Newton's Second Law for Rotation (τ = Iα)
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
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Torque plays the role of force, moment of inertia the role of mass, and angular acceleration the role of linear acceleration. Moment of inertia depends not just on how much mass a body has but on where it sits: mass far from the axis resists spin-up far more. Apply 10 N·m to a flywheel with I = 2 kg·m² and it spins up at 5 rad/s²; the same torque on a flywheel of twice the radius (four times the I) manages only 1.25 rad/s².
Newton's Second Law for Rotation (τ = Iα)
Where
- = Net torque
- = Moment of inertia
- = Angular acceleration
Missing one of these? Work it out first, then come back
- Net torque — Torque, Torque with a Lever Arm (τ = rF sin θ)
- Moment of inertia — Rotational Kinetic Energy, Angular Momentum (L = Iω)
- Angular acceleration — Angular Acceleration, Angular Displacement (θ = ω₀t + ½αt²)