The first gyroscope was invented in 1852 by Leon Foucault (a traditional mechanical gyroscope of this general type is shown in Fig 1). Foucault thought that he could measure the rotation of the earth by using a rotating object that would stay in a fixed position, even as the earth rotated. He would have been correct in theory; however, he could only get an object rotating for a few minutes, which was not enough time to see significant movement of the earth. With the invention of the electric motor, however, gyroscopes suddenly became feasible, as the motors could get an object to rotate indefinitely. This led to the development of the gyrocompass, which was quickly used on ships and airplanes.

Advances in micro-electromechanical systems (MEMS) technology have allowed manufacturers to create complete gyroscope apparatuses on micro-scale chips. Not only that, but MEMS gyroscopes are getting cheaper and smaller with each passing year. These advances in technology and decreases in price are allowing integrated MEMS gyroscopes to be practically used to great effect in many applications.

Although traditional gyroscopes were meant to measure angular displacements, the MEMS gyroscopes of today are used to measure angular speed in degrees per second. A traditional gyroscope, like the one shown in Fig 1, operates based upon the property of angular inertia. This property is observed when a rotating object, like a spinning top, has a strong inertia to directional changes in its rotation axis.

1. Traditional mechanical gyroscope.

This is the same phenomenon that allows us to ride bicycles. The disk in the middle of the apparatus in Fig 1 is rotated at high speeds. This rotation causes the disk to have a great amount of inertia. Therefore, as the apparatus rotates, the disk in the middle will stay in the same angular position. Therefore, changes in angle between the circular hoops and the stationary rotating disk can easily be measured. The rotating portion of a gyroscope can also be effectively used to keep an angular orientation, making gyroscopes very effective for use in compasses.

MEMS gyroscopes
MEMS gyroscopes are even more useful than the traditional forms, given that they typically measure angular velocity rather than angular displacement. Angular velocity measurements are more useful, as they can be integrated over time to give indirect measurements of angular displacement as well as velocity.

There are a variety of techniques employed to be able to sense angular velocity with a MEMS gyroscope. One thing they all typically have in common is that they use a vibrating mass rather than a rotating mass. A vibrating mass resists changes to its axis of vibration, even as the structure it is attached to rotates. Therefore, similar detection of rotation can be achieved by using vibrations instead of full rotations. The latter would be more difficult to achieve in a MEMS device.

The physical phenomenon behind MEMS gyroscopes is the Coriolis Effect. This phenomenon occurs when an object moves in a linear direction inside a rotating reference frame. Please refer to Fig 2. Imagine that you are standing on a spinning merry-go-round at the position marked by t1. If you decide to walk in a straight line towards the outer edge, you will experience the Coriolis Effect.

From physics, we know that any point on the merry-go-round will have an instantaneous velocity of Ωr, where Ω is the rotational velocity and r is the radius at the point on the merry-go-round. Hence each blue velocity vector in Fig 2 has a magnitude of Ωr, and it is the same tangential velocity that you would have if you were standing at any of those points. The constant red velocity vectors show the radial velocity with which you would be walking towards the outside edge. As you approach the outside edge, your tangential velocity would increase. This provides half of the acceleration from the Coriolis Effect, which is equal to Ωv, where v is the radial velocity.

2. Velocity and acceleration vectors present in the Coriolis Effect.
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The second portion of Coriolis acceleration comes from the green acceleration vectors. If you look at the red velocity vectors at t1 and t2, you will notice that their magnitudes are the same, but their directions are different. This directional change in the velocity vector means tangential acceleration in the direction of the green vectors must be present. This acceleration is the second half of the Coriolis acceleration, which also happens to be equal to Ωv. Therefore, if you add the two separate acceleration vectors together, you will have 2Ωv. If you have mass m, this acceleration will exhibit a force on you of 2Ωvm. This force on you will create a reactionary force on the merry-go-round equal in magnitude, but in the opposite direction, for a force of –2Ωvm. Since it is negative this force will be in the opposite direction of the rotation.

If you were to walk back to the center of the merry-go-round, all of the math stays exactly the same, except that the red velocity vectors will now point inward, giving them the opposite sign. Therefore, the final equation for your reaction force will be –2Ω(–v)m, or 2Ωvm. So the magnitude of your reaction force on the merry-go-round will stay the same, but it will now be in the same direction as the rotation if you are traveling inward.