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# Other Units in Physics Help

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By McGraw-Hill Professional
Updated on Aug 29, 2011

## Introduction to Other Units in Physics

The preceding seven units can be combined in various ways, usually as products and ratios, to generate many other units. Sometimes these derived units are expressed in terms of the base units, although such expressions can be confusing (for example, seconds cubed or kilograms to the –1 power). If you see combinations of units in a physics book, article, or paper that don’t seem to make sense, don’t be alarmed. You are looking at a derived unit that has been put down in terms of base units.

The standard unit of plane angular measure is the radian (rad). It is the angle subtended by an arc on a circle whose length, as measured on the circle, is equal to the radius of the circle as measured on a flat geometric plane containing the circle. Imagine taking a string and running it out from the center of a circle to some point on the edge and then laying that string down around the periphery of the circle. The resulting angle is 1 rad. Another definition goes like this: One radian is the angle between the two straight edges of a slice of pie whose straight and curved edges all have the same length r (Fig. 6-4). It is equal to about 57.2958 angular degrees .

Fig. 6-4 . One radian is the angle at the apex of a slice of pie whose straight and curved edges all have the same length r .

## The Angular Degree

The angular degree, symbolized by a little elevated circle (°) or by the three-letter abbreviation deg, is equal to 1/360 of a complete circle. The history of the degree is uncertain, although one theory says that ancient mathematicians chose it because it represents approximately the number of days in the year. One angular degree is equal to approximately 0.0174533 radians.

The standard unit of solid angular measure is the steradian , symbolized sr. A solid angle of 1 sr is represented by a cone with its apex at the center of a sphere and intersecting the surface of the sphere in a circle such that, within the circle, the enclosed area on the sphere is equal to the square of the radius of the sphere. There are 4π, or approximately 12.56636, steradians in a complete sphere.

## The Newton

The standard unit of mechanical force is the newton , symbolized N. One newton is the amount of force that it takes to make a mass of 1 kg accelerate at a rate of one meter per second squared (1 m/s 2 ). Jet or rocket engine propulsion is measured in newtons. Force is equal to the product of mass and acceleration; reduced to base units in SI, newtons are equivalent to kilogram-meters per second squared (kg · m/s 2 ).

## The Joule

The standard unit of energy is the joule , symbolized J. This is a fairly small unit in real-world terms. One joule is the equivalent of a newton-meter (n · m). If reduced to base units in SI, the joule can be expressed in terms of unit mass multiplied by unit distance squared per unit time squared:

1 J = 1 kg · m 2 /s 2

## The Watt

The standard unit of power is the watt , symbolized W. One watt is equivalent to one joule of energy expended for one second of time (1 J/s). In fact, power is a measure of the rate at which energy is produced, radiated, or consumed. The expression of watts in terms of SI base units begins to get esoteric, as you have been warned:

1 W = 1 kg · m 2 /s 3

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