In physics, is $\mathrm{momentum}$ considered a $\mathrm{vector}$ or a $\mathrm{scalar}$ quantity?

• A. $\mathrm{Momentum}$ is neither a $\mathrm{vector}$ nor a $\mathrm{scalar}$; it is a $\mathrm{tensor}$.
• B. $\mathrm{Momentum}$ is a $\mathrm{vector}$ quantity because it has both magnitude and direction.
• C. $\mathrm{Momentum}$ is a $\mathrm{scalar}$ quantity because it only has magnitude.
• D. $\mathrm{Momentum}$ is a $\mathrm{scalar}$ quantity because it is always positive.

Answer: (B)

Verified step by step guidance

1. Recall the definition of momentum in physics: momentum \( \vec{p} \) is defined as the product of an object's mass \( m \) and its velocity \( \vec{v} \), expressed as \( \vec{p} = m \vec{v} \).
2. Since velocity \( \vec{v} \) is a vector quantity (it has both magnitude and direction), and mass \( m \) is a scalar (only magnitude), the product \( m \vec{v} \) results in a vector quantity.
3. Understand that a vector quantity is one that has both magnitude and direction, while a scalar quantity has only magnitude without direction.
4. Therefore, momentum inherits the directional property from velocity, making momentum a vector quantity.
5. Summarize that momentum is not a scalar because it depends on direction, and it is not a tensor in basic classical mechanics; it is correctly classified as a vector quantity.