# Accelerating a glass of a water across a table?

Suppose you have a glass of water on the table (the glass is half-filled, say). You accelerate the glass in a straight line across the table. The effect is that the water inside the glass rises up one side of the glass.

Why does this happen?

I suppose we can ask some other questions, like what is the shape of the water in the glass as a function of the acceleration, and what is the maximum acceleration of the glass such that none of the water spills out.

The equivalence principle tells us that gravity and acceleration are locally indistinguishable. So if you are accelerating your glass with some acceleration $\mathbf{a}$ to the right, then this is indistinguishable from a gravitational acceleration acting to the left (the red line):
If we add the effective gravitational force to the gravitational acceleration $\mathbf{g}$ acting downwards we get a resultant acceleration shown as $\mathbf{a}_r$.
So to work out the shape of the water just calculate the magnitude and direction of the total acceleration $\mathbf{a}_r$ and tilt the glass so the vector $\mathbf{a}_r$ is vertical.