Circular motion does not require a special new interaction. Instead, familiar forces such as gravity, tension, normal force, or friction combine so that their net effect continually points inward.

Circular motion and real forces

When an object moves in a circle, its velocity is constantly changing direction.

The velocity vector $\vec{v}$ is tangent to the circular path, while the centripetal acceleration $\vec{a}_c$ points radially inward toward the center. This geometry is the kinematic reason the net force must have an inward (radial) component during circular motion. Source

That change in direction requires an inward net force. In AP Physics C, the key idea is that the phrase centripetal force does not name a new physical force. It describes the role played by whatever real forces point toward the center.

A common mistake is to draw a separate force labeled “centripetal force” on a free-body diagram. Do not do this. A free-body diagram should contain only real interactions such as weight, tension, normal force, or friction. After those forces are identified, their inward sum is what provides the centripetal force.

The radial force condition

For motion along a circular path of radius $r$ and speed $v$, the net force in the radial direction must match the force required to keep the object turning toward the center.

This equation is not an additional force law. It is Newton’s second law applied specifically in the direction toward the center. The left side must come from actual forces or actual force components.

Only the part of a force that points toward the center contributes to circular motion. If a force is angled, it must be resolved into components, and only its radial component belongs in the centripetal-force equation.

The acceleration of circular motion can be decomposed into a radial component (centripetal) and a tangential component that changes the speed. This decomposition clarifies why only the radial components of real forces appear in $F_{net,r}=mv^2/r$, while tangential components govern speeding up or slowing down. Source

How forces produce circular motion

One force can provide all of it

Sometimes a single real force supplies the entire inward force. For example, tension may be the only force directed toward the center for an object moving in a horizontal circle on a string. In that case, the tension itself is the centripetal force.

This means the analysis is simple: identify the one inward force and set it equal to $mv^2/r$.

Several forces can work together

In other situations, more than one force points inward. Then the inward forces add to produce the required net radial force. If one inward force is large and another is smaller, both still matter because the motion depends on their vector sum.

For AP problems, always ask: which forces have components toward the center at that instant?

A component of a force may matter

A force does not need to point exactly at the center to help produce circular motion. A force at an angle can still contribute through one of its components. This is why choosing axes carefully is so useful. If one axis is taken along the radial direction, the part of the force responsible for circular motion becomes easier to isolate.

Setting up circular-motion force equations

A reliable method is:

• Draw a free-body diagram with only real forces.

• Mark the direction toward the center.

• Choose that direction as the radial axis.

• Resolve angled forces into components if needed.

• Add all radial components algebraically.

• Set the radial net force equal to $mv^2/r$.

The sign of each term depends on your coordinate choice. If inward is positive, inward force components are positive and outward ones are negative. The physics stays the same as long as the signs are used consistently.

The top of a vertical loop

At the top of a vertical loop, the center of the circle is directly below the object, so the inward direction is downward. That makes this position especially important, because gravity already points toward the center there.

If the object is on the inside of a track at the top, the radial forces are typically weight and normal force, both downward when contact exists. The radial equation is therefore based on the sum of those downward forces. If the object is attached to a string, the forces at the top may be weight and tension, again both directed toward the center when the string is taut.

The important limiting case is the instant when the object is just about to lose contact with the track, or the string is just about to go slack. At that threshold, the contact force or tension becomes zero. The only remaining inward force is gravity.

From this condition, $v_{min}=\sqrt{gr}$. This result shows that the minimum top speed depends only on the loop radius and gravitational field strength.

If the object’s speed at the top is smaller than this value, gravity alone would be too much to match the required circular-motion condition without a force in the opposite direction. Since a track cannot pull the object toward itself from the inside and a loose string cannot push, contact is lost. The object then stops following the circular path.

This is why the phrase “gravity alone provides centripetal force” identifies the exact boundary between maintaining circular motion at the top and losing contact there.