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W - watt to work - Mathematics Dictionary

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watt: One watt is defined to be the rate of one joules in one second. Usually represented by the symbol W. It is an SI unit for power - that is, the rate that energy is used with respect to time.

wave: disturbance that propagates through space and time, usually with transference of energy. A mechanical wave is a wave that propagates or travels through a medium due to the restoring forces it produces upon deformation. There also exist waves capable of travelling through a vacuum, including electromagnetic radiation and probably gravitational radiation. Waves travel and transfer energy from one point to another, often with no permanent displacement of the particles of the medium (that is, with little or no associated mass transport); they consist instead of oscillations or vibrations around almost fixed locations.

wavelength: Usually represented by the symbol λ. It is the distance travelled by a mechanical wave in one cycle.

In more abstract terms, it is the length of the minimal interval of domain of a branch of a periodic function that includes one complete cycle of the periodic function. While the idea of waves and wavelength can go beyond periodic functions, the idea is still reliant on how the branch of the function "can" be repeated or can be thought of as repeated.

weight: Symbol: Often represented by the symbol W. The weight of an object is the force applied on other objects directly due to gravity.

The weight of a given object is calculated by multiplying the mass of the object, with the "strength" of the gravity at that place. (it has the unit of N kg-1 - the amount of force due to a certain mass, or equivalently, it has the unit of m s-2 - the acceleration as a result of gravity in the absense of other forces)

It should not be confused with the concept of mass. (intuitively, "the amount of material the object has"; or the more advanced concepts of "the object's 'unwillingless' to accelerate", i.e. inertia.) While mass is an intrinsic property of the object - it's always the same for the same object; weight is extrinsic, it depends on the strength of the gravitational field.

This is why a person has less weight on the moon, not so much because some parts of us are "gone", but because the moon exerts less gravity. While a person, or anything else, would have exactly the same mass on Earth as it has on the moon. (Or anywhere else, for that matter.)

weighted mean: A method for calculating central tendency similar to the calculation of the mean where differnt numbers contribute a varying amount to the overall measure, according to some rule.

For example, we can calculate the "mean" number of students enrolled in a tutorial school over the past 5 years, by giving the recently collected data larger parts towards the value than older data. (As more recent data is likely to be more accurately descriptive of the current situation overall.) See mean.

Wilson's theorem: A theorem that states "if a number n divides (n - 1)! + 1 then it is a prime number" as well as its converse, that "if a number n is a prime number, then it divides (n - 1)! +1".

Wilson's Theorem is usually stated and proved in modulo arithmetics.

work: Symbol: W. For a simple case, with a force that remains constant and movement in the same direction as the force, it is the product of the magnitude of the force and the distance travelled "due to the force". In vector form, work is the scalar product of force and displacement vector. And in the case of a variable force, it is the integral (i.e. "infinite sum of the infinitely small") of their product.

It can be thought of intuitively as the amount of energy "used" due to a force. Although since energy is never "destroyed", the energy "used" is actually simply "transferred" elsewhere. As such, if a force "does nothing", then no work is done, since no object "gained" energy because of the force.

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