This is a simulation of a ball experiencing uniform circular motion, which means it travels in a circle at constant speed. Use the sliders to adjust the speed and the radius of the path.

If you show the vectors, you will see the ball's velocity vector, in blue, and its acceleration vector, in green. The velocity vector is always tangent to the circle, and the acceleration vector always points toward the center of the circle.

If the vectors are shown, and the ball has gone about three-quarters of the way around the circle, you will also see a vector triangle. The vector triangle is showing why the ball's acceleration vector points toward the center. We're thinking about which way the acceleration vector points at the bottom of the circle. The purple vector shows the velocity just before the ball reaches the bottom point, so we can consider it to be the initial velocity. The light blue vector shows the velocity just after the ball passes through the bottom point, so we can consider it to be the final velocity. The black vector therefore represents the change in velocity at the bottom point - note that the change in velocity points up, which is toward the center of the circle for that lowest point. The acceleration is proportional to the change in velocity (it is the change in velocity divided by the time it takes the ball to move from the purple point to the light blue point), so the acceleration points in the same direction as the change in velocity - toward the center.

Simulation written by Andrew Duffy, and first posted on 8-09-2017.

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