Tilted bottle: angle of the water surface

A bottle partly filled with water is tilted 30° from the vertical and left to stand still. What is the angle between the water surface and the axis of the bottle?

Step-by-step

1. The water surface stays horizontal (gravity does not change direction)
   A liquid at rest always has a horizontal free surface
2. Bottle tilted 30° → axis makes 30° with the horizontal
   The angle between the axis and the horizontal is the tilt angle
3. Angle between the lines = tilt angle = 30°
   The angle between the (horizontal) water surface and the bottle axis equals the bottle's tilt

Why it works

A liquid at rest always has a horizontal free surface, because gravity does not change direction. The angle between that horizontal surface and the tilted axis equals the tilt angle.

Common mistakes

• Subtracting 30° from 90° and answering 60°.
• Thinking the water surface tilts together with the bottle.

Related

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