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The moment of inertia depends on how mass is distributed around an axis of rotation, and will vary depending on the chosen axis. For a point-like mass, the moment of inertia about some axis is given by , where is the distance of the point from the axis, and is the mass. For an extended rigid body, the moment of inertia is just the sum of all ...
When Newton's laws are applied to rotating extended bodies, they lead to new quantities that are analogous to those invoked in the original laws. The analogue of mass is the moment of inertia, the counterpart of momentum is angular momentum, and the counterpart of force is torque. Angular momentum is calculated with respect to a reference point ...
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]
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.
r cm is the position vector of the center of mass of the body with respect to the point about which moments are summed, a cm is the linear acceleration of the center of mass of the body, m is the mass of the body, α is the angular acceleration of the body, and; I is the moment of inertia of the body about its center of mass.
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]
The parallel axis theorem, also known as Huygens–Steiner theorem, or just as Steiner's theorem, [1] named after Christiaan Huygens and Jakob Steiner, can be used to determine the moment of inertia or the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of gravity and the perpendicular distance between ...
Rotating unbalance is the uneven distribution of mass around an axis of rotation. A rotating mass, or rotor, is said to be out of balance when its center of mass (inertia axis) is out of alignment with the center of rotation (geometric axis). Unbalance causes a moment which gives the rotor a wobbling movement characteristic of vibration of ...