In introductory mechanics, momentum is defined as $\overrightarrow{p}=m\overrightarrow{v}$. Is momentum a vector or a scalar quantity?

• A. Vector quantity
• B. Scalar quantity
• C. It is a scalar in one dimension but a vector in three dimensions
• D. Neither; it has no direction and no magnitude

Answer: (A)

Verified step by step guidance

1. Recall the definition of momentum in mechanics: momentum \( \vec{p} = m \vec{v} \), where \( m \) is mass (a scalar) and \( \vec{v} \) is velocity (a vector).
2. Since velocity \( \vec{v} \) has both magnitude and direction, multiplying it by the scalar mass \( m \) results in a quantity that also has both magnitude and direction.
3. A quantity that has both magnitude and direction is classified as a vector quantity.
4. Therefore, momentum inherits the directional property from velocity, making momentum a vector quantity.
5. In summary, momentum is a vector because it depends on velocity, which is a vector.