A boy and a girl are riding on a merry-go-round which is lg f3s13jbhydrpruj 6* b1)k llr6 37xturning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. W7 br*y)ujj 3xlk36hgpsr b 1361dflrlho has the greater linear speed?

  A boy and a girl are riding a merry-go-rount wyqy(,7 cbt97j; obud which is turning at a constant rate. The boy is near the outer edge, while tybj;o (btucq77 y,w9the 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 constant ratem 4pu :g 1*joqyow ze(u1js4,o. The boy is near the outer edge, while the girl is closer to* p1 4q:emo(,o4uj wous1gyj z the center. Who has the greater tangential acceleration?

  Consider a rigid body that i qf:ic yau:32i-yj q,pqabn7*b(ak5js rotating. Which of the following is an accurate st*abk::( ji,a2apq 3 c7jbqqni ufyy-5 atement?

  Rolling without slipping dep9 /. 5ph6ave mkoacp+y7ofu3pends on

  Two equal forces are applied to a doo;1nllk jqbfi+ 8i:f0fyng:0yr. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendiculai;g :i08nq0nkl j:f+lfyf 1ybr to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. m0 ce/tb aetdxyl(z85j/xv- p 9k,/ns The first force is applied perpendicular to the door; the second force is applied at 30e to the pla/mdjcx ,a50(l / ep x-nkb/t et98svyzne of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perp uzu2q hyx(u(,endicular to the door. The first force is twice as large as the second force. The ratio of(qu (,yuxz 2hu the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to ch2a t 4(lxa*vsb5vqy1(c s+dpaanges in rotatio4*5 2q v vs(c t+xa(y1bsdlaapn?

  Consider two uniform solid spheres where both have the sa .n-gwuk0p1 uro 9h;pmme diameter, but one has twicmgwn.r1hk up; po09u -e 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 mas hr6g7 hqeoa+q ps,-7ss, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller spherrhh q-spqse+677 a,o ge is

  Consider two uniform solid spheres where one has twice the mass and twog:0rj1e/+yohfq aq )xw7ksxn ) y6 h1ice the diameter of the other. The ratioxra+wo7sfyjh1)xh)1q e0y qokn6 : g/ 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 increase0*dz1rk /h nvxd to 2M and 3R, what happens to the sphere's moment of inernvx1z0 r/ k*hdtia about a central axis?

  If a constant net torque is applied to an object, that object witwmo,7a33 r;a*k hx2hw:b p sall

  The moment of inertia of a solt(g /tw++no 77 d1j0rnsegwzvid 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 1v7poms/* ujc1 9, zyo;di n9vf50 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 the total translational kinetic energy of the bike? Assume th9zv19 /pinvcfsdoyj m 7u *,;oe wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls withovwtj; 7 vwnh;7ut slipping down an inclined plane starting from rest. The linear velocity of 7t ;nvw; hvj7wthe sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping doj4xqi)n vqo fpvi5yxx6 n;t0( 6ra8*ywn an inclined plane starting from rest. The angular velocity of the sphere at the bottom of6y*txq avpf qn56j4;i0vrx()y n x8 oi the incline depends on

  "The total angular momentum of a system of particles changes when0s scj/wbw/+et41 ogg a net external for0go w //4+j1stw ebscgce acts on the system." This statement is

  In what circumstances can the angular velocity of systiy 6m(rup y-avh/x7wm.j9c*k 0xmkqw;0x5rp em of particles change without any change in the system's angular momentmv7pyi kx0*(ckqj/r a59-r ;yxx.6wwm0 uhm pum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction ts7d)) 6d lpsrr,/ 9pzub hnd-sn. 7awwhich may be present. What happens over time to the Earth's angular momentum about the s)db7rw zr.7tpa) ldhnu9/,nd-6 s psSun?

  The Earth moves about the Sun in an elliptical orbit. Aub6yvd1qdt e-lk+, u 6s the Earth moves close to the Sun, then wdl6+,qket y v1-uubd6 hich of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performsfq+p/kmmba0: vgem t n9c *4idb40 c/o a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum nbbfpg/cko+*t mi90m 4/4 m0:ec v qdaabout the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pk dvv)s7f *+3iatt90en(oms*at :otgulling in his outstretched arms close k3ot:*f*7ss+ae )t0vdo9v m ntiag (tto his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstd/gfn-( ;iv: zo 2;7hsl rhhcoretched arms:-z( vh;;dci fh/osrl2g n7ho close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular-wop) 3yclgr 8 momentum.

  What arc length does the( 9x-xb6xf h;6vesko c Earth travel in a three month period in its nearly circular orbit about tec;f6vxb (hx o69k-x she Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lengtk7a7 0adrw-sqh of 0.30 m. What distance does the tip of the second hand sweep through isr07a-dw7a q kn 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per mino a0s1(.i ny8vzgyat1z5+ ihyute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whsj.7u g, 1wcpqtb:/wuat is the frequency of1 u,. 7:pwtqswuc/gj b the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequjxvbdl9 ;shfp 0 v(f9p*5 )mhjency of 0.40 kHz. The period 90jf9*5h;h )lmvp v f (sjdxbpof its rotation is

  A phonograph record ronw6 jue2e b*gu (l y/fd,vw(c)tates at 45 rpm. Through what angle does it turn in 0.20 s?c d g(wwve6*)n,ebfyl2j(/uu

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a po3t vfq .f;n/73ryqq bopf/g .fint on the outer rim move in 2.1 s/ yopf7g/t.q r. n3b;f 3qqffv?

  A bicycle wheel rotates uniformly through 2.0 revolutions jirs h1bw0 ,+:zwp+i*onv7 ah in 4.0 s. What is the average angular7orhz,a vhi n :wp +1w*0jsbi+ speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 sqj ehvfic 1n;6w:3e y3. What is the linear speed of a point 0.10 m from the cenq c3n;:hif3 yvje1 6weter of the wheel?

  A cable car at a ski resort carries oav aqgxg1f+ /9ih *;f(y r-cvskiers 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 c f cxa1(;9rv-/h*yqa +oigvf gar to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 ru w)5-; jjeixi7b qll.ad/s. What is the linear slw;7ii )q5eb-jj ul.x peed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lenai1gob q by4:,gth. If the motor rotates at the r g4by,iqo1:ba ate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.1myw9n 25wv.r/6 o mqpuhc mm.0 rad/s. pm5y / 9mvmou1c6w ..hr2 mwqnWhat is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle w wv7i y*x, gyt/l eeci;r1z4-jheel of diameter 70.0 cm when the bike is4 1/vzxiy, j g-wir;*elce7 ty moving 8.00 m/s?

  How many revolutionslt 1l :p3h h+)5gmkwwc+6 jowk per minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an arti :1 wk+3wwl+)mkgco6ph lth 5jficial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 2z+j hvfqma- +jhok*12fp5m( p 0 m/s. The maximum centpvzfkhpao h( fq-52jm*+1mj+ ripetal 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 cirtoz /3a, )m8cyix pkm-cular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provide3ctki zpy/ma8 )xm, -od 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, is whirled arou(:3txu,j nwdf:qagd ;nd in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the massw dqtf:ajug (; dn3,:x have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0(c jxcw/4irk07 hjid5 cm rolls without slipping 10 m down a lw74chcj rd0 5 xkiij(/ane 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 with a constant angular acceleration q7:wx lmp3fzziz98h4hc- ox/o1r/ d 9 ua bxb7of $4.5 rad/s^2$. 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(*jsqy+7-e k j4iihglj0wo f3- shkd8 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 rqr.tnsllyw6;s;7fwp * , wo-t9z0kq madius automobile tire rotate after starting from rest and acceleratingqr,wm-*;fnztw l0l;. s qpwyot6 sk79 at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at res k-fanmucp: if7*)d j:t, and 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 angular accelefamf:gi -55k yration o:f5 5gf-mkia yf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s whil8bp km yoyt bs183vl37e turning through 2.0 revobtp8ylm3vyb 3ko s7 81lutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniqh3dr yj,ez qryd-z ovad+ )*o8r-9 w;formly from 8.40 m/s to rest over a distancejr)qoedywh;*rq d z+zv3oyr ,a-98-d of 115 m. What is the total number 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 toxiv9l(fl3. pc-p2al k rest over a distance of 115 m. What is tv a. k-(ilx2lc fpp9l3he angular acceleration?

  A wheel of diameter of 68.0 cm slows downi2g8dbjnb 9 3 v:qi3hc uniformly from 8.40 m/s to rest over a distai 2h3g3bjdc8iq: 9bnv nce of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of o iakgd +)iz9e//4 gsf3600 rev/min. When switched off, it rotates 50. dogi/ ik f9)as+/g4ze0 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 requirepa,qisbd 9tl-c91o +q 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 ld sc-op,919+qbaitqrpendicular to the wrench?

  The bolts on a car wheel require tightening to :; 6 zoex (n.-k ,yzliekcqt4ca torque of 90 Nm. If a 30 cm long ceki q4.tez n(klc;yx-z,o6:wrench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofzxmou8j+ kj19 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 mb;9 q fro5pad z5-q4fl is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origip5 4bldzqr of -5q;f9an?

  A solid cylinder of mass 10 kg is pivo hky1mci .49 whocd93lted about a frictionless axis thought the center O. A rope wrapped around3w ol9cim h49dk1y.hc 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 about a frictionless axis thoughq68ns) eog0jc q -zcf(t the center O. A rope wrapped arounf 80ose-(zn g 6cq)cjqd 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 initially held in the horip) l yfebs*1;dxf9r0azontal position, and then released as the free end is allowed to fall. What is r*x ;9 ef)d sfylbp0a1the angular acceleration 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 radiu7pex,lt1r elt xzd 4-(s 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 rlpe ,t4e(xxldt1-7 zN 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 mas*7 ak sge javgh+20;gfa v- i8f.g3nizs 7.07 kg and radius 66.0 cm. What is the angular accel2izgag;g7hg3esnj- 0ai .vff8ka *v +eration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a f))6 wh/pxy tmgrm(mf)rictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the (wmhy)m p))m6t fr/xgmass?

  A rotating flywheel can be used to store energy. If o1 t f(;nksv8imu2ag ,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 inerqkeog-, e,g0etia 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 k3wi*9ph oq+ *lz y8es5h5uqbsg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high incy3ou*b hsw59i 5e8sq+ qhlz*plined 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 gr2yyy*i2/5z0n( y ut2n wn 8gh-ohxw 0.010 m rolls with a speed of 10 m/s. How high up an inclinedniw0hn(-ryx 2zo2ghy 2n8 5yt/* g yuw plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allow x6br d5:1fwmned to roll down an inclined plane. r 6xfb dm:wn15How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of massw(:poe8lcbe5 3o- du w9.skkf 1.5 kg and 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 ofek9co5 8-epok(.wu:dwfls 3 b 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 chajxm:l6/jj;bbpys ) + lnges 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 inertia o*r0zi,i v dbw+ faxy.6f $5.0 \; kgm^{2}$ 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 w fua6ir-.glfj(ew 6k)f,:a/l 1z mhfgith arms extended has a moment of inertia1:e. hwg,fui6/ra(glfk6-zf aj f)l m 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?