In physics, is $p$ (momentum) considered a vector or a scalar quantity?

• A. $p$ (momentum) is neither a vector nor a scalar; it is a tensor.
• B. $p$ (momentum) is a scalar quantity because it only has magnitude.
• C. $p$ (momentum) is a vector quantity because it has both magnitude and direction.
• D. $p$ (momentum) is a scalar quantity because it is always positive.

Answer: (C)

Verified step by step guidance

1. Recall the definition of momentum in physics: momentum \( \mathbf{p} \) is defined as the product of an object's mass \( m \) and its velocity \( \mathbf{v} \), expressed as \( \mathbf{p} = m \mathbf{v} \).
2. Understand that velocity \( \mathbf{v} \) is a vector quantity, meaning it has both magnitude (speed) and direction.
3. Since mass \( m \) is a scalar (only magnitude, no direction), multiplying a scalar by a vector results in a vector quantity.
4. Therefore, momentum \( \mathbf{p} \) inherits the direction from velocity and has both magnitude and direction, making it a vector quantity.
5. Conclude that momentum is not a scalar (which has only magnitude) nor a tensor (which is a more complex mathematical object), but a vector quantity.