A uniform square lamina, of mass 5 kg and side 0.2 m, is rotating about a fixed vertical axis that is perpendicular to the lamina and that passes through its centre. A couple of constant moment 0.06 N m is applied to the lamina. The lamina turns through an angle of 155 radians while its angular speed increases from 8 rad s\(^{-1}\) to \(\omega\) rad s\(^{-1}\). Find \(\omega\). [4]

$I = \frac{1}{3}(5)(0.1^2 + 0.1^2) = \frac{1}{30}$ | B1 | Work-energy principle (M1 A1ft)

$\alpha = \frac{0.06}{\frac{1}{30}} (= 1.8)$ | M1 | M1 for using $C = I\alpha$ with their $I$

$\omega^2 = 8^2 + 2(1.8)(155)$ | M1 | Using $\omega^2 = \omega_0^2 + 2a\theta$ with their $\alpha$

$\omega = 24.9$ (3 sf) | A1 | accept $\sqrt{622}$; 24.939927...

| [4] |

A uniform square lamina, of mass 5 kg and side 0.2 m, is rotating about a fixed vertical axis that is perpendicular to the lamina and that passes through its centre. A couple of constant moment 0.06 N m is applied to the lamina. The lamina turns through an angle of 155 radians while its angular speed increases from 8 rad s$^{-1}$ to $\omega$ rad s$^{-1}$. Find $\omega$. [4]

\hfill \mbox{\textit{OCR M4 2016 Q1 [4]}}