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Angular-Momentum Conservation: Final ω from I₁ω₁ = I₂ω₂ Calculator

ω₂ = I₁·ω₁ / I₂.

When no external torque acts, angular momentum I·ω is conserved. Given an initial moment of inertia I₁ and angular velocity ω₁ and a new moment of inertia I₂ (e.g. an ice skater pulling arms in), this calculator computes the resulting ω₂ = I₁·ω₁ / I₂. Reports both the new angular velocity and the rotational period.

Dr. Helena Ortiz By Dr. Helena Ortiz
Published Last reviewed 1 min read

Inputs

kg·m²
rad/s
kg·m²

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

ω₂ = I₁ω₁ / I₂; T₂ = 2π / ω₂.

In depth

When no external torque acts, angular momentum I·ω is conserved. Given an initial moment of inertia I₁ and angular velocity ω₁ and a new moment of inertia I₂ (e.g. an ice skater pulling arms in), this calculator computes the resulting ω₂ = I₁·ω₁ / I₂. Reports both the new angular velocity and the rotational period.