In this section, we discuss some of the defining quantities, which are used to describe uniform circular motion. These quantities are angular position, angular displacement and angular velocity.

Notably, we shall not discuss angular acceleration. It will be discussed as a part of non-uniform circular motion in a separate module.

** Angular position (θ) **

We need two straight lines to measure an angle. In rotational motion, one of them represents fixed direction, while another represents the rotating arm containing the particle. Both these lines are perpendicular to the rotating axis and passing through the position of the particle.

Angular position (θ) |
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For convenience, the reference direction like x – axis of the coordinate system serves to represent fixed direction. The angle between reference direction and rotating arm (OP) at any instant is the angular position of the particle (θ).

It must be clearly understood that angular position (θ) is an angle and does not represent the position of the particle by itself. It requires to be paired with radius of the circle (r) along which particle moves in order to specify the position of the particle. Thus, a specification of a position in the reference system will require both “r” and “θ” to be specified.

Relation between distance (s) and angle (θ) |
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By geometry,

where s is the length of the arc subtending angle “θ” and “r” is the radius of the circle containing the position of the particle. The angular position is measured in “radian”, which has no dimension, being ratio of two lengths. One revolution contains 2π radians. The unit of radian is related to other angle measuring units as :

1 revolution = 360° = 2π radian

#### Note:

** Angular displacement (Δθ) **

Angular displacement is equal to the difference of angular positions at two instants of rotational motion.

Angular displacement (Δθ) |
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The angular displacement is also measured in “radian” like angular position.

** Angular velocity (ω) **

Angular speed is the ratio of the magnitude of angular displacement and time interval.

This ratio is called average angular velocity, when evaluated for finite time interval and instantaneous angular velocity, when evaluated for infinitesimally small period (Δ→0).

The angular position is measured in “rad/s”.