Rotational Dynamics Calculator

How it works

1. 1Select what you want to solve for: torque (τ) or angular acceleration (α).
2. 2Enter the known quantities — moment of inertia I in kg·m² and the remaining variable.
3. 3The result is computed instantly using τ = I·α, the rotational form of Newton’s second law.

Use cases

• Finding the torque a motor must produce to spin a flywheel to a target angular acceleration.
• Determining how quickly a body accelerates given an applied torque and its moment of inertia.
• Designing shafts, gears, and rotating machinery where torque and inertia must be balanced.

Frequently asked questions

What is the formula, and how does it relate to Newton’s second law?

τ = I·α, where τ is torque (N·m), I is moment of inertia (kg·m²), and α is angular acceleration (rad/s²). It is the rotational analogue of F = m·a — torque replaces force, moment of inertia replaces mass, and angular acceleration replaces linear acceleration.

What is moment of inertia and why does it matter?

Moment of inertia measures how much an object resists changes to its rotation. It depends on the mass and how that mass is distributed about the axis. A hollow cylinder has a higher moment of inertia than a solid one of equal mass and radius, so it needs more torque for the same angular acceleration.

Can you show a worked example?

A wheel with I = 2 kg·m² at a target α = 3 rad/s² needs τ = I·α = 2 × 3 = 6 N·m. Conversely, applying τ = 6 N·m to a body with I = 2 kg·m² gives α = 6 ÷ 2 = 3 rad/s².