{excerpt:hidden=true}*[System|system]:* One [point particle] constrained to move in a circle at constant speed. --- *[Interactions|interaction]:* [Centripetal acceleration|centripetal acceleration].{excerpt}
h4. Introduction to the Model
h5. Description and Assumptions
This model applies to a single [point particle] moving in a circle of fixed radius (assumed to lie in the _xy_ plane with its center at the origin) with constant speed. It is a subclass of the [Rotational Motion] model defined by {latex}$\alpha=0${latex} and _r_ = _R_.
{info}Usually uniform circular motion will be explicitly specified if you are to assume it. (Be especially careful of _vertical_ circles, which are generally _nonuniform_ circular motion because of the effects of gravity. Unless you are specifically told the speed is constant in a vertical loop, you should not assume it to be.) You can also use this model to describe the acceleration in _instantaneously_ uniform circular motion, which is motion along a curved path with the tangential acceleration instantaneously equal to zero. This will usually apply, for example, when a particle is at the top or the bottom of a vertical loop, when gravity is not changing the _speed_ of the particle.{info}
h5. Learning Objectives
Students will be assumed to understand this model who can:
* Explain why an object moving in a circle at constant speed must be [accelerating|acceleration], and why that acceleration will be [centripetal|centripetal acceleration].
* Give the relationship between the speed of the circular motion, the radius of the circle and the [magnitude] of the [centripetal acceleration].
* Define the [period] of circular motion in terms of the speed and the radius.
* Describe the relationship of the [centripetal acceleration] to the [forces|force] applied to the object executing circular motion.
h5. Relevant Definitions
h6. Phase
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{latex}\begin{large}\[ \phi = \cos^{-1}\left(\frac{x_{i}}{R}\right) = \sin^{-1}\left(\frac{y_{i}}{R}\right) \]\end{large}{latex}
h4. | 
