Linear Speed · Andromeda

Definition

Linear Speed ( $v$ ) is the measure of the distance traveled along a curved or straight path per unit of time: $v = s/t$ .

It describes how fast an object is physically moving through space.

Linear Speed ( $v$ ): Defined as the change in arc length $s$ over time $t$ . $v = \frac{s}{t}$
How to read: “The linear speed v equals the distance s divided by the time t.”
Meaning: Distance traveled per unit time along the circular path.
The Connection: Since $s = r\theta$ , we can relate the two speeds through the radius $r$ : $v = r \omega$
How to read: “The linear speed v equals the radius r times the angular speed omega.”
Meaning: Linear speed at the rim is the product of radius and angular speed—illustrating how Non-linearity and scaling (larger r) amplify effects. This is a direct application of the geometry of Euclidean Space and rotational Causality.