Dimensional formula of Potential energy

How to get the dimensional formula of potential energy

1. Start from the definition: potential energy = mass × acceleration due to gravity × length.
2. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
3. acceleration = velocity / time, so acceleration is [L T^-1] / [T] = [L T^-2].
4. force = mass × acceleration, so force is [M] × [L T^-2] = [M L T^-2].
5. gravitational constant = force × length² / mass², so gravitational constant is [M L T^-2] × [L]² / [M]² = [M^-1 L³ T^-2].
6. acceleration due to gravity = gravitational constant × mass / length², so acceleration due to gravity is [M^-1 L³ T^-2] × [M] / [L]² = [L T^-2].
7. Put in the dimension of each part: [M] × [L T^-2] × [L].
8. Add the powers of each base quantity: [M L² T^-2].

Quantities with the dimensions [M L² T⁻²]

• Work
• Energy
• Kinetic energy
• Torque
• Torsional constant
• Gravitational potential energy
• Strain energy
• Heat
• Internal energy
• Electric potential energy
• Work function
• Photon energy
• Binding energy

Equal dimensions do not make them the same quantity. Compare potential energy with the others in the full grid.

Three questions on potential energy

Related quantities

• A Area [L²]
• V Volume [L³]
• x Displacement [L]
• θ Angle [M⁰ L⁰ T⁰]
• Ω Solid angle [M⁰ L⁰ T⁰]
• v Velocity [L T⁻¹]