How to Use Accelerometers to Measure the Angular Velocity

Mount the accelerometer to its measurement axis is on a radius from the center of rotation. That is, if you are measuring the angular velocity of a merry-go-̵7;round, you will place the accelerometer so its measurement axis is along a line from the center to the edge of the platform.

Measure the distance from the center of rotation to the accelerometer. For example, you might put the accelerometer 2.5 meters from the center of a merry-go-̵7;round.

Record the acceleration measured by the accelerometer. Typically, the voltage will be converted to units of ̶0;g,̶1; the acceleration due to gravity at the Earth̵7;s surface. For example, your accelerometer on the merry-go-̵7;round could measure 0.35 g.

Multiply the reading from the previous step by 9.8 to convert the accelerometer reading to standard units. For consistency with good scientific practice, you̵7;re changing it to units of meters per second-squared. Specifically, one g is 9.8 meters/sec^2. For the example, 0.35 g = 0.35 x 9.8 = 3.4 meters/sec^2.

Take the square root of the product of the acceleration times the radius to calculate the instantaneous linear velocity. At the instant of the measurement, the accelerometer is moving perpendicular to the radius connecting it to the center of rotation. The relation between the linear velocity and the measured acceleration is given by v = sqrt (acceleration x radius). For the example problem, this is v = sqrt (3.4 x 2.5) = 2.9 meters/sec.

Divide the instantaneous linear velocity by the radius at which the accelerometer is mounted to convert the linear velocity to angular velocity. The angular velocity measures the rotation rate, in radians per second, and it̵7;s given by omega = v/radius. For the example, this is omega = 2.9 / 2.5 = 1.2 per second, which is about 69 degrees per second, or one full rotation in about five seconds -- a pretty fast merry-go-̵7;round.