What Determines the Direction of Centripetal Force and Acceleration?

AI Thread Summary
Centripetal force and acceleration always act towards the center of the circular path. To maintain an object in circular motion, a force must be applied inward, counteracting the object's inertia that would otherwise cause it to move outward. The equations for centripetal force (mv^2/r) and centripetal acceleration (v^2/r) reinforce that both quantities are directed towards the center of the circle. This inward direction is essential for keeping the object in a stable circular trajectory. Understanding this concept is crucial for solving problems related to circular motion.
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Homework Statement


How do I find the direction of the centripetal force and acceleration?


Homework Equations


mv^2/r - centripetal force
v^2/r - centripetal acceleration

The Attempt at a Solution


Would it be inward or outward the radius?
 
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Think of this: If you wanted to keep a ball rolling in a circular path, which way would you push it (once it has started moving)? Towards the center or away from it?
 
So that would be the same for both acceleration and force?
 
Yes, because F=ma, where F and a are vectors and m is a (positive) scalar.
 

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