In introductory mechanics, what is the SI unit of linear momentum?

• A. $kg\cdot m/s$
• B. $N\cdot s$
• C. $kg\cdot m/s^2$
• D. $J\cdot s$

Answer: (A)

Verified step by step guidance

1. Recall that linear momentum \( \vec{p} \) is defined as the product of an object's mass \( m \) and its velocity \( \vec{v} \), so \( \vec{p} = m \vec{v} \).
2. Identify the SI unit of mass, which is the kilogram (kg), and the SI unit of velocity, which is meters per second (m/s).
3. Since momentum is mass times velocity, multiply the units: \( \text{kg} \times \frac{\text{m}}{\text{s}} \).
4. Understand that this combined unit \( \text{kg} \cdot \frac{\text{m}}{\text{s}} \) represents the SI unit of linear momentum.
5. Note that other units like \( \text{N} \cdot \text{s} \) (newton-second) are equivalent to \( \text{kg} \cdot \frac{\text{m}}{\text{s}} \) because \( 1 \text{N} = 1 \text{kg} \cdot \frac{\text{m}}{\text{s}^2} \), so \( \text{N} \cdot \text{s} = \text{kg} \cdot \frac{\text{m}}{\text{s}} \).