Lecture 7 Circular Motion vector description Polar coordinate system Position Coordinates Component of angular velocity Unit vectors Velocity Relation to Cartesian Coordinates Component of Angular acceleration Acceleration Transformations between unit vectors in polar coordinates and cartesian unit vectors Circular Motion Position Fixed axis rotation Angular Velocity Position Vector Velocity Vector Angle variable Angular velocity Component Magnitude Direction Speed and angular speed Angular speed Velocity The tangential component of the velocity of the object undergoing circular motion is proportional to the rate of change of the angle with time Circular Motion Constant Speed Period and Frequency In one period the object travels a distance equal to the circumference s 2 R vT Period the amount of time to complete one circular orbit of radius R Frequency is the inverse of the period Acceleration and circular motion Fixed axis rotation Angular Acceleration Angular acceleration Component Magnitude Direction Alternative forms of magnitude of centripetal acceleration Parameters speed v angular speed w frequency f and period T Circular Motion Tangential Acceleration When the component of the angular velocity is a function of time The component of the velocity has a non zero derivative The the tangential acceleration is the time rate of change of the magnitude of the velocity When an object moves in a circular orbit the direction of the velocity changes and the speed may change as well For circular motion the acceleration will always have a non positive radial component a due to the change in direction of velocity it may be zero at the instant the velocity is zero
View Full Document
Unlocking...