# Marble on a rotating inclined plane [closed]

A marble moves on a smooth plane which is inclined at an angle θ to the horizontal. The whole plane rotates at constant angular speed ω about a vertical axis through a point O fixed in the plane. Coordinates (ξ, η) are defined with respect to axes fixed in the plane: Oξ horizontal and Oη up the line of greatest slope in the plane. Ensuring that you account for the normal reaction force, find $\xi'', \eta''$.

By considering the marble’s kinetic energy as measured on the plane in the rotating frame, or otherwise, find a constant of the motion.

## [You may assume that the marble never leaves the plane.]

For the last part, am I to assume that the quantity $T=\frac{1}{2}mv^2$ is conserved? This gives me $\frac{\omega^2}{2}(\xi^2+\eta^2\cos^2(\theta))-g\sin(\theta) \eta$ is constant.

## closed as off-topic by Jon Custer, Kyle Kanos, Yashas, John Rennie, Bill NMay 9 '17 at 15:06

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• Welcome to Physics! Please note that this is not a homework help site. Please see this Meta post on asking homework questions and this Meta post for "check my work" problems. – Kyle Kanos May 9 '17 at 1:21
• No the question does not intend that you should assume that kinetic energy is conserved - because that would immediately answer the question of finding a constant of the motion. The question is giving you a clue as to how to find a constant of the motion, by considering KE as measured in the rotating (accelerating) frame of reference. – sammy gerbil May 9 '17 at 19:21