Torque⚠ unverified
Physics / Mechanics · Compute torque from the rotational form of Newton's second law
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| moment_of_inertia | momentofinertia | kg*m^2 | 1.0 | Mass moment of inertia about the axis of rotation |
| angular_acceleration | angularacceleration | rad/s^2 | 1.0 | Angular acceleration |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | τ | N*m | Torque, in newton-metres (N*m) |
The science & history
Understanding the Parameters
- $I$ — rotational inertia; larger $I$ needs more torque for the same $\alpha$.
- $\alpha$ — $d\omega/dt$; constant torque ⇒ constant $\alpha$ (analogue of constant $a$).
- $\tau$ — net moment; also $\tau = r F\sin\theta$ for a single force, but this card uses the $I\alpha$ form. Distinct from motor-nameplate torque calculators such as Motor Torque.
Derivation (Approaching a Proof)
For a rigid body, $L = I\omega$ about a fixed principal axis ($I$ constant). Then $\tau_{\mathrm{net}} = dL/dt = I\alpha$. This mirrors $F = dp/dt = ma$ in translation. Power: $P = \tau\omega$ (rotational twin of $P = Fv$).
History
Euler’s equations and the scalar $\tau = I\alpha$ form are the backbone of introductory rigid-body dynamics and machine element design.
Related Concepts: Newton's Second Law, Moment Of Inertia Disk, Moment Of Inertia Point Mass, Angular Momentum, Rotational Kinetic Energy, Motor Torque
Notes: Registry calculator torque (unverified). Fixed-axis / principal-axis scalar form; not
full 3-D Euler equations.