Which of the following best describes momentum: is it a $\mathrm{scalar}$ or a $\mathrm{vector}$ quantity?

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

Answer: (A)

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. Note that velocity \( \vec{v} \) is a vector quantity, meaning it has both magnitude (speed) and direction.
3. Since mass \( m \) is a scalar (it has magnitude only and no direction), multiplying a scalar by a vector results in a vector quantity.
4. Therefore, momentum \( \vec{p} \) inherits the directional property from velocity, making momentum a vector quantity.
5. In summary, momentum is a vector because it has both magnitude and direction, distinguishing it from scalar quantities which have only magnitude.