The acceleration due to gravity, denoted as g, is commonly taken as a positive value, even though it acts downward toward the center of the Earth. This convention can be a bit confusing at first, so let’s break it down.
In physics, the sign of any vector quantity, including acceleration, is often determined by the coordinate system we choose. In most scenarios, we set up a coordinate system where upward is positive and downward is negative. However, in many contexts, especially when studying free-fall motion, it is simpler to define the downward direction as positive.
This means that when we say the acceleration due to gravity is g ≈ 9.81 m/s², we are indeed indicating that it acts downward. If we were to use a coordinate system with upward as positive, we would represent gravitational acceleration as -g, or approximately -9.81 m/s². The negative sign here would then reflect the direction of the acceleration against our defined positive direction.
Ultimately, the choice of sign is a matter of convenience, and physicists simply need to be consistent with their definitions. When solving problems, it’s essential to stay aware of the coordinate system being used to avoid confusion. Thus, whether we label g as positive or negative will depend entirely on our choice of coordinate system.