Chapter 7: Motion in a Circle Coordinate system for circular motion Period (T): The time interval a particle takes to go around the circle once Speed of a particle Angular position Angular displacement Angular velocity Equation of motion for uniform circular motion Some problems

Coordinate System We have used Cartesian (or XY-) coordinate system so far When a particle traces a circle such a motion is called circular motion In circular motion, the position vector is unchanged unlike in 1- and 2-D motions we discussed so far In circular motion the position of the particle depends on the angle its position vector makes with respect to some reference axis We will introduce (r,θ) coordinate system here which better describes circular motion

Average and Instantaneous Cartesian Coordinate System (Linear Motion) Circular Coordinate System (Circular Motion) Position Angular Position Displacement Angular Displacement Velocity Angular Velocity Acceleration Angular Acceleration

Coordinates for Circular Motion Angular Position (θ) θ measured ccw is positive θ measured cw is negative Angular Displacement(∆θ) = θf – θi Y (x2,y2) r sf +θf (x1,y1) Period (T): The time taken by a particle to complete one revolution si +θi O X -θ

Arc Length (s) Arc length is the distance covered by a particle in circular motion In one full revolution the arc length is 2πr where, r is the radius of the circle Angle (θ) covered in one full revolution = 2π = 360o Relationship between s, r, and θ θ is measured in radian and, 1rad=57.3o

Angular Velocity (ω) Angular velocity is defined as the ratio of angular (displacement/distance) to the time elapsed Average angular velocity = ∆θ/∆t Instantaneous angular velocity = dθ/dt Equation of circular motion that corresponds to linear motion

Example