Question

The moment of inertia is constant, the time period is doubled, and what happens to the angular momentum of the body?

Answer 1

Step 1: Given information

The moment of inertia is constant and the time period is doubled.

Step 2: To find

We have to determine the angular momentum of the body.

Step 3: Calculation

Angular momentum of a body is given as:

$$\begin{gathered} \mathrm{L}=\mathrm{I\omega } \\ \mathrm{L}=\mathrm{I}\times \frac{2\mathrm{\pi }}{\mathrm{T}} \\ \mathrm{L}\propto \frac{1}{\mathrm{T}} \end{gathered}$$

Here,

$\mathrm{L}$ is the angular momentum.

$\mathrm{I}$ is the rotational inertia.

$\mathrm{\omega }$ is the angular velocity.

$\mathrm{T}$ is the time period.

Now,

$$\begin{gathered} \Rightarrow \frac{{\mathrm{L}}_1}{{\mathrm{L}}_2}=\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1} \\ \frac{\mathrm{L}}{{\mathrm{L}}_2}=\frac{2\mathrm{T}}{\mathrm{T}} \\ {\mathrm{L}}_2=\frac{\mathrm{L}}{2} \end{gathered}$$

Therefore, when the time period is doubled by keeping the moment of inertia constant, the angular momentum becomes half.