• Radian is the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
• Angular Displacement (θ) is the angle through which an object moves along the circular path. It is measured in radians.
• Formula: θ = s / r
  Where:
    – s is the arc length.
    – r is the radius of the circle.

2. Angular Speed (ω)

• Angular Speed (ω) is the rate at which an object’s angular displacement changes with respect to time.
• It is expressed in radians per second (rad/s).
• Formula:
  ω = Δθ / Δt
  Where:
    – Δθ is the change in angular displacement (in radians).
    – Δt is the time interval over which the change occurs.

3. Relationships between Angular and Linear Quantities

• ω = 2π / T
  – T is the period (the time taken for one complete revolution).
  – This shows that the angular speed is inversely proportional to the period.
• v = rω
  Where:
    – v is the linear speed (tangential speed) of the object moving in the circular path.
    – r is the radius of the circular path.
    – ω is the angular speed.