Momentum and Newton’s Laws of Motion
📘 Definition of Linear Momentum
Linear momentum (\$p\$) is a vector quantity that describes the motion of an object. It is defined as the product of the object's mass (\$m\$) and its velocity (\$\vec{v}\$):
\$p = m\,\vec{v}\$
- Mass (\$m\$) – measured in kilograms (kg).
- Velocity (\$\vec{v}\$) – measured in metres per second (m/s); includes direction.
- Momentum (\$p\$) – measured in kilogram‑metres per second (kg·m/s) or newton‑seconds (N·s).
🔢 Using the Momentum Formula
- Identify the mass of the object (in kg).
- Determine its velocity (in m/s) and note the direction.
- Multiply mass by velocity to obtain momentum.
- State the result with proper units and direction.
🧮 Worked Example
A 0.15 kg cricket ball is thrown horizontally at 20 m/s. Calculate its momentum.
\$p = m v = (0.15\,\text{kg})(20\,\text{m/s}) = 3.0\,\text{kg·m/s}\$
The momentum of the ball is 3.0 kg·m/s in the direction of its throw.
📊 Quick Reference Table
| Object | Mass (kg) | Velocity (m/s) | Momentum (kg·m/s) |
|---|
| Running student (50 kg) | 50 | 3 (forward) | 150 (forward) |
| Bicycle (12 kg) | 12 | 5 (to the right) | 60 (to the right) |
| Car (1200 kg) | 1200 | 15 (north) | 18000 (north) |
💡 Key Points to Remember
- Momentum is a vector – always include direction.
- If an object is at rest, its velocity is zero, so its momentum is zero.
- In a closed system with no external forces, total momentum before an event equals total momentum after (conservation of momentum).