State the S.I. unit of angular momentum. Obtain its dimensions.

The SI unit of angular momentum is the kilogram-meter squared per second (kg·m²/s).

To obtain its dimensions, let's break down the components of angular momentum:

Mass (M): Measured in kilograms (kg).
Distance (L): Measured in meters (m).
Velocity (V): Measured in meters per second (m/s).
Angular momentum (L) is defined as the product of the moment of inertia (I) and the angular velocity (ω):

L = I * ω

The moment of inertia (I) is the rotational analog of mass for angular motion. Its formula depends on the shape and mass distribution of the rotating object. Since the dimensions of the moment of inertia depend on the specific object, we need to express it in terms of its dimensions:

I = M * L^2

Now, let's combine these equations to obtain the dimensions of angular momentum (L):

L = I * ω
= (M * L^2) * (1/s)

Breaking down the units:

L = kg * m^2 * (1/s)

Thus, the dimensions of angular momentum (L) are: kg·m²/s.