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Movement where the moving body has a circular trajectory and carries a constant angular velocity.
The formulation of this motion is given in polar coordinates. Given an initial angle{\displaystyle \phi _{0}}{\displaystyle \phi _{0}} and an angular velocity {\displaystyle \omega }{\displaystyle \omega }:
{\displaystyle \phi =\phi _{0}+\omega \cdot \mathbf {t} }{\displaystyle \phi =\phi _{0}+\omega \cdot \mathbf {t} }
Related to angular velocity, two concepts are usually used in this model:
Frequency, {\displaystyle \mathbf {f} }{\displaystyle \mathbf {f} }, defined as the number of laps that are made in a given time.
{\displaystyle \mathbf {f} ={\frac {\omega }{2\cdot \pi }}}{\displaystyle \mathbf {f} ={\frac {\omega }{2\cdot \pi }}}
Period, {\displaystyle \mathbf {T} }{\displaystyle \mathbf {T} }, defined as the time it takes the body to make a full turn.
{\displaystyle \mathbf {T} ={\frac {1}{\mathbf {f} }}}{\displaystyle \mathbf {T} ={\frac {1}{\mathbf {f} }}}
Angular magnitudes are related to linear magnitudes as follows:
The length, {\displaystyle \mathbf {l} }{\displaystyle \mathbf {l} } , of an arc determined by an angle {\displaystyle \phi }{\displaystyle \phi }, is given by:
{\displaystyle \mathbf {l} =\phi \cdot \mathbf {r} }{\displaystyle \mathbf {l} =\phi \cdot \mathbf {r} }
The linear velocity of a body in circular motion is given by:
{\displaystyle \mathbf {v_{l}} =\omega \cdot \mathbf {r} }{\displaystyle \mathbf {v_{l}} =\omega \cdot \mathbf {r} }
The distance traveled by a body in circular motion is:
{\displaystyle d=\omega \cdot \mathbf {t\cdot r} }{\displaystyle d=\omega \cdot \mathbf {t\cdot r} }
In all circular motion there is a centripetal acceleration that varies the direction of the moving body.
{\displaystyle \mathbf {a_{c}} =\omega ^{2}\cdot \mathbf {r} }{\displaystyle \mathbf {a_{c}} =\omega ^{2}\cdot \mathbf {r} }
The centripetal acceleration is perpendicular to the velocity vector, pointing toward the center of the circular trajectory.