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.
Understanding Physics: Centripetal Force
Circular motion is a useful example of why speed alone does not describe motion fully. A runner moving around a track can keep the same speed on the stopwatch while continually changing the direction of travel. In each short moment, the velocity points along the track.
A moment later, it points in a slightly different direction. The combined effect of many small direction changes produces an acceleration toward the middle.
This is why a force can change motion without making an object speed up or slow down. The force acts sideways relative to the instant-by-instant motion.
The physical source of the inward force depends on the situation. When a ball is swung on a string, the string pulls the ball inward through tension. When a car turns on a flat road, static friction between the tyres and road supplies the needed force.
Static friction means the tyre grips without sliding across the road. If the road is icy, the available friction may be too small, so the car cannot follow the intended curve. On a roller coaster loop, the track pushes on the car through a normal force.
For an orbiting Moon or satellite, gravity provides the inward pull. A free body diagram should show these real forces first. The inward net result is found by adding their radial components.
Vertical circles show that the required inward net force is not always supplied by one force alone. At the bottom of a loop, both the track force and gravity can point toward the center, depending on the object. At the top, gravity points toward the center while the track force may point there too, or may become zero if contact is just about to be lost.
A rider may feel pressed into a seat at the bottom because the seat must push strongly upward. This feeling is not an outward force pulling the rider away from the center.
The apparent outward effect is inertia. The body tends to continue in its current straight-line direction while the seat, string, road, or gravity changes that direction.
When solving problems, first mark the center of the path and choose inward as a direction. Then draw every real force with its direction. Decide which components point inward and which point outward.
Their net inward amount must equal mass times speed squared divided by radius. Units help catch mistakes. Mass is measured in kilograms, speed in metres per second, radius in metres, and force in newtons.
Notice the square on speed. Doubling speed requires four times the inward force for the same radius.
Doubling the radius halves the required force at the same speed. These relationships explain why sharp turns need low speeds and why road curves are often made wider or banked.
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.