Write the dimensional formula of angular momentum. Is it scalar or vector ?

Explanation

To find the dimensional formula of angular momentum and determine whether it is a scalar or vector quantity, we can follow these steps:

### Step 1: Understand the Definition of Angular Momentum
Angular momentum (L) is defined as the cross product of the position vector (r) and the linear momentum (p). Mathematically, it can be expressed as:
\[ L = r \times p \]
where \( p = mv \) (linear momentum), with \( m \) being mass and \( v \) being velocity.

### Step 2: Substitute Linear Momentum into the Angular Momentum Formula
Substituting the expression for linear momentum into the angular momentum formula gives us:
\[ L = r \times (mv) \]
This can be rewritten as:
\[ L = m (r \times v) \]

### Step 3: Identify the Dimensions of Each Component
Now, we need to find the dimensions of each component involved in the expression for angular momentum:
- The dimension of mass (m) is:
\[ [m] = M \]
- The dimension of the position vector (r), which is a length, is:
\[ [r] = L \]
- The dimension of velocity (v) is:
\[ [v] = LT^{-1} \]

### Step 4: Combine the Dimensions
Now we can combine these dimensions to find the dimensional formula of angular momentum:
\[ [L] = [m] \cdot [r] \cdot [v] = M \cdot L \cdot (LT^{-1}) \]
This simplifies to:
\[ [L] = M \cdot L^2 \cdot T^{-1} \]

### Step 5: Write the Final Dimensional Formula
Thus, the dimensional formula for angular momentum is:
\[ [L] = M L^2 T^{-1} \]

### Step 6: Determine if Angular Momentum is a Scalar or Vector Quantity
Angular momentum is a vector quantity because it has both magnitude and direction. It is represented as a vector in physics.

### Final Answer
The dimensional formula of angular momentum is:
\[ M L^2 T^{-1} \]
And angular momentum is a vector quantity.

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