Angular displacement is usualn;h) rk..bsuro -tz+o1yg3w sly express in units of

  Angular velocity is expres+dou (hzz+*kl sed in units of

  Angular acceleration */dxjqr ia3x9kh( rbb1d5 a1z is expressed in units of

  A boy and a girl are riding on a v , r +ypu)gg.5ozdc,v ,4teetmerry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girp5o.z vyd,ve)4t,tg,gu+ cerl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round6n,iobh9ri 6tlj1 a8l;+ft we which is turning at a constant rate. The boy is near the outer edge, and the girl is closer tl;l n+o ht1bia8fwj 6i9,er6 to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round whict3 dn g 5u2v80tgkuau:h is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greatetv3n 2atgu 805 kug:dur linear speed?

  A boy and a girl are ridingul6+ ckvnfk*q frd w)3sjb 6/; a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl i)r bf fn6sk3c6q/ dw *l;vk+ujs closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-rountnok o3-a:es;9o ha) zo,jkf4 d which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has t; )k 9okofj:,-a3tzn sohoea4he greater tangential acceleration?

  Consider a rigid body that is rotdg f2 ,.-klpeou8 2tx3rognt1ating. Which of the following is an accurate statemen t-p.2ktu8lo xnd2,ef31o rg gt?

  Rolling without slipping depends es7ux7t0 v )t/+e xm g1irfb,oo3pp7 bon

  Two equal forces are applied to a door. The first force is applied at the mi+uz:3eq l n97r:d8vvyr5-j 1 dsteox xdpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicu zl: qrn+t 5v38edx uorsvjx7-:9y 1delar to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door yx(rqr rh pc6 un 2xpk 4hxt().rx8u+0at the doorknob. The first force is applied perpendicular to the door; the second force n2084krxhc (.uhrrx q rpt)u6 xp+y(x is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied tc0 v6p9 rht(gwdrfd/:o a doorknob, perpendicular to the door. The first force is twice as large as thert:whg (6vd fpc/ 90dr second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure (;y*gq5 b1 yfq9npbea l-p 3lyan object's resistance to changes in rotati3g 5balqp1* nl(;- efybypq y9on?

  Consider two uniform solid spheres bb3ed4bcyr/g vl: vt9i259erwhere both have the same diameter, but one has twice the mass of the other. tdvrlb9be4y b2 i/e c5grv39: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 +e e,eze :,dwrtwice the radius of the+,dw rzee,:e e other. The 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 the mass andfx)hh9ol, j , (0q*j1jlmbubw twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller m)(bh,*,jmjljhfqb o lxuw091oment of inertia is

  A uniform solid sphere has mass M and rad +m*lkxb m4b.9q*dgj hius R. If these are increased to 2M and 3R, what happens to the spg *m+b9m4bdh.kxlj *qhere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wil5 eibt84miuk 8jz .(rwl

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2. c+,9jn(6p ogf: r1dvjei jyz7If this cylindf7 p vyc9jg +(rjz,1 id6:ojneer rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg ggr f6cm512tsd3ej;l, 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 whdget1scf gmjr 36l ;52eels 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 withouq4gqv, ;rg3hkv:h ( n rs :q/hnuo5qa+t slipping down an inclined plq(gs aun4q:r5q3gqv/r ;:v+nh hh k,o ane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere4sk 5 cfbuy-+o6polv( l+pia 6 of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angulav5lik 4+f+s(ppbu6 ao-y oc6lr velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a nq e2(t21*lsxa.l(y ja.yzhjk et external force acts on the system." This statems2l z (1j a*xlh.atk(ye.j2q yent is

  In what circumstances can the angular velocity of system of particles changpu64/ ;w kmnooe without noo6 w/um;4kp any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which xnoq,;c zt jdfxl*(2 9may be present. What happens over time to thet;ljxdnc ,*2(fq9xzo Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Ear cikf0hac hdf/5f2o qlo97e: se*;bo6th moves close to the Sun, then which of the following best describes0f5scq6l9o *;2e of7e/ hf:akchbd oi the orbiting speed of the Earth about the Sun?

  An ice skater performsib(7a lk;n mzre- *h5s a pirouette (a fast spin) by pulling in his outstretched h-(5ksz me; rlain *7barms close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstxjj uai8sbu/x0o3 ),wev*; q xretched arms close to his body. What happee*)v3qu/o8ui xsj jwax,0;bxns to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretcbld* iv /tcl8s:3fdv+hed arms close tov*3 :c+ lfsvbi8t/ddl his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentum.bz0sxrdz,o9(t p +qq*

  What arc length does the Earth travel in a three month period in its nearly c( b1o3bni* hfof14t8 m7twsxtircular orbit about the Sun with a radius of b13o 8swhttof 7*nf(b 1i txm4$1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does thr1f c-uo4 tdsop)0at2y g.ju us,ls1s.y)v7k e tip of the sec 1.,s7ugs0) -oys.4 1r2tufuj)ypa otksvdclond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions pxr,a1n nh 1x2s 9,bi0m2kppg ger minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 18 o6uiau sbkwvk*.ed2n:e j*4.0 s. What is the freque bans vi6 eu.81kdko e*:2uw*jncy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. They5wx+2h;e4pd s/c9l vt xqg usdy1.1g periopy; /2euw9qv+ 4 115ly.cgstd gdxxh sd of its rotation is

  A phonograph record rotatw-nt-d p +ig4jes at 45 rpm. Through what angle does it turn in 0.20 s tnd-4p-wjig +?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point -.59gro4szek jg:i tp,sgku 7on the outer rim move in 2.1 s? szpj k -ti.s7eg,:kgo4r95gu

  A bicycle wheel rotates uniformly/gj /xz.3cm nw through 2.0 revolutions in 4.0 s. What is the average angular spm/ cjx/g.n 3wzeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4/b0rnuul.m lzt9-wm-)v, fha.0 s. What is the linear speed of a point 0.10 m fnlu -.v)-l,uh a m0zwr9m/tbfrom the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable *l, ii2gk zfv8which 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 in 12 l8,ivfz2g *ki minutes?

  A wheel of radius 1.0 m is rotating with a constant angular ylvl( xwdy4c2sjya6 w b-:wc6uj/ ,e0speed of 2.0 rad/s. What is the linear speed of a point on the wheel's rijwx42/b vy se,6a-yluwj cc y(lw:d60m?

  The cutting cord on a gas-powered weed cutter l73pwo ; )rbunis 0.16 m in length. If the motor rotates at the rate of 20 r37u;b)n rw lopev/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 2.0 rad/r 5o4r;ql,e4 9ezh mnmir7jb)s. What is the centripetal acceleration of a point on the w qbe;)ior4j4hl 9 75re mznm,rheel's rim?

  What is the centripetal acceleration of a point on the perimetl: o )mc8qh7zber of a bicycle wheel of diameter 70.0 cm when the bike is moving b :m hco)7qlz88.00 m/s?

  How many revolutions per minute (rpm) must t7 eg8a6o*2i wm 7h/xxqpfa1 fa circular, rotating space station (r = 1000 m) rotate to pro 7xf8*7e/xah2i 6pafwq1og t mduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a 3;zcf8kyb5 k4*couce flat circular curve of radius 50 m with a speed of 20 m/s. The max 8z4c3uyc5ck o;ek *fbimum centripetal 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 spl30)yu;bi 9e4v zur ap/y ukd1eed of 20 m/s. The maximum centripetvyar/udpz k41bi; u9u)e3l0y al 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 th/ bnuthz4 mq(+u- r-yg*l 2)iet6qa jce end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can 2j *-umn rq4(t-z+a hlyi/cq)gbet6uwithstand 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 4woh*wfr 1dpz86w(5pkago 5f kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s.f*p g4(wzrdkw5wo hop1a8f 6 5
(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 aqys.bv 4ilnt l.kjg: ek77, .dcceleration 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 ac2k2fj(8ian ue: f ond0celeration 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 rotm 7bv+d) zj5k6lhi o+ x+(qgscy,ha4s ate after starting from rest and accelerating at a con hzxad(mvko4,)7qs c+y gs 65++hj ilbstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an abq0b06 s81cznp(n2mt emk8 k s3blpa1 ngular 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 accelerg.o64/t-8z77j aj-rptuy qn a i;pxro ation of a7r4qj8p.7 ooy 6-ipgtxua ;j/rztn -$-5.0 \; rad/s^2$. 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 b urlzq2ld,xj;9 *l9gwhile turning through 2.0 revolutions. What is the average angular acc lb9l uz rj2*;,gx9qldeleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rez h dsqc6h,z9y:cxj74: hym3bst over a distance of 115 m. What iy d3 yzhcm, z4xjbhc::s6qh97s the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.w 2v.wag mez7fe69twbw(p, / n0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the e7 69/bw.(wn, ztga2wwf vpem angular acceleration?

  A wheel of diameter of 68.0 cm slows down uni l vnc1/m:opq.s l*3hyformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to cocl.hlv *m qyns1p/:3 ome to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 360 sicb1 lfiz32;2v *d o)ub2haf0 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to r23bz 2 db ;i*)hvcusf21 ilfaoest.
(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 requi7era7)*li* ygfm.zc6fwv uqf z oy 7vg)bj4+8 re tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required w vu*7a7vw4egg cf7+by z8)*qj6)o rifzm y l.fhen the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 301hbes 9osel(+ cm long wrench is used, what is to s9h1lbe e+(she magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertms2 /ico)jb*aia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mas,ao7zk ds m. :+h23irsx5v udfwy,d8 qs m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of iney5szv7, 8a+uf:s hm3qd 2wodx id,.r krtia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thhz ew78q2w 4e.ov f0bhought 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 exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of8. ob4wzeq h7vh20ewf the cylinder?

  A solid cylinder of m. .2 ; msyqr.h;5hgwutsqob7 pass 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 exerts a force F2 = 6.0 N downward. How map;q.2q.;gwuyro5ssb.hmt 7hny 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 horizo) tk1uzevh -m)ntal position, and then released as the free end is allowed to fall. What is the angular accel h)u1)mzketv -eration 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 radius 30 cm anhvzs6,2g cfl.d mass 1.5 kg. Neglect the mass of the axle and sprocket. I6,hlg2vf .szc f 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 frirncx4)jq(/7cr1rfb o0dvhpn21 wak- ctionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelerat7 qvc1non-x2fk1h r)0(p/r 4c adjwbrion of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulleyqb;sql3g6 8o y of mass 7.07 kg and radius 66.0 cm. What is theoq;b3ql6 sy 8g acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to styt ft01e)jho5ka-5nlwf s/)ove l 1:rore $1.00 \times 10^{6} \; J$ 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 inerf+b tc71q(o,bgkozj 47dk f)ftia 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 radr- scqe)5bwo;ius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclinedbcr)qo ;e- w5s plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls w crh.wq c,x8d5r+ avu8ith a speed of 10 m/s. How high up an inclined .+r5a h r8vudw8,cq xcplane 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 allowed j vi)p x1rec3s 2tu.e9l2qiv+ to roll down an inclined plane. How fast is it moving after du1 jii+9 lev v e)t2xcps3.2qrropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cma+dp3w:xf y 2h rolls without slipping down a 35e incline that if:3ywd +h xa2ps 7.0 m long. Assume it started from 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 momeh q1d5fdg n ,7yp+hl9i)2bnps ntum 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 inoti.bou5:qfw3q dlop84txcs4- dh:1* qt,pfertia 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 rad8tv46 ,uuhgkk /s with arms extended has a moment of inertia 84u,g ht uvkk6of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?