of the circle. The angular speed ω , is the rate of change of angular distance. It is related to velocity v by v = ω R . The acceleration is a c = ω R .
If T is the time period of revolution of the object in circular motion and ν is its frequency, we have ω = π ν, v = πν R, a c = π ν R POINTS TO PONDER . The path length traversed by an object between two points is, in general, not the same as the magnitude of displacement. The displacement depends only on the end points; the path length (as the name implies) depends on the actual path. The two quantities are equal only if the object does not change its direction during the course of motion.
In all other cases, the path length is greater than the magnitude of displacement. . In view of point above, the average speed of an object is greater than or equal to the magnitude of the average velocity over a given time interval. The two are equal only if the path length is equal to the magnitude of displacement.
. The vector equations ( .33a) and ( .34a) do not involve any choice of axes. Of course, you can always resolve them along any two independent axes. .
The kinematic equations for uniform acceleration do not apply to the case of uniform circular motion since in this case the magnitude of acceleration is constant but its direction is changing. . An object subjected to two velocities v and v has a resultant velocity v = v + v . Take care to distinguish it from velocity of object relative to velocity of object : v = v − v .
Here v and v are velocities with reference to some common reference frame. . The resultant acceleration of an object in circular motion is towards the centre only if the speed is constant. .