Phy 201
I have been working the problem sets and have noticed that the x and y components have different units; pounds, miles, meters, etc.I assume that as long as the same units are used throughout the problem that the x and y components can be assigned any reasonable unit, and that the angle will always be in degrees. Is this assumtion correct?
Since cos(theta) and sin(theta) are unitless numbers, R cos(theta) and R sin(theta) will always have the units of R, whatever R happens to represent (e.g., miles, pounds, meters, m/s, or whatever).
The x and y components will therefore be in the same units, and whatever units those are, they will be the units of the resultant.
The arcTan, or inverse tangent, can be applied only to a unitless number. If the x and the y components are in the same units, then the units of Rx and Ry will be the same. In this case Ry / Rx will be unitless (the units will divide out), and arcTan(Ry / Rx) will make sense. You can't take the inverse tangent of a quantity that carries units.