Editing Circular motion (section)

==== Velocity ====
Figure 1 illustrates velocity and acceleration vectors for uniform motion at four different points in the orbit. Because the velocity {{math|'''v'''}} is tangent to the circular path, no two velocities point in the same direction. Although the object has a constant ''speed'', its ''direction'' is always changing. This change in velocity is caused by an acceleration {{math|'''a'''}}, whose magnitude is (like that of the velocity) held constant, but whose direction also is always changing. The [[acceleration]] points radially inwards ([[centripetal]]ly) and is perpendicular to the velocity. This acceleration is known as centripetal acceleration.

For a path of radius {{mvar|r}}, when an angle {{mvar|θ}} is swept out, the distance traveled on the [[wikt:periphery|periphery]] of the orbit is {{math|1=''s'' = ''rθ''}}. Therefore, the speed of travel around the orbit is
<math display="block">v = r \frac{d\theta}{dt} = r\omega ,</math>
where the angular rate of rotation is {{math|''ω''}}. (By rearrangement, {{math|1=''ω'' = ''v''/''r''}}.) Thus, {{math|''v''}} is a constant, and the velocity vector {{math|'''v'''}} also rotates with constant magnitude {{math|''v''}}, at the same angular rate {{math|''ω''}}.