Rotational Speed and Angle

This function calculates the relationship between rotational speed, angle, radius and time.

The rotational speed is the speed on a circular path, calculated from the distance and the time required. This function calculates the speed from the section of a circular path whose length is defined by the angle and the time required.

To perform the calculation, use the radio button to select which value should be calculated. Then enter the required values and click the 'Calculate' button.

Formulas for rotational speed

The rotational speed is the quotient of the distance covered on the circular path and the time required for a full circle.

\(\displaystyle v=\frac{2· π· r}{T}\)

\(T\) is the time required for a 360° circuit.

The rotational speed is calculated from a partial circle whose arc is defined by Δφ:

\(\displaystyle v=\frac{Δs}{t}\)     \(\displaystyle Δs=\frac{2· π· r ·Δφ}{360°} \)

\(t\) is the time required for distance \(Δs\)

Relationship between the rotational speed and the angular velocity.

The angular velocity is calculated from   \(\displaystyle ω=\frac{v}{r} \)

\( v=ω · r\)