Changing gravity
One of my first year students, Alex, is experimenting with rotating bodies of water for his investigation. This made an unexpected link to the topic my second year HL class have just been studying, general relativity.
The surface of a body of water is always perpendicular to the direction of the gravitational field. This is horizontal for a non accelerating body of water but if the water accelerates forwards the water will settle at an angle. This can be explained by considering the forward acceleration to be equivalent to a gravitational field backwards. Adding these two fields gives the resultant gravitational field perpendicular to the surface. The tangent of angle is proportional to the acceleration. The centripetal acceleration of a rotating body of water is proportional to the distance from the centre (a = ω2r), this means that tangent of the angle of the surface will be dependent on x so a curve is formed. Saying that the tangent of the surface angle is proportional to the radius is the same as saying that the derivative of the equation of the curve is proportional to x. This would mean that y = kx2 + c. The surface is a parabola.