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Water Accelerometers and Circular Motion

Consider the special path of a circle. The natural coordinates to use with a circle are plane polar coordinates, r and q. These are shown on the circle. Unit vectors are also defined, and , each having magnitude of 1. The points radially outwards from the center, and the points tangentially, in the direction of increasing angle.

If the object stays in a circle, the value of r is constant. Suppose that the object has a speed v and is going around the circle in a counterclockwise direction, write an expression for the velocity using a unit vector.

Experiment: You will stand on a rotating platform and measure the acceleration with a water accelerometer.

Predicting radial acceleration. You will hold the accelerometer in a radial direction, but at two positions, one close to your body, and one at arm's length. The center of the rotation is to the left of the page.

	Near body (prediction)	Arm's Length (prediction)
Center of Circle

Predicting tangential acceleration. You will hold the accelerometer parallel to your body, and consider the case where you rotate at constant speed (moving to the right) and at increasing speed (moving to the right.)

Constant speed (prediction)	Increasing speed (prediction)

Now make measurements.

Radial	Near body (prediction)	Arm's Length (prediction)
Center of Circle

Tangent

Constant speed (prediction)	Increasing speed (prediction)

Summarize the results of your measurements in a couple of sentences.