Circular Motion: Why Turning Always Means Accelerating

A definition of acceleration you might not expect

Acceleration is any change in velocity — and velocity includes direction, not just speed. That means an object moving in a perfect circle at a totally constant speed is still accelerating the entire time, because its direction is constantly changing.

Centripetal acceleration

This constant “turning” acceleration is called centripetal acceleration, and it always points toward the center of the circle — never forward, backward, or outward. That might feel backwards if you’ve ever been on a tight turn in a car and felt thrown outward; that sensation is actually your body’s inertia (Newton’s first law) resisting the inward pull, not an actual outward force.

What provides the inward pull

Centripetal acceleration doesn’t come from a special “centripetal force” that exists on its own — it’s provided by whatever force happens to be available in a given situation:

• For a car turning a corner, it’s friction between the tires and the road.
• For the Moon orbiting Earth, it’s gravity.
• For a ball on a string being swung in a circle, it’s tension in the string.

If that inward force suddenly disappeared — the string snaps, the tires lose traction on ice — the object wouldn’t fly outward in a straight line away from the center. It would fly off in a straight line tangent to the circle, in whatever direction it was already moving at that instant.

Why this matters

Circular motion explains everything from why roads are banked on sharp highway curves, to why astronauts experience apparent weightlessness in orbit (they’re in constant freefall toward Earth, just moving sideways fast enough to continually “miss” it), to how a centrifuge separates substances of different densities. Any time something turns, this same idea is at work.

Check your understanding

3 practice questions in the style of AP Physics. Pick an answer to see if you got it, plus a short explanation. Where numbers are needed, use g = 9.81 m/s². These questions were written for this site and are not College Board questions.

1. A ball moves in a horizontal circle at a constant speed. In what direction is its acceleration?

AAlong the circle, in the direction it is movingBAway from the center of the circleCToward the center of the circleDIt has no acceleration, since its speed is constant

2. A ball slides on a smooth, horizontal table in a circle, held by a string. Viewed from above, it moves counterclockwise. When the ball is at the top of the circle, moving to the left, the string breaks. What does the ball do next?

AIt moves straight toward the center.BIt keeps curving along the circle.CIt moves straight away from the center.DIt moves in a straight line to the left.

3. A car goes around a flat curve at speed v. If it goes around the same curve at speed 2v, its centripetal acceleration is

A2 times larger.B4 times larger.Cthe same.Dhalf as large.

Want the real thing? The College Board posts freepast AP Physics 1 exam questions ↗.