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The angular momentum of m is proportional to the perpendicular component v ⊥ of the velocity, or equivalently, to the perpendicular distance r ⊥ from the origin. Angular momentum is a vector quantity (more precisely, a pseudovector) that represents the product of a body's rotational inertia and rotational velocity (in radians/sec) about a ...
The moment of inertia I is also defined as the ratio of the net angular momentum L of a system to its angular velocity ω around a principal axis, [8] [9] that is =. If the angular momentum of a system is constant, then as the moment of inertia gets smaller, the angular velocity must increase.
A diagram of angular momentum. Showing angular velocity (Scalar) and radius. In physics, angular mechanics is a field of mechanics which studies rotational movement. It studies things such as angular momentum, angular velocity, and torque. It also studies more advanced things such as Coriolis force [1] and Angular aerodynamics.
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 ...
A set of 180° rotations carries any orientation of one torus into an orientation of the other with the opposite point aligned with the angular momentum vector. If the angular momentum is exactly aligned with a principal axes, the torus degenerates into a single loop. If exactly two moments of inertia are equal (a so-called symmetric body ...
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.
The moment of force, or torque, is a first moment: =, or, more generally, .; Similarly, angular momentum is the 1st moment of momentum: =.Momentum itself is not a moment.; The electric dipole moment is also a 1st moment: = for two opposite point charges or () for a distributed charge with charge density ().
Angular momentum is the product of moment of inertia and angular velocity: =, just as p = mv in linear dynamics. The analog of linear momentum in rotational motion is angular momentum. The greater the angular momentum of the spinning object such as a top, the greater its tendency to continue to spin.