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The moments of inertia of a mass have units of dimension ML 2 ([mass] × [length] 2). It should not be confused with the second moment of area, which has units of dimension L 4 ([length] 4) and is used in beam calculations. The mass moment of inertia is often also known as the rotational inertia, and sometimes as the angular mass.
Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
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]
A list of moments of inertia formulas for standard body shapes provides a way to obtain the moment of inertia of a complex body as an assembly of simpler shaped bodies. The parallel axis theorem is used to shift the reference point of the individual bodies to the reference point of the assembly.
With respect to a coordinate frame whose origin coincides with the body's center of mass for τ() and an inertial frame of reference for F(), they can be expressed in matrix form as:
An arbitrary shape. ρ is the distance to the element dA, with projections x and y on the x and y axes.. The second moment of area for an arbitrary shape R with respect to an arbitrary axis ′ (′ axis is not drawn in the adjacent image; is an axis coplanar with x and y axes and is perpendicular to the line segment) is defined as ′ = where
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Examples of fictitious forces are the centrifugal force and the Coriolis force in rotating reference frames. To apply the Newtonian definition of an inertial frame, the understanding of separation between "fictitious" forces and "real" forces must be made clear. For example, consider a stationary object in an inertial frame.