1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. Example