Which expression correctly defines centripetal force for an object of mass m moving at speed v around a circle of radius r?

Which expression correctly defines centripetal force for an object of mass m moving at speed v around a circle of radius r?

• A. F_c = m v^2 / r
• B. F_c = m v r
• C. F_c = m r^2 / v
• D. F_c = v^2 / r

Answer: (A)

When an object moves in a circle at constant speed, it experiences centripetal acceleration toward the center with magnitude a_c = v^2 / r. By Newton’s second law, the net inward force equals m a_c, so the centripetal force has magnitude F_c = m v^2 / r. This expression correctly combines mass, speed, and radius to give a force that points toward the circle’s center. The other forms don’t match the concept or the units of force: m v r would have the wrong dimensions for force; m r^2 / v also has incorrect units; v^2 / r is an acceleration, not a force.

When an object moves in a circle at constant speed, it experiences centripetal acceleration toward the center with magnitude a_c = v^2 / r. By Newton’s second law, the net inward force equals m a_c, so the centripetal force has magnitude F_c = m v^2 / r. This expression correctly combines mass, speed, and radius to give a force that points toward the circle’s center.

The other forms don’t match the concept or the units of force: m v r would have the wrong dimensions for force; m r^2 / v also has incorrect units; v^2 / r is an acceleration, not a force.