Lecture on Uniform Circular Motion Using a Vinyl Record Player

Introduction

Definition: A body is in uniform circular motion if it moves in a circular path at constant speed.
Examples:
- Tip of the second hand of a clock
- Rotating fan blades
- Merry-go-round
- Satellite orbiting Earth

Angular Displacement:
- Angle swept by the radius vector in a time interval.
- Full circle: 360° or 2π radians.
- Right-hand thumb rule determines direction.
Angular Velocity:
- Rate of change of angular displacement.
- Formula: ω = Δθ/Δt, unit: radians/second.
- Example calculation: For 360 degrees in 2 seconds, ω = π radians/second.
Time Period (T) and Frequency (f)
- Time period: Time to complete one revolution.
- Frequency: Number of revolutions per second, unit: Hertz.
- Relationship: T = 1/f

Angular Displacement and Linear Displacement:
- θ = s/r where s is arc length and r is radius.
- s = rθ
Linear Velocity (v) and Angular Velocity (ω):
- v = rω
- Larger radius results in larger linear velocity.
Acceleration in Circular Motion:
- Even at constant speed, direction changes, so there is acceleration.
- Centripetal Acceleration (Ac): Directed towards the center, Ac = v²/r or Ac = ω²r.

Angular Acceleration (α):
- Rate of change of angular velocity.
- Formula: α = Δω/Δt, unit: radians/second².
- Linear or tangential acceleration (at) related: at = rα
Net Acceleration
- In non-uniform circular motion, net acceleration: a_net = √(at² + Ac²)

Example Problem: Calculate linear velocity and centripetal acceleration for a body of mass 5 kg in a circle of 14 cm diameter at 300 RPM.
Encouragement to solve and comment answers.