# Effect of Friction on Ball Rolling Down a Ramp

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This Demonstration shows the translational velocity of a ball, projected in 2D, as it moves down a ramp. There are two limiting cases, one with no friction and one with friction, so there is no slippage of the ball. With friction, there is both translational and rotational kinetic energy as the ball rolls down the ramp. When there is no slippage, the ball slides down the ramp with no rotation.

Contributed by: Athena Hung and Caili Chen (June 2014)
"Special thanks to the University of Illinois NetMath Program and the mathematics department at William Fremd High School."
Open content licensed under CC BY-NC-SA

## Details

Snapshot 1: the initial position of the ball; the velocity at this time is 0

Snapshot 2: after a time, and at a height, the ball has moved down to its current position

Snapshot 3: after the same time, and at the same height, the ball has moved down to its current position; this position is different from the position of snapshot 2

The final velocity of the sliding object is , while the final velocity of the rolling object is , where is the gravitational acceleration, is the height of the ramp, is the mass of the object, is the radius of the object, and is the moment of inertia of the ball, .

This Demonstration was written in Making Math.

## Permanent Citation

Caili Chen

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