Uniform Circular Motion
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
$\alpha=0$
and r = R.
Problem Cues
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.
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, and why that acceleration will be centripetal.
- 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 applied to the object executing circular motion.
Model
CompatibleSystems"> Compatible Systems
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A single point particle.
RelevantDefinitions"> Relevant Definitions
LawsofChange"> Laws of Change
DiagrammaticRepresentations"> Diagrammatic Representations
Relevant Examples
ExamplesInvolvingUniformCircularMotion"> Examples Involving Uniform Circular Motion
ExamplesInvolvingNon-UniformCircularMotion"> Examples Involving Non-Uniform Circular Motion
AllExamplesUsingtheModel"> All Examples Using the Model
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