Centripetal Force
Inward force needed for circular motion.
Formula
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Example
Keeps a car on a curve
How it works
When an object moves in a circle, its velocity is constantly changing direction, so it must have an acceleration toward the center of the circle. Newton’s second law then says a net inward force is required, and that force depends on how much mass is moving, how fast it is moving, and how tight the circle is. The formula F = mv²/r shows that faster motion needs much more force because speed is squared, and smaller radii need more force because the path curves more sharply.
When to use it
Use this formula whenever something is moving in circular or curved motion and you want the required inward net force, such as a satellite in orbit, a stone on a string, or a rider on a rotating ride. It is especially useful when mass, speed, and radius are known and you need the centripetal force.
Worked example, step by step
A 0.50 kg ball is tied to a string and swung in a circle of radius 1.2 m at a speed of 4.0 m/s. F = mv² / r F = (0.50 × 4.0²) / 1.2 F = (0.50 × 16) / 1.2 F = 8.0 / 1.2 F = 6.67 N Final answer: The centripetal force is about 6.7 N toward the center.
Common mistakes to avoid
- using the outward "centrifugal force" instead of the inward net force
- forgetting to square the speed in v²
- mixing up the radius with the diameter or using the wrong units
Did You Know?
The force that keeps you in a curving car seat points inward, toward the centre — there is no real outward force.
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