At the far end of the room you will see a large number wheel. To the left of this there is a puzzle. Solve this puzzle and you will get a hammer. Based on the note from the ground you will see that something happens when you hit the red circles with the hammer. Use the hammer on one of the red circles to rotate the room. Keep spinning the room to reveal the orange driver tool inside one of the segments. Solve the puzzle and collect the orange driver tool. In the first segment of the room is a puzzle on the wall that has a gear inside. Rotate the first segment of the room so that the gear falls into the little collection hole on the bottom. Combine this gear with the orange driver tool.
Rotate the rooms until the bottom segment of the number wheel is visible. Use the orange driver tool on this to access a mini-game that is a little bit tricky. The goal of the game is to get the number down to 0. Spinning the wheel so that a red number is selected will subtract from the total and a blue will add to the total. If the number goes below 0 or above 200 you fail and have to start again. With a little calculation, you should be able to figure out the way in which you need to spin the wheel so that you get the total value down to 0.
A new platform will have risen up from the floor. Use the driver tool on this platform to rotate all of the rooms. Rotate them so that all of the lines on the floor in each of the segments line up. This will allow you to solve the puzzle to obtain the shotgun. Once you get the shotgun, shoot the switch and press the button.