An old light globe hangs by a wire from the roof of a train. What angle does it make with the vertical when the train is accelerating at

Dealing with accelerating reference frames can be tricky. I found the most intuitive way to go is to let the tension in the rope be

, the mass of the globe be

, and let the angle between the rope and the vertical be

.

The force

acts downwards. The force

acts to the right. Therefore to balance those forces,

, by division.