A classic physics demonstration involves a glass of water placed in the middle of a flat board. If strings are then tied to the four corners of the board and the strings are swung rapidly in a vertical circle, the glass of water will remain in the center of the board as it spins and no water will spill out of the glass, even when it is upside-down.
a. Draw two free-body diagrams for the glass, one when it is at the top of the circle and one when it is at the bottom of the circle.
b. The board has a mass of 1.55 kg, the full glass of water has a mass of 0.250 kg, and they are rotated on 1.10-meter-long strings of negligible mass. If the glass feels a 38.0-N force from the board at the bottom of the circle, how fast is the glass moving around the circle?
c. What is the minimum angular speed the glass and board must have to prevent the string from going slack?