Centripetal Force

Overview

This lesson explains why an object moving at constant speed in a circle is still accelerating. Its velocity is always changing direction, so the resultant force must act towards the centre of the circle.

What You Need to Know

• Centripetal means “towards the centre”; it describes the direction of the acceleration and resultant force.
• The velocity is tangential, but the acceleration and resultant force are radial.
• The acceleration equations are a = r omega^2 and a = v^2 / r.
• The force equations are F = mr omega^2 and F = mv^2 / r.

How to Work Through It

1. Draw force and velocity arrows for an object at several points around a circle.
2. Use the acceleration equations before adding mass to calculate force.
3. Practise choosing between the v-form and omega-form of each equation.
4. Explain the physical source of the centripetal force in each example.

Check Your Understanding

• Why can an object accelerate while its speed stays constant?
• In a force diagram, which arrow points towards the centre?
• Which equation is most direct when the question gives radius and period?

Common Mistakes

• Treating centripetal force as an extra force instead of the resultant force towards the centre.
• Drawing the force in the direction of motion rather than perpendicular to the motion.
• Forgetting to square v or omega in the acceleration and force equations.

Next Steps

• Rework any calculation where the direction of force or acceleration was unclear.
• Prepare to apply this model to physical situations such as strings, tracks, and circular orbits.