# Conservation of Angular Momentum

## Problems from IIT JEE

**Problem (IIT JEE 2003):**
A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved?

- centre of the circle.
- on the circumference of the circle.
- inside the circle.
- outside the circle.

**Solution:**
In uniform circular motion, the force on the particle passes through centre of the circle so its torque about this point is zero and angular momentum remains conserved.

**Problem (IIT JEE 1997):**
A mass $m$ is moving with a constant velocity along a line parallel to the $x$-axis, away from the origin. Its angular momentum with respect to the origin,

- is zero
- remains constant
- goes on increasing
- goes on decreasing

**Solution:**
The angular momentum of the particle about the origin O is given by,
\begin{align}
\vec{L}&=m\vec{r}\times\vec{v}\nonumber\\
&=m(r\cos\theta\,\hat\imath+r\sin\theta\,\hat\jmath)\times (v\,\hat\imath)\nonumber\\
&=-mvr\sin\theta\,\hat{k}=-mvh\,\hat{k}.\nonumber
\end{align}
Since $v$ and $h$ are constant, $\vec{L}$ remains constant.