Angular Acceleration Calculator
Enter the starting and ending angular velocity and the time to find angular acceleration, alpha = (omega_f - omega_i) / t. Add a moment of inertia for torque.
How to use the angular acceleration calculator
- Enter the initial and final angular velocity in rad/s.
- Enter the time in seconds over which the change happens.
- Optionally add a moment of inertia to also get the net torque.
Examples
Spinning up
omega_i = 0, omega_f = 20 rad/s, t = 4 s
alpha = 5 rad/s^2
With a moment of inertia
alpha = 5 rad/s^2, I = 0.5 kg x m^2
torque = 2.5 N x m
Frequently asked questions
What is the angular acceleration formula?
Angular acceleration is alpha = (omega_f - omega_i) / t, the change in angular velocity in rad/s divided by the time in seconds, giving rad/s^2.
How do I get torque from angular acceleration?
Torque equals the moment of inertia times the angular acceleration, tau = I x alpha. Enter a moment of inertia and the tool returns the net torque.
What does a negative angular acceleration mean?
A negative value means the object is slowing its spin. For example, going from 20 rad/s to 0 over 4 seconds gives alpha = -5 rad/s^2.
What units are used?
Angular velocity in rad/s, time in seconds and angular acceleration in rad/s^2. Moment of inertia is in kg x m^2 and torque in newton-metres.
Can the time be zero?
No. The time must be greater than zero, since dividing by zero time would give an undefined acceleration.
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