the speed of circular motion can be measured by the ratio of the arc length traveled by an object to the time taken. if an object moves from m to n, it passes point a at a certain time t. in order to describe the speed of movement when passing near point a, we can start from this moment and take a short period of time △t. during this time, the object moves from a to b, and the arc length passed is △l. the ratio △l/△t reflects the speed of the object's movement, which is called linear speed and is represented by v, that is, v=△l/△t. linear speed also has average value and instantaneous value. if the time interval taken is very small, the instantaneous linear speed is obtained.

note that when △t is small enough, arc ab almost becomes a straight line, and the length of arc ab is almost the same as the length of line segment ab. at this time, △l is the displacement of the object from a to b. therefore, v here is actually the instantaneous speed in linear motion, but it is now used to describe circular motion.

linear velocity is a vector with magnitude and direction. for an object in circular motion, the direction of its linear velocity changes all the time and always points to the tangent direction of the point.

circular linear speed calculator:

linear speed: v = 2*pi*r / t

here:

r = radius

t = time period