A-Level Physics: Circular Motion Revision

Angle Measurement: Radians

• Conversion between degrees and radians:
  • Degrees to Radians: Multiply by π, divide by 180°
  • Radians to Degrees: Multiply by 180°, divide by π
• Common conversions:
  • 360° = 2π radians (complete circle)
  • 180° = π radians
  • 90° = π/2 radians

Time Period and Frequency

• Time Period (T): Time for one complete cycle
• Frequency (f): Number of cycles per unit time
• Relationships:
  • T = 1/f
  • f = 1/T
• Velocity of circular motion:
  • v = 2πr / T, where r is the radius

Angular Velocity (ω)

• Definition: Angular displacement in a given time
• Equations:
  • ω = 2π/T
  • ω = 2πf
• Relation to linear velocity:
  • v = ωr

Unit Conversion: RPM to Radians/Second

• Multiply by 2π and divide by 60
• Example: 200 RPM = 200 x 2π / 60 ≈ 21 rad/s

Centripetal Force

• Definition: Net force causing circular motion
  • Always directed towards center
  • Perpendicular to linear velocity
  • Examples: tension, gravitational force, friction
• Formula: F = mv²/r
• Centripetal Acceleration:
  • a = v²/r

Circular Motion: Speed vs. Velocity

• Constant Speed: Magnitude of velocity is constant
• Changing Velocity: Direction changes due to centripetal acceleration
• Reason for constant speed:
  • Force is perpendicular to motion (no work done)
  • Work done is zero if force and displacement are perpendicular

Experiment: Investigating Circular Motion

• Setup: Bung on string through glass cylinder connected to mass
• Procedure:
  • Measure mass (m) with balance
  • Calculate weight (mg)
  • Measure radius (r) with ruler
  • Time 10 oscillations for accuracy
• Calculations:
  • v = 2πr / T
  • Plot graph of force (mg) vs. v² to verify centripetal force formula
  • Determine mass of bung using gradient of force vs. v² graph

Circular Motion at an Angle

• Examples: Car turning, conical pendulum
• Forces:
  • Split normal reaction R into R cos θ and R sin θ
  • R cos θ balances weight (mg)
  • R sin θ provides centripetal force
• Calculations:
  • Rearrange equations to solve for unknowns
  • v = sqrt(gr tan θ)

Vertical Circular Motion

• Examples: Washing machine, roller coaster
• Position Analysis:
  • Position 1: Forces in same direction (R greatest)
  • Position 2: Forces in opposite directions
• Newton's Second Law:
  • Position 1: mv²/r = mg + R
  • Position 2: mv²/r = R - mg

Final Notes

• Review past paper questions to solidify understanding
• Experiment with different setups/data interpretations

End of Lecture