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

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.