SIMPLIFIED: "2.10: Centripetal Force"

Link: https://phys.libretexts.org/Bookshelves/Conceptual_Physics/Introduction_to_Physics_(Park)/02%3A_Mechanics_I_-_Motion_and_Forces/02%3A_Dynamics/2.10%3A_Centripetal_Force 

Note: The above image is from the original article.

The article linked above talks about centripetal force. Centripetal force is different from just a “force”, because centripetal force is any force that keeps an object moving in circular motion. The centripetal force for any object will ALWAYS point towards the center of the circle. If the centripetal force did not point towards the center of the circle, the object would no longer be moving in a circular path. The mathematical equation for centripetal force is this: 

F_c = (m times v²)/r. F_c represents centripetal force, m represents the mass of the object, v represents the velocity of the object, and r represents the radius of the circle that the object is moving in. Since this centripetal force is the force that is required to keep an object moving in a circle, increasing the velocity or mass of the object will require MORE centripetal force to keep it moving in a circular path. However, increasing the radius of the circular path will decrease the amount of centripetal force you need to keep the object moving in a circular path because radius is the variable in the denominator of the equation. 

You might know Newton’s second law, which states that F = ma. When studying circular motion, an object moving in a circular path has an acceleration of v²/r. Therefore, if you plug that acceleration into F = ma, you will get the centripetal force equation that I wrote in the first paragraph. Here is a real world example of centripetal force: you can tie a string to a ball and swing the ball in a circle. If you were to cut the string, the ball would start flying in a straight line in some direction. This is because of inertia: the ball naturally doesn’t want to change its direction, so unless the centripetal force is acting on it, it won’t move in a circular path.