Angular Displacement Calculator

Rotational Motion Analysis

Calculate angular displacement, velocity, and acceleration for rotating objects and circular motion.

Calculator

Formula:
Δθ = θ₂ - θ₁

About Angular Displacement

Angular displacement is the angle through which an object rotates about a fixed axis.

Symbol:

Δθ (theta)

Units:

Radians, degrees, revolutions

Features

  • Basic displacement (θ₂ - θ₁)
  • Constant velocity motion
  • Constant acceleration motion
  • Multiple angle units
  • Angular velocity calculation
  • Final velocity calculation
  • Real-world examples
  • Copy results

Formulas

Basic:

Δθ = θ₂ - θ₁

Constant Velocity:

Δθ = ωt

Constant Acceleration:

Δθ = ω₀t + ½αt²

Final Velocity:

ω = ω₀ + αt

Unit Conversions

1 revolution:

= 2π rad ≈ 6.283 rad

= 360°

1 radian:

≈ 57.296°

≈ 0.159 rev

1 degree:

≈ 0.01745 rad

≈ 0.00278 rev

Applications

  • Rotating machinery (motors, turbines)
  • Wheels and gears
  • Planetary motion
  • Pendulums and oscillations
  • Robotics (joint rotation)
  • Sports (golf swing, baseball pitch)
  • Engineering design
  • Physics education

Key Concepts

Important Terms:

Angular Velocity (ω): Rate of change of angle (rad/s)

Angular Acceleration (α): Rate of change of angular velocity (rad/s²)

Period (T): Time for one complete revolution

Frequency (f): Number of revolutions per second (Hz)