Define momentum as mass × velocity; recall and use the equation p = m v

1.6 Momentum

What is Momentum?

Momentum is a measure of how hard it is to stop a moving object. It depends on two things: how heavy the object is (its mass) and how fast it is moving (its velocity). Think of it like the “push” a moving car has when it rolls down a hill. The heavier the car or the faster it goes, the bigger the push.

Mathematically we write this as:

\$\,p = m v\,\$

Units of Momentum

Momentum is expressed in kilogram metres per second (kg·m/s).

If you multiply a mass in kilograms by a velocity in metres per second, you get kg·m/s.

Quick Example 🚗

Suppose a 1500 kg car is driving at 20 m/s.

Its momentum is:

\$\,p = 1500 \, \text{kg} \times 20 \, \text{m/s} = 30\,000 \,\text{kg·m/s}\,\$

That’s a huge push! If the car were to collide with a stationary object, that object would feel a force proportional to this momentum.

Momentum Table 📊

Mini Quiz 🧠

1. What is the momentum of a 50 kg ball moving at 4 m/s?
   Answer: \$200\,\text{kg·m/s}\$
2. If a 1200 kg truck travels at 15 m/s, how much momentum does it carry?
   Answer: \$18\,000\,\text{kg·m/s}\$
3. Which has more momentum: a 5 kg object moving at 10 m/s or a 2 kg object moving at 25 m/s?
   Answer: Both have 50 kg·m/s, so they have equal momentum.

Key Takeaways

• Momentum is a vector quantity: it has both magnitude and direction.
• Formula: \$p = m v\$.
• Units: kg·m/s.
• Momentum is conserved in isolated systems (no external forces).
• Think of momentum as the “push” or “weight” of motion.