define and use linear momentum as the product of mass and velocity

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

1. Identify the mass of the object (in kg).
2. Determine its velocity (in m/s) and note the direction.
3. Multiply mass by velocity to obtain momentum.
4. 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

💡 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).