In introductory mechanics, momentum is defined as $p=mv$. Is momentum a vector or a scalar quantity?

• A. Momentum is a scalar quantity.
• B. Momentum is neither vector nor scalar because it depends on mass and speed.
• C. Momentum is a vector quantity.
• D. Momentum is a scalar in one dimension but a vector in two or three dimensions.

Answer: (C)

Verified step by step guidance

1. Recall the definition of momentum: \(\mathbf{p} = m \mathbf{v}\), where \(m\) is mass (a scalar) and \(\mathbf{v}\) is velocity (a vector).
2. Since velocity \(\mathbf{v}\) has both magnitude and direction, multiplying it by the scalar mass \(m\) results in momentum \(\mathbf{p}\) having both magnitude and direction as well.
3. Quantities that have both magnitude and direction are called vector quantities, while those with only magnitude are scalars.
4. Therefore, momentum inherits the directional property from velocity, making momentum a vector quantity.
5. In summary, momentum is a vector quantity because it depends on velocity, which is a vector.