Centripetal Force: How F = mv²/r Controls Circular Motion

Centripetal Force & Circular Motion Interactive Simulation 

This interactive physics simulation helps students visualize the mechanics of uniform circular motion.

1. Understand the Math: See how changing speed (v), radius (r), and mass (m) directly impacts the required net force (F = mv²/r) on a live parabolic graph.
2. Real-World Scenarios: Apply the math to physical examples, including string tension, road friction, and gravitational orbits.
3. Visualize Inertia: Use the "Cut the Force" tool to instantly remove the centripetal force, proving that objects will travel in a straight line along the tangent (Newton's First Law) rather than flying directly outward

Is centripetal force a new force, and what does it depend on?

In short: Centripetal force is not a separate force. It is the name for the net force toward the center that keeps an object on a circle. Even at a steady speed the velocity keeps turning, so there is an acceleration a = v²/r pointing at the center, and Fnet = mv²/r. That inward pull is supplied by real forces such as tension, friction on tires or gravity.

Common doubts

• “Should I add a centripetal force to the free-body diagram?” No. Draw only the real forces. The centripetal force is their net toward the center, not an extra arrow.
• “What happens if the inward force disappears?” The object does not fly outward. It continues in a straight line along the path it was following at that instant.
• “What if I double the speed or the radius?” Doubling v makes the required force four times as large, doubling r halves it, and doubling m doubles it.

Change the speed, radius and mass in the simulation above, or press CUT THE FORCE, and watch the required net force respond.

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