Mechanics
Newton's Second Law (Rotation)
Rotational analog of Newton's second law.
Variables
τN·m
Net torque
Sum of torques
In SI units: kg·m²/s²
Ikg·m²
Moment of inertia
Rotational inertia
Allowed values: 0 or more
αrad/s²
Angular acceleration
Rotational acceleration
Derivation
Rotational equivalent: τ = Iα (compare F = ma).
Your notes
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Check value
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- I = 2 kg·m² (Moment of inertia)
- α = 3 rad/s² (Angular acceleration)
Result: τ = 6 N·m
Other mechanics formulas with the same quantities
- Angular Acceleration (Rotational Motion) shares Angular acceleration
- Rotational Kinetic Energy (Rotational Motion) shares Moment of inertia
- Angular Momentum (Rotational Motion) shares Moment of inertia
- Rotational Kinematic 1 (Rotational Motion) shares Angular acceleration
- Rotational Kinematic 2 (Rotational Motion) shares Angular acceleration
- Rotational Kinematic 3 (Rotational Motion) shares Angular acceleration
Where this formula is listed
- Mechanics formulas, under Rotational Motion, alongside Angular Velocity, Linear-Angular Velocity Relation, Centripetal Acceleration, Centripetal Force and Moment of Inertia (Disk/Cylinder).
- In the mechanics list it comes after Moment of Inertia (Point Mass) and before Rotational Kinetic Energy.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Newton's Second Law (Rotation) formula?
Newton's Second Law (Rotation) is written τ = Iα. Rotational analog of Newton's second law. It belongs to Mechanics, under Rotational Motion.
What are the units in τ = Iα?
In SI units, τ is net torque, measured in kg·m²/s²; I is moment of inertia, measured in kg·m²; α is angular acceleration, measured in rad/s².
How is the Newton's Second Law (Rotation) formula derived?
Rotational equivalent: τ = Iα (compare F = ma). The result is τ = Iα.