Question

A stone is attached to the end of a string and whirled in horizontal circle, with uniform speed then

• A. its linear and angular momentum are constant
• B. only linear momentum is constant
• C. its angular momentum is constant but linear momentum is variable
• D. both are variable

Answer 1

The correct option is C its angular momentum is constant but linear momentum is variable

Let the mass of the stone be $m$ which is moving with uniform speed $v$ in a circle of radius $r$.

The magnitude of velocity is constant but the velocity vector keeps changing its direction at every instant. Hence the linear momentum of the stone changes its direction continuously.

Angular momentum $\overrightarrow{L}=m(\overrightarrow{r}\times \overrightarrow{v})=mrv$ $\hat{z}$

Hence the angular momentum is constant in magnitude and always points in z axis.