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Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics, and described by Isaac Newton in his first law of motion (also known as The Principle of Inertia). [1]
In this case, the moment of inertia of the mass in this system is a scalar known as the polar moment of inertia. The definition of the polar moment of inertia can be obtained by considering momentum, kinetic energy and Newton's laws for the planar movement of a rigid system of particles. [15] [18] [25] [26]
Newton's second law is sometimes presented as a definition of force, i.e., a force is that which exists when an inertial observer sees a body accelerating. In order for this to be more than a tautology — acceleration implies force, force implies acceleration — some other statement about force must also be made.
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Sylvester's law of inertia states that the number of coefficients of a given sign is an invariant of , i.e., does not depend on a particular choice of diagonalizing basis. Expressed geometrically, the law of inertia says that all maximal subspaces on which the restriction of the quadratic form is positive definite (respectively, negative ...
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In an inertial frame of reference (subscripted "in"), Euler's second law states that the time derivative of the angular momentum L equals the applied torque: = For point particles such that the internal forces are central forces, this may be derived using Newton's second law.