Angular displacement is usually express in uni .5t+k37gtvtfco x,6q u)p/2t vugbcets of

  Angular velocity is expr:*xdk k7 h aj)z0f8h7zisqij3xiz,(t/zt, bpessed in units of

  Angular acceleration is expressejs7q kjh;h h5ljl./q3d in units of

  A boy and a girl are riding on a merry-gm7hji g,cq- uca 174yzo-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 thz1 7,uh q-ic jmcy7ga4e greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is5mm ch67) 4jlv mtwg5s turning at a constant rate. The boy is near the outer edge, j7m6cgm 4t)lw5vmsh 5and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round n 9(stk)89dxex0xu;a ah uw9pwhich is turning at a constant rate. The boy is near the outer edge, and the girl is closer txpxd;(0 hexs9 9n9awa 8u)kt uo the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turnine wj ,dh::ce(zg at a constant rate. The boy is near the outer edge, while the girl is closcjw( heez :,:der to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is q2sv j0-9d 7*y0tfygm+zdb is turning at a constant rate. The boy is near the outerzm0jb2tyq+ v0g-sdysd 9f7* i edge, 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 isj+e23 okl drw* an accurate stl3or e 2+kdj*watement?

  Rolling without slippingm x 0p44unpipvl48c,ysmm ,s: depends on

  Two equal forces are applied to a door. The fir li68 cidpkb/39o2fpo st force is applied at the midpoint of the door; the second force is applied at the doorknob. Both fof d3ikcb /2i86pl9opo rces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorkn kc yrcz.m78sll)tum+o7e+2/ nbk a 7qob. The first force is applied perpendicular to the door; the 87c 7 7c l/rk+ e+ktnsmmoz2lba).qu ysecond 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 the do pip,ig be:s+5d:pz8j7 k7jeke 0s;d oor. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the second i8zpd e:oe j+s ; ,d7pigsbp:keki0j 57s

  What is the quantity used to measure an object's resistance to ch279sa ounsx /j7ue a3manges in rotatiou usm39a2oea/7nx j s7n?

  Consider two uniform solid spheres where both have the same diameter, but one he0l (fjwy;ww 4as twice the mass of the other. The rat 4wjfw(wel0; yio 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 twiceftm 1r*gzf8.z kw4;pr the radius of the other. The ratio of the larger sphe4kfrfp wrt .8z;1*m gzre's moment of inertia to that of the smaller sphere is

  Consider two uniform so;wl.x 8i0r6mgtrl 3ntlid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia tr glr.nlt i;xm8306 wto that of the smaller moment of inertia is

  A uniform solid sphere has mass M and 9m6hrb+mcv.dw 7j jgs.* 6t g; mkjem-radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia m6jd6mjm.cbmhw ; +ej r9s. -g7kgv*tabout a central axis?

  If a constant net torque is applied to an object, that object wi- 6oi+wj gockg ,sq5;lll

  The moment of inertia of a solid c;yas01:xxt uk ):hkanylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kineti0n)ak:: ushykta;xx 1 c energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has z rg:7.ni8bw ; e+mneqxhgk:6 q/y rf:a mass of 10 kg and a radius of 30 cm q ;r7r.n/g: wbk8fxi zgyeq:+6neh: m. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphervnrkm/c3vb;6n1ps (d e of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the invb;c 1(k3 r6snd/ mpvncline depends on

  Suppose a solid sphere of mass M and radius R rolls withjlt;2cz42wi tr07j km j0m2hdt m4gl 9out slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on 9zl mt4 0j2ihck4mj ;g2t2tm7ldw0jr

  "The total angular momentum of a system of particles changes when a net extern08 .lcpnzu6z an1k1snd b- k5u2kjb f6al force acts on the system." This statemenk.d 6nf0 5z2n b8zcuk1jsnk-b pal61ut is

  In what circumstances can the angular velocit503 /a6*els n 2 ezrjlibe9exwy of system of particles change withlrn3s6ej/0eb92a *ie e zxwl5out any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. c:ylmnxz 40c,Ignore any friction which may be cc4 l,ynxzm0: present. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth mov0fc siq hquth.:/y+ e:: 4rdvces close to the Sun, then which of the following best describes the orbiting speed of :0q yfrv/4hcche .+:i :sdqtuthe Earth about the Sun?

  An ice skater performs a pirouett)pv-c8a7 0jxkjq hx. te (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotati0ht qc .pxx7)va-jk8jon?

  An ice skater performs a pirouette (a fast spin) by pula5 ugmjo7(ap :umis k-8bv33u ling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axujabp85vg k 7iam-um3u o3 :(sis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstreoe a vfz,t1g4vp7bu01tched arms close to his body. What happens to his momen,vg14ob v a10u7zfptet of inertia about the axis of rotation?

State the law of conservation of angular momentum.r;5 rmsvr+ 8tfs7v xu.(7ls kr

  What arc length does the Earth travel in a three month peri24 e.vvpdbkkj27ta j-od in its nearly circular orb 47kakepj.tdv-vb2 j2it about the 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 distance does the tip8daqt ok.27dr of the second hand sweep through in 3 minutes and 45 seconda .k2d rtd87oqs?

  How many rad/s is 25 revolutim,q5(j vef .qbru;ftcgeu7* y82m/noons per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolumi1ty.j/g lk+ tions in 4.0 s. What is the frequency of the wheel's rotationl1t+ ij.yk/m g?

  A pulsar (a rotating neutron star) emits pulses at a frequencu5,dw d-dofo80zrc ,(z 1d5k3ybdx y 7 pv*pdly of 0.40 kHz. The period of its rotation isudo3z5 *c5w bdxdy0kvy dpl(,7f z1o pd8,-dr

  A phonograph record rotates atug0w3 : dyh,rl 45 rpm. Through what angle does it turn in 0.20 s3gdylwh,: u 0r?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point onyxaiy g-7 fsc90 ;riw0(mu m7f the outer rim move in 2.rsxf-f7iy;0i7mmyc9g ua ( w01 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What iza1khx*p/3 /edt1q*xl7ollrb-m q j di4 ei0) s the averag p i03qx7lora x zlldh**j1bt1k// - deem)qi4e angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 f9hh4/ zno uf;revolutions in 4.0 s. What is the linear speed of a o 9/4hffuz hn;point 0.10 m from the center of the wheel?

  A cable car at a ski resoaq v 0-xgi/4. u0i zgyl0n(btwi4l,myrt carries skiers 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 x/n44zw 0u0gi lyl yibg,mv(0 a-.qtito make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotatingad7-x g)wjwy 2 with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wha 2gy)-wjxw7 deel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 h0,rko(q;d ec m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed ocder ;(qhk0,of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular spee4yd*pr7v me e9d of 2.0 rad/s. What is the centripetal acceleration of a point oy 4pemve97d *rn the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of ) jhr5 muwk-s,a bicycle wheel of diameter 70.0 cm when the bike is moving 8.js5h, )rwkum- 00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space st x77mqi8o/ a3j ;svxmqation (r = 1000 m) rotate to produce an artificial gravity of 38 mi 7jaxvq 7m/oq;xs$9.80 \; m/s^2$?

  A car is negotiating adw/pq/ um67gk flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fricti7 k/m qp/u6wgdon) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circulary/, .5 nl ubx1,a:ccn.mapzpl curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fr l zncnpaul,ab,myx. .:1/p5c iction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the enwxm01 mo.5ue ad of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maxix .uaw5m1 oe0mmum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radiubeycjoo*h+o,z 7 v *e0fjk/(is 9.0 cm rolls without slipping 10 m down a lane at 4.3 eo*k jb vjoyo,7/c* fezi 0h+(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 c8t g *pkgziqxk3 x;*nxc93p( donstant 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 accellp)athp1;te)u pzi rs1tz+: d;mm:6leration 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 ro-w4 mk1ubh hwh3(z5 fbtate after starting from rest and accelerating at a constant angular accelera- 4k w3b (uh1mzhbhwf5tion of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleraq7*lecnvw/l n/)fm-r tion of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates0 f:i9:xrodxd(qgo (k with a constant angular acceleration ofr09k(oiodd x( qxf:g: $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and rw9+k p*xmv.mpf 7gtew9isnk5u 0:ic9m z v 9/heaches an angular speed of 6.0 rad/s while turning through 2.0 revep9m wu i90w:xnc97zg+v khfpis 9kvmt*5./m olutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uvl0 3ffdymteo4u4( y1 niformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in clv1(ot0ef f4dyy3 m 4uoming to rest?

  A wheel of diameter of 68.0 cm slow bf 3jdt0rej3+s down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular accelerati+eb t3 30frdjjon?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest overpfhh 95lgwy,xiv1x *4 a distance of 115 m. How long does it take for the wheel to come to thip1*95 yfxgvxlhwh,4 e stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of3 7id uxjwwtdy j8u bm,/q60j) 3600 rev/min. When switchedd 7 qmwj)ybxd6utw3u jji,08/ 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 ton m 9(,. hgjgos;sidm3 a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requirehi j(n;s.gg m,m9os3d d when the force is perpendicular to the wrench?

  The bolts on a car wheel req2q, kf *9gtwlzuire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude ofgkl 92wtzqf ,* the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment 5sd4 ;szmm ac9of 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 m is at thvl 59v9:la gkee origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia aboutlg9 v:k9aev5l the origin?

  A solid cylinder of mass 10 kg is pivoted about a f+- 29ffffk9fgq2q ftu rictionless 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. (See Fig. 8-1.) What is the angular accelerati9 2fk2fq +fffqg-utf9 on of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thov l 1wzrv0xm /hxl4g ;us;.jl.ught 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 many radians does the cylinder rotate through in the first 5.0 seconds, if it 4.x lr; z/lj slh1 ux.g0mw;vvstarts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held in ty g3p.i;2isj* zgzltr0j5s2j ux*7 1ac, gsglhe horizontal position, and then released as the free end is allowed to fall. What is the angular accelts.g , yu*1ic* jagj503rs;2 gzjl pig2lzxs7eration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to b5i6uc eb5sy y/e a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle anb6usy ye5 i5c/d 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 does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionleiy.h(dx 55jxe ss disk pulley of mass 7.07 kg and radius 66.0 cm. What is the ane5x hjd. ix5(ygular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped 70a.sq0htkn2q ig t 3qsp z:w)around a frictionless disk pulley of masshstq.0s kz 0q:3it7 awg)2pnq 7.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If itydo77 ;zs cqo. 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 inertin+/p6 yd8m5 gyja4kkja 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 mokiwi l t4hsl)go(o8 /g7gcd l ::1fv* starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when itv/8owl(:4gsci 1l : dgl)g ofh* otki7 reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speedon+ad 5f;n1f irs;n)m of 10 m/s. How high up an inclined plane can it cli+fon dm;1n 5;sin)a rfmb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and aef/htgx zs,p9i )* izz366fyf llowed to ze6p,6g f)zf9izx sfiy /3 ht*roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of ma/ 7xv qt*v3z 7l(hg fufc-v2njss 1.5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0l u vft7v2f c7qvz(j*3ng h/x- 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 momentum changes by8q)bhpg-a b2y o/8nvm0k 5xlh $20 \; kgm^{2}/s$ 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 moh3i8tr-ga 9 l jgxs(u b.*he7vment 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 with arms extended has a moment of ine/mjyv0m;l b.zx14 9aet/09 n icbhz oirtia o /jz 40iavto0xmbl1ey9 cmb;zh. i/n 9f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?