Angle of rotation carts on a Ferris wheel move along a circle around the center point of that circle. If a cart moves around the wheel once, the angle of rotation is 360 degrees. If the cart was stuck halfway, at the top of the wheel, at that point its angle of rotation was only 180 degrees. This is also referred to as the "order of symmetry." Angles are commonly measured in degrees, radians, gons (gradians) and turns, sometimes also in angular mils and binary radians. They are central to polar coordinates and trigonometry. Angle of rotation In mathematics, the angle of rotation
Pendulum (mathematics) spring from its equilibrium position assumes the small angle approximation. The Lagrangian is then which leads to the following set of coupled differential equations: Adding and subtracting these two equations in turn, and applying the small angle approximation, gives two harmonic oscillator equations in the variables formula_61 and formula_62: with the corresponding solutions where and formula_66, formula_67, formula_47, formula_69 are constants of integration. Expressing the solutions in terms of formula_53 and formula_54 alone: If the bobs are not given an initial push, then the condition formula_73 requires formula_74, which gives (after some rearranging): Pendulum (mathematics) The mathematics of pendulums are