Centripetal force is given by F_c = m v^2 / R. If the speed v increases, how does F_c change?

Centripetal force is given by F_c = m v^2 / R. If the speed v increases, how does F_c change?

• A. Increases linearly with v
• B. Increases with v^2
• C. Independent of v
• D. Decreases with v^2

Answer: (B)

In circular motion, the inward (centripetal) force that keeps an object moving along a circle is tied directly to how quickly it’s going and how tightly it’s curved. The centripetal force is F_c = m v^2 / R. Here, mass m and radius R are held constant, so the only changing factor is speed v. Because v is squared, the force grows with the square of the speed. If you double the speed, the centripetal force becomes four times larger; triple the speed, and the force becomes nine times larger. For a concrete example, with m = 2 kg and R = 4 m: - At v = 3 m/s, F_c = 2*(3^2)/4 = 4.5 N. - At v = 6 m/s, F_c = 2*(6^2)/4 = 18 N. This shows the quadratic dependence on speed. So increasing speed increases the centripetal force, and the increase follows v^2, not a linear relationship.

In circular motion, the inward (centripetal) force that keeps an object moving along a circle is tied directly to how quickly it’s going and how tightly it’s curved. The centripetal force is F_c = m v^2 / R. Here, mass m and radius R are held constant, so the only changing factor is speed v. Because v is squared, the force grows with the square of the speed. If you double the speed, the centripetal force becomes four times larger; triple the speed, and the force becomes nine times larger.

For a concrete example, with m = 2 kg and R = 4 m:

• At v = 3 m/s, F_c = 2*(3^2)/4 = 4.5 N.

• At v = 6 m/s, F_c = 2*(6^2)/4 = 18 N.

This shows the quadratic dependence on speed.

So increasing speed increases the centripetal force, and the increase follows v^2, not a linear relationship.