Curvilinear and Circular Motion
When a body follows a curved path its velocity is always changing direction — even when its speed stays the same.
Big Idea: In curvilinear motion a body moves along a curved line, so the direction of its velocity changes from point to point. The simplest and most important case is uniform motion around a circle. To describe it we use two speeds: the linear speed v (how many metres per second the body covers along the circle) and the angular speed ω (how many radians per second the radius turns through). They are linked by the neat formula v = ωR.
By the end of this topic you will be able to:
- explain why velocity in curvilinear motion is directed along the tangent,
- define the period T and frequency ν of circular motion,
- calculate linear speed with v = 2πR/T,
- calculate angular speed with ω = 2π/T and use v = ωR,
- find the centripetal acceleration with a = v2/R = ω2R.