Angular velocity is defined as the rate of change of angular displacement with time.
we can shorten the equation by using symbols alone:
The SI Units of angular velocity is radians per second (rads-1)
Consider the equation that relates angular displacement in radians with the arc length made by the object:
to get the rate of change of speed, we divide both sides with t as they both represent displacement of the object.
but distance s when divided by time gives velocity. That is;
where v is the linear velocity representing the velocity of the object along the circular path.
Hence the equation above becomes:
hence, the angular velocity can be expressed in terms of linear velocity and radius as show in equation below:
similarly, linear velocity can be expressed in terms of angular velocity as v=ωr.
An object in circular motion has both linear and angular velocity. The time taken to make one complete circle is called the periodic (T) and is given by T= circumstances/speed.
Let us now consider the time taken for a body to make one complete circle in a circular path. At that one circle, it will have covered the circumference of a circle and the time taken to complete such one revolution is called periodic time (T).
from the equation time = distance / speed
and circumference = 2πr, hence
Example question
A metallic ball is whiled in a horizontal circle making 5 revolution s per second.Determine:
- Period T
- angular velocity and
- linear speed v