why is it that when you shake a can of coke there is more pressure when you open it?

There actually is less pressure when the can is opened. Pressure and volume have an inverse relationship meaning V increase, P decrease. The friction of the molecules creates the gas that wants to expand. When the can is opened, there is a decrease of pressure and there is an increase of available space for the molecules to go. The volume of the gas can now expand and goes the liquid with it.

There is not. Shaking a can of Coke or other softdrink causes the formation of air bubbles due to the friction of the ingredients. When the can of Coke is opened, the air bubbles are subjected to a rapid decrease in pressure, causing them to expand and push out Coke with them.

You're increasing the kinetic energy of the material and due to Boyle's law the CO2 is being released from solution.

There are probably physicists on the board that can give the math but that's the basic answer.