Imagine slinging a stone tied to a string around your head at a constant velocity. As it whirls around your head, the stone moves with a uniform circular motion. It continually changes direction, while at the same time not changing its speed. In uniform circular motion, you know that there is constant centripetal acceleration. Centripetal means "center seeking", so the centripetal acceleration always points towards the center of the circle. You can use the concepts of uniform circular motion in problem solving as well.
Uniform Circular Motion
\(\large\mathsf{ T = \frac{1}{f} }\)
\(\large\mathsf{ f = \frac{1}{T} }\)
\(\large\mathsf{ v_c = \frac{C}{T} = \frac{\pi \times 2r}{T} }\)
\(\large\mathsf{ a_c = \frac{v^2}{r} }\)
You have seen and practiced using these equations in problem solving to help you solve for period, frequency, and velocity of an object in uniform circular motion. Now, let's turn our attention to the forces involved with the motion. Newton's First Law helps us explain what is happening in terms of the forces on an object that undergoes uniform circular motion.
Question
Do you remember what Newton's First Law states?
Newton's First Law states that an object will resist a change in its motion unless an unbalanced force acts on it.
Because of Newton's First Law, we can assume there is also a force causing the acceleration. Since the acceleration is towards the center of the circle, the force will be also. We call this the centripetal force or the "center seeking" force.
