\[\tau = I\alpha\]
Variables
tautorque (N·m)
Imoment of inertia (kg·m²)
alphaangular acceleration (rad/s²)
Description
What is this formula?
This equation relates torque, moment of inertia, and angular acceleration in rotational dynamics. It is the rotational equivalent of Newton's Second Law.
When to use it
Use this formula when analyzing rotating objects such as flywheels, motors, gears, turbines, and mechanical systems subjected to torque.
Example
A rotating disk has a moment of inertia of 4 kg·m² and experiences a torque of 20 N·m.
Data:
tau = 20 N·m
I = 4 kg·m²
Formula:
alpha = tau/I
Substitution:
alpha = 20/4
Result:
alpha = 5 rad/s²
Applications
Rotational mechanics, motor design, industrial machinery, robotics, aerospace engineering, and mechanical system analysis.