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

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

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

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.