To calculate the velocity of an object undergoing uniform circular motion with a constant radius and period, you can use the formula for the circumference of a circle.
The formula for the circumference of a circle is given by:
C = 2πr,
where C represents the circumference and r represents the radius of the circle.
In uniform circular motion, the object travels the circumference of the circle in one period (T). Therefore, the distance traveled by the object in one period is equal to the circumference of the circle.
Now, velocity is defined as the distance traveled per unit time. In the case of uniform circular motion, the velocity of the object is tangential to the circle and can be calculated by dividing the distance traveled in one period by the duration of the period.
So, the velocity (v) of an object undergoing uniform circular motion with a constant radius (r) and period (T) can be calculated as:
v = (2πr) / T.
This formula gives you the velocity of the object in terms of the radius and period of its circular motion.