Mass, inertia and linear momentum
Key idea: Mass measures resistance to a change in motion. Momentum combines that inertia with velocity, so direction matters.
Continue where you stopped
The core idea
H1 Physics 8867 · Lesson 2 of 3
Check your understandingBy the end of this lesson, you should be able to
- Explain mass as a measure of inertia.
- Define linear momentum and use its vector direction.
- Compare momenta using a declared sign convention.
Learn the idea
Big question: Why can two objects have equal momentum magnitudes even when their masses and velocities are different?
Mass describes resistance to acceleration
Inertia is not a force stored inside an object. It is the tendency to resist a change in velocity, measured by mass. At the same resultant force, a larger mass has a smaller acceleration; at the same acceleration, it requires a larger resultant force.
Momentum combines this inertia with motion. Because velocity is a vector, momentum depends on the chosen reference frame and sign convention. Mass remains a positive scalar even when momentum is negative.
Check your understanding: Can a stationary truck have less momentum than a moving tennis ball?
Yes. In the chosen frame the stationary truck has zero momentum, while the moving ball has non-zero momentum.
Key ideas
- Zero velocity means zero momentum in the chosen frame.
- Equal momentum magnitudes can point in opposite directions.
- Use kg m s⁻¹, not newtons, for momentum.
Relationships to know
p = mv
Follow the reasoning
Worked example
Compare unequal vehicles with equal momentum magnitudes
Question: A 900 kg car moves east at 20 m s⁻¹. A 1200 kg car moves west at 15 m s⁻¹. Compare their momenta using east as positive.
Step 1: Attach signs to velocity
Why: Direction enters through velocity, not through mass.
Working: v₁ = +20 m s⁻¹ and v₂ = −15 m s⁻¹.
Step 2: Calculate each momentum
Why: Linear momentum is the product of mass and signed velocity.
Working: p₁ = 900(+20) = +1.80 × 10⁴ kg m s⁻¹; p₂ = 1200(−15) = −1.80 × 10⁴ kg m s⁻¹.
Step 3: Interpret rather than merely compare numbers
Why: A vector comparison needs magnitude and direction.
Working: |p₁| = |p₂|, while their signs are opposite.
Answer: The cars have equal momentum magnitudes, 1.80 × 10⁴ kg m s⁻¹, in opposite directions.
Check: The heavier car needs the smaller speed to produce the same momentum magnitude.
Now try it with support
Practise with support
A 0.20 kg ball moves east at 15 m s⁻¹ and rebounds west at 10 m s⁻¹. Find its initial and final momenta with east positive.
Hints
- Westward velocity is negative.
- Calculate each state separately before finding any change.
View the guided answer
pi = 0.20(15) = +3.0 kg m s⁻¹; pf = 0.20(−10) = −2.0 kg m s⁻¹.
Your turn
Practise independently
Compare the momenta of a 900 kg car moving east at 20 m s⁻¹ and a 1200 kg car moving west at 15 m s⁻¹ using east as positive.
Check your answer
The eastward car has p = 900(20) = +1.80 × 10⁴ kg m s⁻¹. The westward car has p = 1200(−15) = −1.80 × 10⁴ kg m s⁻¹. Their magnitudes are equal and their directions are opposite.
Common mistakes and exam guidance
Watch out for
- Ignoring direction because both masses are positive.
- Confusing momentum mv with kinetic energy ½mv².
In an exam
- State the positive direction once, then keep signed velocities throughout.
- If asked to compare vectors, discuss both magnitude and direction.
Put the ideas together
Exam-style practice [5 marks]
Trolley A has mass 0.40 kg and velocity +3.0 m s⁻¹. Trolley B has mass 0.60 kg and velocity −2.0 m s⁻¹. Find each momentum and the total momentum. Explain what the result does—and does not—tell you about their motion.
Plan before you answer
- Use one sign convention for both trolleys.
- Add signed momenta.
- Distinguish total momentum from individual motion.
View the marking points and model answer
Marking points
- Finds pA = +1.2 kg m s⁻¹.
- Finds pB = −1.2 kg m s⁻¹.
- Obtains total momentum zero.
- States that the individual trolleys are still moving.
- Explains that zero total momentum means their vector momenta cancel in this frame, not that each momentum is zero.
Model answer
pA = 0.40(+3.0) = +1.2 kg m s⁻¹ and pB = 0.60(−2.0) = −1.2 kg m s⁻¹. Total momentum is zero. The trolleys are not stationary; their equal and opposite momenta cancel in the system total for this reference frame.
Finish from memory
Three-question recap
Define linear momentum.
Check
The product of mass and velocity, p = mv.
What does a negative momentum mean?
Check
It points opposite the chosen positive direction.
Is inertia a force?
Check
No. It is a body’s resistance to a change in velocity and is measured by mass.
Continue with the next resource in this course.
Course and syllabus information
- Course
- GCE A-Level H1 Physics
- Edition
- GCE A-Level H1 Physics 2027