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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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a

$- \frac{5}{2} {mR}^{2} ω \hat{k}$

b

$\frac{7}{3} {mR}^{2} ω \hat{k}$

c

$- \frac{9}{2} {mR}^{2} ω \hat{k}$

d

$\frac{5}{2} {mR}^{2} ω \hat{k}$

answer is A.

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Detailed Solution

$\begin{array}{l} \vec{L_{O}} = l_{CM} \vec{ω} + m (\vec{r} \times \vec{v}) = \frac{1}{2} {mR}^{2} ω \hat{k} + m (4 R \hat{i} + 3 R \hat{j}) \times (ωR \hat{i}) \\ = \frac{1}{2} {mR}^{2} ω \hat{k} - 3 {mR}^{2} ω \hat{k} = - \frac{5}{2} {mR}^{2} ω \hat{k} \end{array}$

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