Solution: Motion Map for Circle

Return to current sectionCircular Motion Model.

In the diagram below, you can drag the black dot pointed to by initial radial vector r0 and the blue dot pointed to by 
r(t). The standard angle values (zero at the rightward horizontal, increasing in the CCW direction) are shown at
the upper left of the diagram, updating as the dots are moved. In the general case, θ(
t) can be any function of time.
Its time derivative is designated 
ω(t). For Uniform Circular Motion (UCM), ω is a constant. Multiplying any vector
in the plane on the left by the unit CW bivector
i rotates the vector a quarter turn CCW. We can see the direction of
the velocity vector {
v(t) = ω(ti r(t)} in the diagram riding along with r(t). A green unit circle is also shown, as well
as the purple arclength
s = rθ created by the blue dot's motion.

© David Hestenes 2005, 2014