Physics, kinematics, free fall motion

Question

I'm confused about the role of the minus sign in gravitational acceleration calculations.g (9.8 m/s²) is always positive because it represents the magnitude of gravity and magnitude can never be negative. But when we put a negative sign ( -9.8 m/s²) is it really just indicating direction? If so, the magnitude should stay the same whether we write it as +9.8 or -9.8, right? If I use a minus sign wouldn't it change the value of the magnitude when doing calculations?

But I thought about it for a while and I know that it would only change the magnitude if, in the calculation, I'm directly adding or subtracting g to another value. In all the equations i know of motion for free fall, g is multiplied or divided by something. Is my reasoning correct? What about for other calculations with vectors, like force or velocity.

Answer 1

Your second paragraph is correct, the sign (+/-) of the gravitational force is only important if you are combining forces. If gravity is the only force acting on the object, no sign is needed because you generally already know the direction.

But as soon as you have multiple forces acting on an object, direction matters. Since we almost always think of gravity as pulling us down, in the negative y direction, the gravitational force is typically written with a (-) sign. If you exert an upwards force on an object, directly opposite gravity, tha force is written as a positive (+). Hope this makes sense!

Answer 2

The magnitude is always 9.81 m/s^2

The direction is always downwards.

Whether you use positive sign or negative sign depends on your x-y reference.

If your y axis is pointing up, you will take -9.81 for calculating the gravitational force.

If your y axis is pointing down, you will take 9.81 for calculating the gravitational force.

All other forces on the object are also positioned with respect to the x-y reference.