User:T.Randall.Scales/sandbox

Circular acceleration
Transverse acceleration (perpendicular to velocity) causes change in direction. If it is constant in magnitude and changing in direction with the velocity, we get a circular motion. For this centripetal acceleration we have


 * $$ \mathbf{a} = - \frac{v^2}{r} \frac{\mathbf{r}}{r} = - \omega^2 \mathbf{r}$$

where: The formula is dimensionless, describing a ratio true for all units of measure applied uniformly across the formula. If the numerical value of $$ \mathbf{a}$$ is measured in meters per second per second, then the numerical values for $$v\,$$ will be in meters per second, $$r\,$$ in meters, and $$ \omega \ $$ in radians per second.
 * $$v\,$$ is orbital velocity of orbiting body,
 * $$r\,$$ is radius of the circle
 * $$ \omega \ $$ is angular speed, measured in radians per unit time.