Question

A single axis accelerometer is mounted on a rotating wheel so that its measurement axis is along a radius vector which is perpendicular to the wheel’s axis of rotation at a distance, R. The wheel’s rotation axis is tilted at an angle θ from the local vertical direction in a constant gravity field, ?⃗. For example, at θ = 0, the wheel’s rotation axis is aligned with ?⃗ and the accelerometer’s measurement axis is in the local horizontal plane (perpendicular to ?⃗).

(a) Draw a free body diagram for the accelerometer, showing the measurement axis for the accelerometer, ?̈, the tilt angle θ, and the direction of ?⃗.

(b) Using the diagram you developed in part (a), derive an equation for the specific force measured by the accelerometer when the wheel is rotating at constant angular velocity ?0.

(c) The entire apparatus is now placed on a spacecraft in a circular orbit around the Earth and the wheel’s axis is titled with respect to the vertical direction at angle θ. Neglecting any minor perturbation forces, what is the specific force measured by the accelerometer when the wheel is rotating at constant angular velocity ?0? Show your answer by analysis, including any explanations as needed.

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Answer 1

(b) As per the above diagram, we can see that the g vector can be resolved along the axis of measurement and the force due to gravity along the axis of measurement would be, mg sin . So the total force measured by the accelerometer is,

(c) When the entire apparatus is placed on a spacecraft in circular orbit, there would be weightlessness and force due to gravity along the measurement axis will be nullified. So the accelerometer will only be measuring the centripetal force caused due to rotation of the wheel.