A disc of mass m and radius R moves in the X-Y plane as shown in figure. The angular momentum of the disc about the origin O at the instant shown is

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$- \frac{5}{2} m R^{2} ω \hat{k}$

$\frac{7}{3} m R^{2} ω \hat{k}$

$- \frac{9}{2} m R^{2} ω \hat{k}$

$\frac{5}{2} m R^{2} ω \hat{k}$

answer is A.

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Detailed Solution

$\begin{array}{l} L = I_{c m} ω + m (\vec{r} \times {\vec{v}}_{c m}) \\ = \frac{1}{2} M R^{2} ω \hat{k} + m (4 R \hat{i} + 3 R \hat{j}) \times (ω R \hat{i}) \\ = - \frac{5}{2} M R^{2} ω \hat{k} \end{array}$

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