Final answer:
The period in uniform circular motion is equal to the ratio of the circumference to the speed. It is calculated by dividing the circumference of the circular path by the tangential or average speed of the object in motion.
Step-by-step explanation:
In uniform circular motion, the period (T) is defined as the time required for one complete rotation. To find the value equal to the period in terms of speed and dimensions of the circular path, one must understand the relationship between tangential speed, circumference, and period. The correct expression for the period is the ratio of the circumference to the speed. This relationship is derived from the fact that the tangential speed or average speed (u) is equal to the circumference (C) divided by the period (T). Therefore, if we rearrange the equation, we get T = C / u, confirming that the period is the ratio of the circumference to the speed.
When learning about circular motion in physics, one might also come across terms like 'radius of curvature' which is simply the radius (r) of the circular path, and it's important to distinguish this from other circular measurements like the circumference.