Which is a vector quantity?

Options

A. Angular momentum
B. Work
C. Potential energy
D. Electirc current

Explanation

To determine which of the given options is a vector quantity, we will analyze each option step by step.

### Step 1: Analyze Angular Momentum
- **Definition**: Angular momentum (L) is defined as the product of the moment of inertia and angular velocity. It can also be expressed as \( L = R \times P \) where \( R \) is the position vector and \( P \) is the linear momentum.
- **Formula**: \( L = MVR \) or \( L = R \times (MV) \)
- **Nature**: Angular momentum has both magnitude and direction, making it a vector quantity.

### Step 2: Analyze Work
- **Definition**: Work (W) is defined as the dot product of force (F) and displacement (S).
- **Formula**: \( W = F \cdot S \cos(\theta) \)
- **Nature**: Since work is calculated using the dot product, it results in a scalar quantity. Thus, work is not a vector quantity.

### Step 3: Analyze Potential Energy
- **Definition**: Potential energy (P) is the energy possessed by an object due to its position or configuration.
- **Formula**: For gravitational potential energy, \( P = mgh \) (where \( h \) is height).
- **Nature**: Potential energy has only magnitude and no direction, making it a scalar quantity.

### Step 4: Analyze Electric Current
- **Definition**: Electric current (I) is defined as the rate of flow of electric charge (Q) over time (T).
- **Formula**: \( I = \frac{Q}{T} \)
- **Nature**: Although electric current has a direction (flow of charge), it is treated as a scalar quantity in circuit analysis because it does not obey vector addition in the same way that true vector quantities do.

### Conclusion
Based on the analysis:
- **Option 1**: Angular momentum is a vector quantity.
- **Option 2**: Work is a scalar quantity.
- **Option 3**: Potential energy is a scalar quantity.
- **Option 4**: Electric current is a scalar quantity.

Thus, the correct answer is **Option 1: Angular Momentum** is the only vector quantity among the options provided.

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