Is gravity positive or negative? Sign of acceleration of gravity with free fall example.
My students often ask me "is gravity positive or negative?", but the answer depends on what we mean by "gravity": are we talking about the little g in the formulas or the actual acceleration?
The most important point here is that little g is ALWAYS positive. The definition of little g is the magnitude of the acceleration induced by gravity; in other words the length of the acceleration vector. This is an inherently positive quantity and has a value of about 9.8m/s^2.
What about the sign of acceleration of gravity, say in a free-fall problem? The answer depends on how you set up your coordinate system for the problem. If we choose a coordinate system in which up is positive, then the acceleration caused by gravity will be negative: a_y=-g=-9.8m/s^2. Note that negative g is negative, because g is just the magnitude of the acceleration of gravity!
If we choose a coordinate system in which down is positive, then the acceleration caused by gravity is positive: a_y=+g=+9.8m/s^2 because the acceleration of gravity points in the positive direction for the coordinate system.
