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What is the difference between orbital and angular velocity?

Answer #1

Level 2 (without higher mathematics)
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Orbital velocity and angular velocity of a circular disk
Disk with angular velocity \(\omega\) and two different orbital velocities \(v_1\) and \(v_2\) shown as examples.

The angular velocity \( \boldsymbol{\omega} \) always points in the direction of the rotation axis (i.e. perpendicular to the rotation disk) and does not change its direction during a uniform circular motion. It indicates the angle covered by a mass point of the disk per time. In contrast to the orbital velocity, the angular velocity of a rotating disk is the same for all mass points (of which the disk is composed).

The orbital velocity \( \boldsymbol{v} \) on the other hand, is tangential to the circular orbit and points in a different direction at every point on the disk (because of the rotation). The orbital velocity is larger the farther away a point of the circular disk is from the axis of rotation. The point which is closer to the axis of rotation must cover a smaller circumference of the circle than a point which is further away from the axis of rotation.

The magnitude \(\omega\) of the angular velocity and the magnitude \( v \) of the orbital velocity are linearly related:

Formula anchor

Here \( r \) is the perpendicular distance of a point from the axis of rotation.