Centripetal force is the net inward force that keeps an object moving in a circular path. Even if the object moves at constant speed, its velocity is changing because its direction keeps changing. That change in velocity means the object has an acceleration directed toward the center of the circle.
Understanding centripetal force helps explain turns in cars, spinning rides, satellites, and planets in orbit.
The inward acceleration is called centripetal acceleration, and its size depends on the object's speed and the radius of the path. A faster object or a tighter turn requires a larger inward force. Centripetal force is not a new kind of force, but the name for the net force pointing toward the center, which may come from friction, tension, gravity, or a normal force.
If the inward force disappears, the object moves off tangent to the circle instead of continuing to curve.
Key Facts
- Centripetal acceleration points toward the center of the circle.
- a_c = v^2/r
- F_c = ma_c = mv^2/r
- For circular motion with period T, v = 2πr/T
- Centripetal force is the inward net force, not a separate force added to the free-body diagram.
- At any point in circular motion, velocity is tangent to the path while centripetal acceleration is radial and inward.
Vocabulary
- Centripetal force
- The net force directed toward the center of a circular path that keeps an object moving in a circle.
- Centripetal acceleration
- The inward acceleration of an object in circular motion caused by the continuous change in direction of its velocity.
- Tangential velocity
- The velocity of an object in circular motion directed along the tangent to the circle at that instant.
- Radius
- The distance from the center of the circular path to the moving object.
- Period
- The time required for one complete revolution around a circular path.
Common Mistakes to Avoid
- Pointing centripetal force in the direction of motion is wrong because the force points toward the center while velocity points tangent to the path.
- Treating centripetal force as an extra force is wrong because it is the name for the net inward force produced by real forces such as friction, tension, or gravity.
- Using diameter instead of radius in F_c = mv^2/r is wrong because r must be the distance from the center to the object, not the full width of the circle.
- Assuming constant speed means zero acceleration is wrong because acceleration can come from a change in direction, even when speed stays constant.
Practice Questions
- 1 A 0.50 kg ball moves in a horizontal circle of radius 1.2 m at a speed of 4.0 m/s. Calculate the centripetal acceleration and the centripetal force.
- 2 A 900 kg car travels around a flat curve of radius 60 m at 15 m/s. What inward friction force is required to keep the car moving in the curve?
- 3 A satellite moves in a nearly circular orbit around Earth. Explain why gravity can act as a centripetal force even though the satellite does not fall straight down to Earth.