Angular displacement is usually expresss4adtz/s79 7 oh moui*b bl41b in units of

  Angular velocity is expressed in units *vsh7nbn2b vhmw0 5 ;wof

  Angular acceleration is expressed in units ofkhm9 px b7 ccf:dtx,p 0n0+xyx v:1br3

  A boy and a girl are riding on a merry-go-round which is turninalz5hpv;)lj3 g at a constant rate. The boy is near the outer edge, and tja3pz;h) 5l vlhe 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 bi; 6-twym+n8a/ejw:) fk4eu q (gvjaturning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angulajw46g( w+8m-f vat)k/e buy;ie n aqj:r speed?

  A boy and a girl are r*9.d:wtycxua myye8) h ( gr1riding on a merry-go-round which is turning at a constant rate. The boy is near the outer me u.yr*x1ctwr98:agdh )(yy 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 v56fnvou.yd * which is turning at a constant rate. The boy is near tu .vv*6fdny5o he 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 a*bk v m8vubup h2;97zw8 ak4euds3m)x t a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater t7b8kbz u*8sdh9v42m3)vexu m k;w au pangential acceleration?

  Consider a rigid body that isynpfp m:9a1q t);t,lu) lzdz8dq94o e rotating. Which of the following is an accurate stateme)ouqd t)1 9p;zqfly8zd49tp nm, le:ant?

  Rolling without slipping depends o u)+ 5v*s+.a tkyq6c jnmp6txhn

  Two equal forces are applied to a door. The first force is applied at the mi cib0vlcc98w) dpointv c l9c0cw)b8i of the door; 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 at the doorknob. d6 n663utjnhvThe first force is applied perpendicular to the door; the s6d vju3t66nhnecond 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 tdhl )7l2wgu5(rc2kz i he door. The first force is twice as large as the second force. The g2 5cr dkll7(2izw)hu ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistl1if af2d5vov b9nq5 (ance to changes in rotation19ofaf5 dqviv b5l2(n?

  Consider two uniform solid spheres wherewu,lh rc(l:(iot 5f )/huf9mmney: k7 both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to tha) h:lkih(,/l9 mo:n uc(um 7f5ewfyt rt of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has ((b,xtnm :b*hvw7ywu:v; ef +mbkr * itwice the radius of the other. Timwutvwkx(+e;** : :7b(b,yhmnv brf he 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 0(b mr juzlhgq2*k.4 (bz +kdhthe mass and twice the diameter of the other. The ratib( k2hd z*lmju0rb+zkq 4gh(.o of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and ra+f4kph zuuvr 7vsm8 4cnz 6af,b4(rm (dius R. If these are increased to 2M and 3R, what happe4 ms4cz8rp((a 4h+fnkubuzvr f6,7mvns to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied5e1l5tzyjb m 9 to an object, that object will

  The moment of inertia of a solid l6w jlls wg.;: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, ony zxtn5)f/ tfm1p74nhe 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)/nx 1zpf4m5fyh7t nt the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slippingcu1(,eyh b 7 j+xc/)jkp 2 nszx,e*obi down an inclined plane starting from rest. The linear velocity of the sphere at the bo /j +2cb,e1)7 os*nipj ,kcbxy ueh(zxttom of the incline depends on

  Suppose a solid sphere of mass M and rayt6rs 36df8d5g e2q- i suge1zdius R rolls without slipping down an inclined plane starting from rest. The anq y2zee-6gfdutr615gsd3 8sigular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when auhklr72a m)o 8;.1 +bmy fohpy net external force acts on the system. o blam12k;+8 rp.yfu7hh myo)" This statement is

  In what circumstances can the angular velocity of system of particles chank5x 2m,*yka :hlkt*jtge without any change in the system's j:mk,kxk2lht*ty* a 5angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore azyd7z l wn q1fa/+rtzl8+25is ny friction which may be present. What happens over timlfrzwan+12/ 5 8z7tqs+ zylide to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ellipt8 nhe )fa;wwe;ical orbit. As the Earth moves close to the Sun, then which of the following best describe8ew ;;)wnhafes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a k:0n3f)e i5kjtlpr+4x b 3hs rfast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about tx+i r4k 5 3ths3f bprlnj:)0ekhe axis of rotation?

  An ice skater performs a pirouetuke4ati0-55h mh0pudfa.mn 8e ka 1 c9te (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic eneraak m.8cp 0-d5tm9kfe0han u4e5 hu1igy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his oexjjq u2 q6d(/utstretched arms close to his body. What happens to his moment of inertia about the axis ofuq qjd2 (6/jxe rotation?

State the law of conssfjtf8k 2z0 3jervation of angular momentum.

  What arc length does the Earth travel in a three month period in its neag9x12wquq(hkve yi 6v0ga0;d rly circular orbit about 2ha9 v10gyvde( xi0gw6qk ;q uthe Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distas8di5vg f3wu16hqb z +nce does the tip of the second hand sweep through in 3 minutes and 45 seconds?53 dhzqwgb+6us8f iv1

  How many rad/s is 25 revolutions per minute equivalen s6ezb* /edzxnt6ks +4t to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thea4m ggl;urab4z-o0.q frequencaz 0-;lbgro.mgua4q4y of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequencyg+ bvw:fef11nd dlm oi/e17w4*rtz a0 of 0.40 kHz. The period of its rotatioa ge+w:4 me117bd r0ifwtozldvf1* /nn is

  A phonograph record rotates at 45 rpm. Through what angle :e8ic q f:c g g(9mu6cd2ymqx*5j;blf does it turn in 0.20 s?mui9 g5 (mb6:2j8q* d qceg;cxf yclf:

  A wheel of diameter 26 cmf 8+ iyf344,akf ns;oigpv iu( turns at 1500 rpm. How far will a point on the outer rim move in 2.1 s?s vii+8faunf4,oyigpk(f 43;

  A bicycle wheel rotates uniformly thvt; h5tl hzfu:k4a g-7rough 2.0 revolutions in 4.0 s. What is the average an u5;zhv- g:7akh tt4lfgular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutiovms f/((gno;9xuyz1naj pg w1;3c8 nsns in 4.0 s. What is the linear speed of a point 0.10 m xn ;fv3m sa (1gcz sp9o/;n wj1n(g8yufrom the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. j 6nib624a77b,y1y ur ra9pnckub9g kThe cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate fo 6bc4irgb6aayypbn791 2rkuk u,n97jr the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with k s 3.p z,aqzhkmbz41z6jl3/va constant angular speed of 2.0 rad/s. What is the linear speed of a point onz /zlj qz3sz6vmp 1a3 kbk,4.h the wheel's rim?

  The cutting cord on a gas-powered weed cutter iqh4fz4uh bs4)kyy:l 6s 0.16 m in length. If the motor rotates at thezyh6 l:b4u4) hq4ykfs rate 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 speerq9+uj p+ c:npd of 2.0 rad/s. What is the centripetal acceleration of a point orpuq9j c+pn+:n the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicyc 8u.fky7,ge:fldjn ; ,yhafa2le wheel of diameter 70.0 cm when thdyl8,kfy.,f ;e g7 f2ahj a:nue bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a cib8iusq c l:/s usewfi8toy. 9 4jy255lrcular, rotating space station (r = 1000 m) rotate to produce an artificial gravity oblt4 o.wy e8cisyi:l u8/u595j 2sfsqf $9.80 \; m/s^2$?

  A car is negotiating a flat circular cur jy. 7 o1d::h6dqjcj-grgog3hve of radius 50 m with a speed of 20 m/s. The maximum centripetal:j1 gog.dq73gd:6 o jr h-yhjc 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 curve of radius 50 m with a speed of 20 m8r83 xe f.vrp- j /xjeiize:3m*: 6feemmve- m/s. The maximum centripetal force (provided by static friczme e*e88xxf3.jjm6ie -ve i-rm r/ev m3::fption) 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 around in*(o.)t h5iqp txif.z hh0z9r: 1cjyww a smooth level table. If the maximum tension that the string can withr1 .f*5z: qh.)ci9j xy(0 hot zthwpiwstand 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 ro:b x2n1s3sxdo lls without slipping 10 m down a lane atsxnbs32x: do 1 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 acceler/3c6 5 h)srnxjnh*(e zmk w-yaation 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 at hvdc1x (-ebume5j2:ngular 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 frca .ek8p rgnkc qh0p.l:q4z ;.om rest zgca84k;e k.cq0hp: n.lp r .qand 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 an angular acceleration xe:bkf4u8 ddj 8 4o*/nvdip3mof $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s f cmwy1r-.n9x;.lnyndecelerates with a constant angular acceleration n;9yyc1mr wlxn. fn- .of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and r6ziii61dmi omw.k i.aw0 8v u9b u5yu3eaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is t3imywm89 i6 vki. uwai dui50o 1z.6ubhe average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ov c 8/tjoza,g8oer a distance of 115 m. What is the totc/8azto g8j ,oal number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows dow:dqs g:z- mqw0y0.g-xeanv p0n uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular ac0p--y m0:wv:gd asgnqeq .0zxceleration?

  A wheel of diameter of 68.0 cm slo b,s.giyg tq94ws down uniformly from 8.40 m/s to rest over a distance of 115 m. How long doe9bstg.4qy ,i gs it take for the wheel to come to the stop?

  A centrifuge in a medical laborarmn7)ksljuw c 3w( 9.ktory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 timecjk)ln wm3rk( 7 s.9wus 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 9g;p 1jhn0d y ned0.t,q0 Nm. If a 30 cm long wrench is g. 0y1n;e dhd np,j0qtused, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheeliv ddv+e mxv)6a2/os. require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude ofvd/ avvs .)6exd 2i+om the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner56w 3(po m ty9e7zb y0trcbwsc6 )mbx6tia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as foll7tg po8xc0hq ,ows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at c p7o,txq h08gx = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axisz10h/p9;wd5 mtyeilg thought the center O. A rozipl1wt5 yh0/ m;eg 9dpe 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.vz7+fxh) s2*rym ty-r f c/nn kg is pivoted about a frictionless axis thought the center O. A rope whr+x/t)2mzn7 s.nyffv c *-yr rapped 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 initially held in t, nbvawdsby fnd:; ish g,32y16r x-0lhe horizontal position, bd3r:,y; b1vfg nsd-i wh a6xl2n y,0sand 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 ML2/3.)

  Consider a bicycle wheel to be an0/yhn9( / g9ns1 qc ymxepp, ds5(vsk ring of radius 30 cm and 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.s( cvp / dkny,sy59qngx /e m0ns9hp1(0 cm for 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs o eezm7f,-ewq 0n a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of th qme-,7 eez0fwe pulley?

  A 1.53-kg mass hangs on a roppb)nv-i 4:(-snq hfj ie0 rm1j2trsz(e wrapped around a frictionless disk pulley of mass 7.07 kg and res:qjjtn z-n(r) f( bsm10 i2hpr4- viadius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store ener b z7hy3dw0etki5r+)wgy. 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 i kh9o r,+9ik;l7j uipfnertia 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 and radius 0.010 m startp gxl+yrjtr3agje 5,i v8 .2 dsk+wt/3s from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere+slw3.2xdv5pgj ,aj/rt +k iyt 8erg3 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 spx k-w qvel2m *zz*7hs9eed of 10 m/s. How high up an inclined plane can it climb before 2x*qk zl z7*w9 esmvh-coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allotr m* /i+a,cnp bs*ku9wed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?a cbtn9m*usri* ,k+p/

A solid sphere of mass 1.5 kg and radius 15 cm rolls wiyl*3cs+; t46 mfde +8qiqioqb, 0txpk thout slipping down a 35e incline that is 7.0 m long. Assume it started t4p*+o+c q8m;syl0 ,6xbeqf3 tkii qdfrom 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 chv:m9eij.2w;bz t m/v banges 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 inevbi+-wpwua bll+460 y rtia 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 5.0v+w4hpg11hwf 0 rad/s with arms extended has a moment of inertia oww141 vghh p+ff
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?