Angular Acceleration Calculator

Use our angular acceleration calculator to find acceleration using velocity and time.

Calculate:

Angular Acceleration:

Acceleration Formula

\alpha=\frac{\omega_{t}-\omega_{0}}{t}

Learn how we calculated this below

How to Calculate Angular Acceleration

Angular acceleration refers to the rate at which the angular velocity of an object changes with respect to time. Just as linear acceleration is concerned with changes in velocity in linear motion, angular acceleration deals with changes in rotational speed.

Angular acceleration is a vector quantity, which means it has both a magnitude and a direction. It is particularly important in disciplines such as mechanical engineering, aerospace, and any field that involves rotational dynamics of objects.

Angular Acceleration Formula

The equation for angular acceleration α is derived by finding the change in angular velocity ω over a time period t.

Thus, the angular acceleration formula states:

\alpha=\frac{\omega_{t}-\omega_{0}}{t}

The angular acceleration α is equal to the change in angular velocity ω divided by the time period t.

For example, let’s imagine a disc initially at rest starts spinning and reaches an angular velocity of 30 radians per second in 5 seconds.

The first step to finding the angular acceleration is to identify the initial angular velocity (ω at time 0) and the final angular velocity (ω at time t).

\omega_{0}=0\ rad/s

\omega_{t}=30\ rad/s

Then, you’ll need to determine the time period or interval over which the change in velocity occurs.

t=5\ seconds

And finally, substitute the values in the formula above to find the angular acceleration α.

\alpha=\frac{30-0}{5}=6\ rad/s^{2}

So, the angular acceleration of the disc is 6 radians per second squared (rad/s²).

You might also be interested in our angular velocity calculator.

Angular Acceleration Calculator

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