A-Level Physics: Circular Motion Revision

Radians and Angle Measurement

• Conversion between degrees and radians:
  • Degrees to radians: Multiply by π and divide by 180
  • Radians to degrees: Multiply by 180 and divide by π
• Common angle values:
  • 360° = 2π radians
  • 180° = π radians
  • 90° = π/2 radians

Time Period and Frequency

• Time Period (T): Time to complete one full circle
  • Relationship: T = 1/frequency (f)
• Velocity of a circular path:
  • Velocity (v) = Circumference (2πr) / Time Period (T)

Angular Velocity (ω)

• Angular Velocity: Angular displacement per unit time
  • Formulas:
    • ω = 2π / T
    • ω = 2πf
• Relationship with Linear Velocity:
  • v = ωr
  • Angular displacement (Δθ) in one second is given by ω
• Conversion from RPM to radians/s:
  • Multiply by 2π, then divide by 60

Centripetal Force and Acceleration

• Centripetal Force: Net force causing circular motion
  • Always directed towards center
  • Perpendicular to linear velocity
  • Examples: Tension, gravitational force, frictional force
  • Formula: F = mv²/r
• Centripetal Acceleration:
  • a = v²/r
  • Direction changes, speed remains constant as velocity is vector

Work Done in Circular Motion

• Speed doesn't change as net force is perpendicular to velocity
• Work Done = Force x Displacement x cos(θ)
  • With θ = 90°, cos(θ) = 0, so Work Done = 0

Experimentation in Circular Motion

• Setup:
  • Bung on string through glass cylinder
  • Vary mass or radius
  • Measure mass with balance, radius with ruler, time with stopwatch
• Calculate:
  • Time Period by averaging
  • Velocity: v = 2πr/T
  • Centripetal Force: Plot graph of force (mg) vs velocity²
  • Straight line through origin confirms formula

Circular Motion at an Angle

• Car turning, normal reaction R split into components:
  • R cos(θ) = mg (balance of weight)
  • R sin(θ) provides centripetal force: mv²/r
• Conical Pendulum:
  • Tension components: T cos(θ) = mg, T sin(θ) = mv²/r
• Calculating Speed:
  • Use tan(θ) relationships: v = √(gr tan(θ))

Vertical Circular Motion

• e.g., washing machine drum, mass on string, roller coaster loop
• Forces in different positions:
  • Position 1: mv²/r = mg + R
  • Position 2: mv²/r = R - mg
  • R greatest in position 2

Conclusion

• Comprehensive review of circular motion concepts
• Essential to practice past paper questions for mastery

Note: Additional practice and exercises are crucial for full understanding and preparation for exams.