Angular Momentum Calculator
Angular momentum and rotational energy, and the new speed if the moment of inertia changes.
Results
Angular momentum
94.2478
kg·m²/s
Angular velocity
62.8319
rad/s
Energy
2960.881
J
Rotational speed
1500.0
rpm
Energy
7402.203
J
What this tool does
Angular momentum is conserved when nothing twists the system from outside, so pulling mass closer to the axis makes it spin faster — the skater's trick. Notice the energy goes up, not just the speed: that extra energy comes from the work the skater does pulling their arms in against the outward pull.
Formula
L = I × ω ; E = ½ I ω²
Variables
| Symbol | Meaning | Unit |
|---|---|---|
i | Moment of inertia | kg·m² |
n | Rotational speed | rpm |
i2 | Moment of inertia | kg·m² |
L | Angular momentum | kg·m²/s |
W | Angular velocity | rad/s |
EN | Energy | J |
N2 | Rotational speed | rpm |
E2 | Energy | J |
Worked example
- Moment of inertia1.5 kg·m²
- Rotational speed600 rpm
- Moment of inertia0.6 kg·m²
- Angular momentum94.2478 kg·m²/s
- Angular velocity62.8319 rad/s
- Energy2960.881 J
- Rotational speed1500.0 rpm
- Energy7402.203 J
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.