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

< A-level Mathematics‎ | OCR‎ | M4

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

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

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

• ${\displaystyle \omega _{1}=\omega _{0}+\alpha t\,}$
• ${\displaystyle \theta =\omega _{0}t+{\frac {1}{2}}\alpha t^{2}}$
• ${\displaystyle \theta ={\frac {1}{2}}(\omega _{0}+\omega _{1})t}$
• ${\displaystyle \omega _{1}^{2}=\omega _{0}^{2}+2\alpha \theta }$
• ${\displaystyle \theta =\omega _{1}t-{\frac {1}{2}}\alpha t^{2}}$

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.