Angular Acceleration Calculator Formula
Understand the math behind the angular acceleration calculator. Each variable explained with a worked example.
Formulas Used
Angular Acceleration
alpha = (omega_f - omega_i) / timeVariables
| Variable | Description | Default |
|---|---|---|
omega_i | Initial Angular Velocity(rad/s) | 0 |
omega_f | Final Angular Velocity(rad/s) | 10 |
time | Time(s) | 4 |
How It Works
Angular Acceleration
Angular acceleration is the rate of change of angular velocity.
Formula
alpha = (omega_f - omega_i) / t
This is the rotational analogue of linear acceleration a = (v_f - v_i) / t.
Worked Example
A flywheel speeds up from rest to 10 rad/s in 4 seconds.
omega_i = 0omega_f = 10time = 4
- 01alpha = (omega_f - omega_i) / t
- 02alpha = (10 - 0) / 4
- 03alpha = 2.5 rad/s²
Frequently Asked Questions
What does negative angular acceleration mean?
Negative angular acceleration means the rotational speed is decreasing (angular deceleration) in the chosen positive rotation direction.
How is angular acceleration related to torque?
By Newton's second law for rotation: tau = I * alpha, where tau is torque and I is moment of inertia.
What are the units of angular acceleration?
Radians per second squared (rad/s²).
Ready to run the numbers?
Open Angular Acceleration Calculator