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Angular Momentum Calculator

Calculate angular momentum and the speed change conservation implies when inertia changes.

About Angular Momentum Calculator

With no external torque, angular momentum is conserved, so reducing inertia must raise angular speed proportionally. Note that rotational energy is not conserved — pulling mass inward requires work, which appears as extra energy. A skater pulling their arms in spins faster for exactly this reason, and the energy increase comes from the muscular work of pulling in.

Formula

Angular Momentum

L = I ω, conserved without external torque, so I₀ω₀ = I₁ω₁

L
Angular momentum
conservation
Holds when no external torque acts

Worked example

With the default values below, Angular Momentum Calculator returns Angular Momentum of 15.0796. Change any input above and every figure here is recalculated in your browser.

Inputs used

Moment of inertiaminimum 0 kg m2
1.2 kg m2
Rotational speedminimum 0 rpm
120 rpm
New moment of inertiaminimum 0 kg m2
0.6 kg m2

Results

Angular Momentum
15.0796 kg m2/s
New Rotational Speed After the Change
240.00 rpm
Angular Velocity
12.5664 rad/s
Rotational Energy Before
94.748 J
Rotational Energy After
189.496 J

Step by step

  1. 1Values used
  2. 2Angular Momentum
  3. 3Angular Momentum= 15.0796 kg m2/s
  4. 4New Rotational Speed After the Change= 240.00 rpm
  5. 5Angular Velocity= 12.5664 rad/s
  6. 6Rotational Energy Before= 94.748 J
  7. 7Rotational Energy After= 189.496 J

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Angular Momentum calculated?

L = I ω, conserved without external torque, so I₀ω₀ = I₁ω₁ With no external torque, angular momentum is conserved, so reducing inertia must raise angular speed proportionally. Note that rotational energy is not conserved — pulling mass inward requires work, which appears as extra energy.

Why does Angular Momentum matter?

A skater pulling their arms in spins faster for exactly this reason, and the energy increase comes from the muscular work of pulling in.

What values do I need to enter?

This calculator takes 3 inputs: Moment of inertia, Rotational speed, New moment of inertia. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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