Physics overview
What is rotational dynamics?
Rotational dynamics explains how torque produces angular acceleration in an object with a particular moment of inertia.
Formula
Rotational dynamics formula
Torqueτ = Iα
- τ is torque in N·m.
- I is moment of inertia in kg·m².
- α is angular acceleration in rad/s².
Worked example
An object has I = 4 kg·m² and α = 3 rad/s²
- Write the formula: τ = Iα.
- Substitute the values: τ = 4 × 3.
- Calculate torque: τ = 12 N·m.
Rearranged equations
Solve for moment of inertia or angular acceleration
Moment of inertia
I = τ ÷ α
Divide torque by angular acceleration.
Angular acceleration
α = τ ÷ I
Divide torque by moment of inertia.
Physical relationship
Torque, inertia, and angular acceleration
For a fixed moment of inertia, greater torque produces greater angular acceleration. For a fixed torque, a larger moment of inertia produces less angular acceleration.
Units
Standard SI units
Use newton meters for torque, kilogram square meters for moment of inertia, and radians per second squared for angular acceleration.
Real-world applications
Where rotational dynamics is used
- Motors, turbines, and rotating machinery.
- Wheels, gears, and flywheels.
- Vehicle drivetrain analysis.
- Robotics and mechanical systems.
- Sports and rotating body motion.
Calculation limits
Important assumptions
- All entered values must be greater than zero.
- Net torque is treated as constant.
- Moment of inertia is defined for the selected rotation axis.
- Vector direction is not represented.
- Units are not converted automatically.
Related tools
Continue your rotational analysis
Use the Torque Calculator for force and lever-arm calculations.
Use the Moment of Inertia Calculator for common rotational shapes.
Questions and answers
Rotational dynamics calculator FAQ
What formula does the rotational dynamics calculator use?
It uses τ = Iα, where torque equals moment of inertia multiplied by angular acceleration.
What is rotational dynamics?
Rotational dynamics studies how torque, moment of inertia, and angular acceleration affect rotating objects.
How do you calculate moment of inertia from torque?
Divide torque by angular acceleration using I = τ ÷ α.
What units are used for torque?
Torque is measured in newton meters, written as N·m.