Question

# The angular momentum and the moment of the inertia are respectively:A. Vector and tensor quantities.B. Scalar and vector quantitiesC. Vector and scalar quantitiesD. Vector and vector quantities

Hint: Angular momentum of a particle is the cross product of its position vector and its linear momentum. Moment of inertia of the particle is the product of the particle’s mass and its perpendicular distance from the axis of rotation.

Let us first understand what the angular momentum and the moment of inertia are.
When a particle is in a rotational motion, we define its angular momentum and moment of inertia.
Suppose a particle of mass m is rotating about a fixed axis. The angular momentum of the particle is defined as the cross product of its position vector ($\overrightarrow{r}$) and its linear momentum ($\overrightarrow{p}$). The resultant vector of a cross product of two vectors is always a vector. Therefore, angular momentum is a vector quantity.
The value of angular momentum is given as $\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}$ .
The moment of inertia of the particle is defined as the product of its mass and the square of the perpendicular distance of the particle from the fixed axis of rotation.
The value of moment of inertia of a particle of mass m, which is at a perpendicular distance of d from the fixed axis of rotation is given as $I=m{{d}^{2}}$.
Moment of inertia is only a magnitude and has no specific direction. Therefore, it is a scalar quantity.
Therefore, the angular momentum and the moment of the inertia are vector and scalar quantities respectively.

So, the correct answer is “Option C”.

Note: When we deal with angular momentum and moment of inertia of a particle, the most important thing is the axis about which we are measuring both quantities.
Angular momentum and moment of inertia are always measured about an axis.
Without the axis, both the quantities do not have any meaning.