Search results
Results from the WOW.Com Content Network
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 ...
In mathematics and physics, the right-hand rule is a convention and a mnemonic, utilized to define the orientation of axes in three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish the direction of the force on a current-carrying conductor in a magnetic field.
The angular momentum of the very large number of charged particles that make up a current therefore is: = (), where ρ is the mass density of the moving particles. By convention the direction of the cross product is given by the right-hand rule .
The fundamental equation describing the behavior of a rotating solid body is Euler's equation of motion: = = + = + = + where the pseudovectors τ and L are, respectively, the torques on the body and its angular momentum, the scalar I is its moment of inertia, the vector ω is its angular velocity, the vector α is its angular acceleration, D is ...
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 ().
Then the angular position of that point is the angle θ from a reference axis (typically the positive x-axis) to the vector r ⊥ (t) in a known rotation sense (typically given by the right-hand rule). Angular velocity: the angular velocity ω is the rate at which the angular position θ changes with respect to time t: = The angular velocity is ...
Angular momentum; Couple; D'Alembert's principle ... the formulation of correct equations of motion in a ... along the axis of rotation according to the right-hand rule.
The direction of the torque can be determined by using the right hand grip rule: if the fingers of the right hand are curled from the direction of the lever arm to the direction of the force, then the thumb points in the direction of the torque. [8]