6.Bl APPENDIX VI.B: THE GYROSCOPE The basic parameter of a gyroscope is its angular momentum !!_, a vector quantity along the spin axis, whose direction is determined by the right-hand rotation rule. Its magnitude His the product of the moment of inertia of the gyroscope about its spin axis and its angular velocity. The moment of inertia I is a measure of the geometric distribution of mass in a body relative to an axis, and is defined by: (6 .Bl) where IX is the moment of inertia about the x-axis; dm is a differential element of mass; 1 is the perpendicular distance from the x-axis to the element dm. The integral is taken over the entire mass of the body. Defining the z-axis as the ·spin axis of the gyro (positive-z by the right-hand rotation rule), we have: (Hin kg-m 2 /sec) = (Iz in kg-m 2 ) (win radians/sec) (6 .Bl) A fundamental property of a gyroscope is that, in the absence of applied torques, it maintains the angular orientation of its spin axis fixed relative to an inertial frame of reference. However, this property does not affect the gyro's response to a force applied through its center of mass. That force will cause the gyro to accelerate in the direction of the applied force according to the traditional: (Force applied) = (Mass of gyroscope) (acceleration caused by force) In particular, a gyro under gravitational forces only (which always apply themselves through the center of mass) will behave like a nonrotating body. For example, it will move about LS and
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