Centripetal force ($F_c$) is the force that keeps an object moving in a circle. This force is connected to the mass of the object ($m$) and how fast it’s moving in a straight line ($v$). We can describe this relationship with an easy formula:

$F_c = \frac{mv^2}{r}$

In this formula, $r$ stands for the distance from the center of the circle to the object.

Important Points to Remember:

• Mass Impact: If you double the mass of the object, the centripetal force also doubles, as long as the speed and radius stay the same.

• Speed Impact: When the speed goes up by 50% (like moving from 10 meters per second to 15 meters per second), the centripetal force increases by about 2.25 times. This shows just how important speed is!

• Radius Impact: If the radius ($r$) gets smaller, the centripetal force goes up for the same mass and speed. This means we need to apply more force to keep the object moving in a circle.

Centripetal force is essential for things like cars going around curves or planets circling the sun. Understanding how mass, speed, and radius affect this force helps us see how objects behave in circular motion.