Net torque
Total torque required about the fixed axis.
Physics · Mechanics · Motion & Energy
Rotational dynamics — torque, inertia and acceleration
Relate net torque to the angular acceleration of a rigid body about a fixed axis. Choose the unknown quantity; positive means counterclockwise as viewed in the diagram.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Angular acceleration
Signed change in angular velocity per second.
Moment of inertia
Positive inertia inferred from torque and acceleration with matching signs.
Relation and numerical substitution
τ = I × α—
Rigid body, fixed axis and constant strictly positive moment of inertia. τ is the net external torque, including any friction torque.
01Formulas and symbols
Formulas used
τ
τ = I × αNet torque for a given inertia and angular acceleration.α
α = τ / IAngular acceleration produced by the net torque.I
I = τ / αInertia inferred when α ≠ 0.02Assumptions and limits
Scope of validity
- Rigid body, fixed axis and constant strictly positive moment of inertia. τ is the net external torque, including any friction torque.
03Validation example
Reference numerical case
- For I = 2 kg·m² and τ = 6 N·m: α = 6 / 2 = 3 rad/s².
- Conversely, τ = 2 × 3 = 6 N·m and I = 6 / 3 = 2 kg·m². With τ = −6 N·m, α = −3 rad/s².
04References
Technical references
FAQ
Does zero torque mean the body is stopped?
No. With constant I, τ = 0 gives α = 0: angular velocity stays constant, but its value is not determined here.
Can I be calculated when α = 0?
If τ is also zero, any positive inertia fits and I is indeterminate. If τ is nonzero, the inputs are inconsistent with this model.
05Principle and interpretation
For the same torque, doubling I halves α. The sign of α follows the net torque, not necessarily the current direction of rotation. Use the related torque calculator to determine a moment from force geometry.
06Model limits
This scalar model excludes moving axes, precession and variable inertia. It does not calculate angular velocity or rotation angle. Zero or negative inertia is not admissible.
07Common mistakes
Use a mass moment of inertia in kg·m², not an area second moment in m⁴. Enter net torque rather than motor torque alone when resisting torques act.