How to use it
- Choose a rigid body, a point mass or conservation.
- Rigid body: enter the moment of inertia (find it with the moment of inertia calculator) and the angular speed.
- Point mass: enter the mass, speed, distance from the axis and the angle between the radius and the velocity (90° for circular motion).
- Conservation: enter I and ω before and the new moment of inertia I₂.
Formulas
- Rigid body: L = I × ω, kinetic energy E = ½ I ω²
- Point mass: L = m × v × r × sin θ; seen from the axis I = m r²
- Conservation (no outside torque): I₁ ω₁ = I₂ ω₂, so ω₂ = ω₁ × I₁ ÷ I₂
- 1 rpm = 2π ÷ 60 rad/s, 1 °/s = π ÷ 180 rad/s
Worked example
A wheel with I = 4 kg·m² spins at 2 rad/s: L = 4 × 2 = 8 kg·m²/s and E = ½ × 4 × 2² = 8 J.
A skater with I = 4 kg·m² turning at 2 rad/s pulls in the arms to I₂ = 1 kg·m²: ω₂ = 2 × 4 ÷ 1 = 8 rad/s, four times faster. The energy rises from 8 J to ½ × 1 × 8² = 32 J.
A 2 kg ball moving at 3 m/s at 4 m from the axis, at right angles: L = 2 × 3 × 4 = 24 kg·m²/s.
Tips
- Use rad/s inside the formula. The calculator converts rpm and °/s, but by hand multiply rpm by 0.10472 first.
- Conservation needs no outside torque. Friction at the pivot slowly takes angular momentum away.
- The direction matters too. Angular momentum is a vector along the axis; this calculator gives its size.