Build a quantity from its dimensions.

Build a quantity by multiplying/dividing known quantities (m, v, a, F, r, t, G, h, c…); live M, L, T exponent bars show its dimensional formula.

Assemble G from F, r and masses so the bars read [M⁻¹ L³ T⁻²]; then find a power combination of G, h, c that is dimensionless in L and T except a length (Planck length).

Treating constants such as G or h as dimensionless; confusing pressure and energy density as different dimensions.

• The dimensions of a quantity are the powers to which the base quantities are raised to express it; they describe its nature, not its size.
• Each base quantity is one dimension, written in square brackets: [M] for mass, [L] for length, [T] for time, [A] for electric current, [K] for thermodynamic temperature, [mol] for amount of substance and [cd] for luminous intensity.
• In mechanics every quantity can be written with [M], [L] and [T] alone. Volume is [L³]; force = mass × acceleration is [M L T⁻²].
• Magnitudes do not enter: speed, initial velocity, final velocity and change in velocity all have the same dimensions, [L T⁻¹].
• The dimensional formula shows which base quantities appear and with what powers, zero powers included: volume [M⁰ L³ T⁰], velocity [M⁰ L T⁻¹], acceleration [M⁰ L T⁻²], density [M L⁻³ T⁰].
• A dimensional equation sets a quantity equal to its dimensional formula, for example [F] = [M L T⁻²] or [ρ] = [M L⁻³ T⁰].
• A dimensional formula can be read off from any defining equation: momentum = mass × velocity gives [M L T⁻¹]; work = force × distance gives [M L² T⁻²].

Teaching this idea? Put the simulation on your own page or LMS with this code.