Rigid Body
A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.
Rigid Body Dynamics
Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).
Three identical point masses of mass M are fixed at the corners of an equilateral triangle of sides l as shown. Axis A runs through a point equidistant from all three masses, perpendicular to the plane of the triangle. Axis B runs through M1 and is perpendicular to the plane of the triangle. Axes C, D, and E, lie in the plane of the triangle and are as shown.
a)Determine an expression in terms of M and l for the moment of inertia of the masses about Axis A.
b)Determine an expression in terms of M and l for the moment of inertia of the masses about Axis A.
c)Determine an expression for the moment of inertia of the masses about Axis D in terms of M and l. Axis D is parallel to the base of the triangle.
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