Rotational MotionMedium
Question
A thin horizontal disc is rotating about a vertical axis passing through its fixed centre $O$. Its angular momentum is $L_{A}$ and $L_{B}$ computed about points $A$ and $B$, respectively, with $OB = 2 \times OA$. The value of $\frac{L_{A}}{L_{B}}$ is:
Options
A.1
B.2
C.$\ \frac{1}{4}$
D.$\ \frac{1}{2}$
Solution
Sol. [Key Concept: Rotational dynamics of a rotating disc]
$\overrightarrow{L} = \overrightarrow{r} \times \overrightarrow{P} + I_{cm}\overrightarrow{\omega}$
$\overrightarrow{P} = 0$ for both axis
So ${\overrightarrow{L}}_{A} = {\overrightarrow{L}}_{B} = I_{cm}\overrightarrow{\omega}$
$$\frac{{\overrightarrow{L}}_{A}}{{\overrightarrow{L}}_{B}} = 1$$
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