Kinetic and potential energy describe motion and stored energy in physical systems. This calculator computes them across linear motion, rotation, gravity (near-surface and two-body), and springs—helping you understand mechanical energy conservation in real-world applications from vehicles to orbital mechanics.
Core Formulas
- Linear Kinetic Energy (KE): K = ½mv², where m is mass (kg) and v is velocity (m/s). Energy of linear motion. Example: A 1000 kg car at 20 m/s has K = ½(1000)(20²) = 200,000 J = 200 kJ.
- Rotational Kinetic Energy (KErot): Krot = ½Iω², where I is moment of inertia (kg·m²) and ω is angular speed (rad/s). Energy of spinning objects. For a solid disk: I = ½mr².
- Gravitational Potential (Near-Surface): Ug ≈ mgh, where g is gravitational acceleration (9.81 m/s² on Earth) and h is height above reference level. Valid when h « planet radius. Example: Lifting 10 kg to 5 m height: U = (10)(9.81)(5) ≈ 491 J.
- Gravitational Potential (Two-Body): U(r) = -GMm/r, where G = 6.674×10-11 N·m²/kg² is the gravitational constant, M is central body mass, m is object mass, and r is separation distance. Negative value indicates bound system. Used for orbital mechanics and large altitude changes.
- Elastic (Spring) Potential: Us = ½kx², where k is spring constant (N/m) and x is displacement from equilibrium (m). Energy stored in compressed or stretched springs. Hooke's Law: F = -kx.
- Mechanical Energy Conservation: Etotal = K + U = constant when only conservative forces act (no friction, air resistance, or other dissipative forces). ΔK + ΔU = 0, so energy transforms between kinetic and potential forms.
Units: SI units are standard (J for joules, kg, m, s). The calculator supports unit system switching for convenience. Always verify dimensional consistency: 1 J = 1 N·m = 1 kg·m²/s².