Circular Motion

Things are moving with circular motion or demonstrating cyclical behaviour all around us. The Earth circles the Sun, the Moon circles the Earth. From the wheels on the cars we ride in, to the way we eat, sleep, and play every day, circles and cycles are everywhere.

In physics, we describe uniform circular motion with the period, or the time it takes to make one revolution around the circle. Then if we know the circumference of the circle, we can determine the angular velocity in degrees or radians per second.

w = 360°/T (for degree/seconds)


w = 2π/T (for radians/seconds)

The speed is distance / time or

s = C/T (meters/second) where C = 2πR, and R is the radius of the circle.

For an object to go in a circle and not fly off in a straight line, there has to be a centripetal acceleration toward the center of the circle, and it is given by

a = 2πs/T = w2R (meters/second 2)

If we know that the acceleration downward due to gravity is -9.8 m/s2, and we have a bucket of water swinging on a rope that is 1 meter in length, then what would be the period with which we would swing the bucket around so that the water doesn't fall out of the bucket? (In other words, there is at least a 9.8 m/s2 centripetal acceleration of the bucket.)

Bucket of water swinging on a rope

For the answer, you can use the interactive diagram at the top of the page, and set the radius R to 1, and then try different angular velocities w until the acceleration a is at least 9.8 m/s2.

Subject Index for all interactive diagrams - Physics - Kinamatics - Circular Motion

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