A-level Mathematics/OCR/M4/Rotation of a Rigid Body

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In M1 you learnt the five formulae for motion with constant linear acceleration:

  •  v = u + at \,
  •  s = ut + \frac {1}{2} at^2
  •  s = \frac {1}{2}(u+v)t
  •  v^2 = u^2 + 2as \,
  •  s = vt - \frac {1}{2} at^2

We can consider motion with constant angular acceleration in the same way:

  •  \omega _1 = \omega _0 + \alpha t \,
  •  \theta = \omega _0 t + \frac{1}{2} \alpha t^2
  •  \theta = \frac{1}{2}(\omega _0 + \omega _1)t
  •  \omega _1^2 = \omega _0^2 + 2\alpha\theta
  •  \theta = \omega _1 t - \frac{1}{2} \alpha t^2

While the first set of formulae cover the displacement, velocity and acceleration in terms of straight-line distance, the second set cover the same quantities but for rotating objects.