Angular Acceleration Torque
Torque needed to angularly accelerate a rotating mass.
Formula
Variables
Example
I=0.2, α=5: τ = 1 N·m
How it works
This formula states that the torque required to change a body’s rotational speed equals its rotational inertia times its angular acceleration. It is the rotational counterpart of Newton’s second law: just as more mass requires more force to speed up linearly, a larger moment of inertia requires more torque to speed up or slow down rotation. The relationship comes from how mass is distributed around the axis of rotation, which determines how hard it is to rotate the object.
When to use it
Use this when analyzing motors, gears, wheels, arms, or flywheels that are being sped up or slowed down. It is especially useful in robotics and control for sizing actuators and predicting how much turning effort is needed for a desired change in rotational motion.
Worked example, step by step
Given: I = 0.75 kg·m², α = 4 rad/s² Step 1: Write the formula: τ = Iα Step 2: Substitute the values: τ = 0.75 × 4 Step 3: Calculate: τ = 3.0 N·m Final answer: The required torque is 3.0 N·m.
Common mistakes to avoid
- Using mass instead of moment of inertia
- Mixing up angular acceleration with angular velocity
- Forgetting that torque units are N·m, not just N
Did You Know?
Sizing a robot's motors starts with the peak torque needed to accelerate its own arm inertia.
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