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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 ().
One radian is defined as the angle at the center of a circle in a plane that subtends an arc whose length equals the radius of the circle. [6] More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, =, where θ is the magnitude in radians of the subtended angle, s is arc length, and r is radius.
tan −1 y = tan −1 (x), sometimes interpreted as arctan(x) or arctangent of x, the compositional inverse of the trigonometric function tangent (see below for ambiguity) tan −1 x = tan −1 (x), sometimes interpreted as (tan(x)) −1 = 1 / tan(x) = cot(x) or cotangent of x, the multiplicative inverse (or reciprocal) of the ...
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
Additionally, an angle that is a rational multiple of radians is constructible if and only if, when it is expressed as / radians, where a and b are relatively prime integers, the prime factorization of the denominator, b, is the product of some power of two and any number of distinct Fermat primes (a Fermat prime is a prime number one greater ...
In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph.If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia.
A point mass does not have a moment of inertia around its own axis, but using the parallel axis theorem a moment of inertia around a distant axis of rotation is achieved. Two point masses, m 1 and m 2 , with reduced mass μ and separated by a distance x , about an axis passing through the center of mass of the system and perpendicular to the ...
Its SI unit is the radian per second per tesla (rad⋅s −1 ⋅T −1) or, equivalently, the coulomb per kilogram (C⋅kg −1). [citation needed] The term "gyromagnetic ratio" is often used [2] as a synonym for a different but closely related quantity, the g-factor. The g-factor only differs from the gyromagnetic ratio in being dimensionless.