Circular Motion Waye County Public Schools Wayne County ：圆周运动韦恩县公立学校的韦恩县

1、circular motionquestions for considerationohow do we measure circular motion?owhat is a radian?owhat are the angular analogs of linear motion?owhat is centripetal acceleration?circular motionohow do we measure circular motion?ntypically use radians.nangle subtended by an arc equal in length to the c

2、ircles radius.circular motionocircumference (distance around) = 2rnso 2 radians = one full circle.nso radians = 180oto convert rad to deg:ndeg = rad x 180/n1 rad = 57.3oto convert deg to rad:nrad = deg x /180n1 = 0.0175 radcommon anglesarc lengthoarc length (s)nmeasured in meters along circumference

3、 of circle.angular displacementoangular displacement ()nmeasured in radians.nccw rotation = +ncw rotation = - os = r+-circular motionoa wheel with r = 5.00 m spins counterclockwise so that an ant resting on the top travels 12.0 meters along the rim. through what angular displacement did the wheel ro

4、tate?ns = rn12.0 m = (5.00 m)()n = 2.40 radr = 5.00 m12.0 mangular velocityoangular velocity ()n =oexpressed as rad/s.ocan also be given in terms of revolutions per unit time.nrevolutions per minute (rpm)o1 rpm = (2 rad) / (60 s) = 0.105 rad/sttangential velocityotangential velocity (v) the instanta

5、neous velocity of an object moving in a circular path.nimagine a bucket being swung around on a rope.nthe bucket has a tangential velocity that is perpendicular to the rope.nif the rope breaks, the buckets tangential velocity will become its linear velocity.tangential velocityoformula for tangential

6、 velocity:nv = roa child is riding a merry-go-round that is rotating at 30 rpm. how fast is the child moving if she is 2.5 m from the center?ngiven:o = 30 rpmor = 2.5 mnwant:ov = ? tangential velocityofirst, convert rpm to rad/s:n30 rpm = (30 * 2 rad) / (60 s) = 3.14 rad/sov = rnv = (2.5 m)(3.1 rad/

7、s) = 7.8 m/stangential velocityoa satellite moves around the earth in a circular orbit with r = 10,000 km. if the satellite takes 2.76 hours to complete one orbit, calculate the satellites angular and tangential velocities.ngiven:or = 10,000 kmot = 2.76 hrnwant:o = ?ov = ?tangential velocityo = / tn

8、 = (2 rad) / (2.76 hr)n = 2.28 rad/hrov = rnv = (10,000 km)(2.28 rad/hr)nv = 22,800 km/hrcentripetal accelerationocan something accelerate but maintain a constant speed?nyes, if it changes direction.oacceleration = change in velocity / timeochange in velocity =nspeed up,nslow down,nor change directi

9、on.centripetal accelerationocentripetal acceleration (ac) causes a change in direction.nperpendicular to direction of motion.nmeasured in m/s2.oac = v2r= 2rcentripetal accelerationcentripetal accelerationoan amusement park ride spins riders around so fast that they are seemingly stuck to the walls. if the ride has a radius of 3.50 meters, what angular velocity (in rpm) is necessary to create a centripetal acceleration of 20.0 m/s2?ngiven:or = 3.50 moac = 20.0 m/s2nwant:o (in rpm) = ?centripetal a