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Inertia (Mass)

Key idea: Learn what inertia means and why a larger mass gives greater resistance to changes in motion (O Level Physics 6091).

  • SEC G3 Physics 2027
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Learning objectives

  • Distinguish contact forces from non-contact forces
  • State that mass measures the amount of matter in a body
  • Describe a gravitational field as a region where a mass experiences gravitational force
  • Define gravitational field strength as gravitational force per unit mass
  • Apply weight = mass × gravitational field strength
  • Distinguish mass from weight
  • Describe the effect of balanced and unbalanced forces on a body
  • Describe ways a force may change motion
  • Identify action–reaction pairs on interacting bodies
  • Draw free-body diagrams for force systems in at most two dimensions
  • Solve three-force static equilibrium graphically
  • Apply resultant force = mass × acceleration
  • Relate mass to resistance to change in motion
  • Explain the effects of friction on motion
  • Describe falling with and without air resistance, including terminal velocity
  • Describe a moment as a force's turning effect in everyday examples
  • Apply moment = force × perpendicular distance from the pivot
  • State the principle of moments for a body in equilibrium
  • apply the principle of moments to new situations or to solve related problems
  • show an understanding that the weight of a body may be taken as acting at a single point known as its centre of gravity
  • Explain qualitatively how centre-of-gravity position affects stability

1. Definition

Inertia is the tendency of a body to resist a change in its state of rest or uniform motion (constant velocity).

Mass is a measure of inertia: a larger mass means greater resistance to changes in motion.

2. Key Ideas

  • Inertia is a property of matter (it is not a force).
  • Bigger mass → bigger inertia → harder to start, stop, speed up, slow down, or change direction.
  • If the resultant force is zero, velocity does not change (Newton’s first law): see Balanced Forces and Newton’s First Law.
  • For constant mass, the link between force and inertia is:
    • Fᵣₑₛᵤₗₜₐₙₜ = ma
    • for the same force, bigger m → smaller a (see Unbalanced Force)
  • Mass is a scalar quantity; SI unit: kilogram (kg).
  • Mass is measured using a beam balance or electronic balance (not a spring balance).
  • Mass is different from weight (weight is a force): see Gravitational Field Strength & Weight.

3. Detailed Explanations

A. What inertia looks like in real life

A body “keeps doing what it is doing” unless a resultant force acts on it:

  • at rest → stays at rest
  • moving at constant velocity → continues at the same velocity (same speed and direction)

In everyday life, objects often slow down because friction and air resistance provide a resultant force opposite the motion (see Friction and Terminal Velocity).

B. Mass is a measure of inertia

If you apply the same resultant force to two objects, the one with the larger mass accelerates less:

a = Fᵣₑₛᵤₗₜₐₙₜ/m

So larger mass means greater resistance to changes in motion (greater inertia).

C. Example: why a heavier object is harder to move

Effect of mass on acceleration for the same forceThe same horizontal push acts on a light empty pail and a heavier sand-filled pail. The lighter pail has greater acceleration and the heavier pail has smaller acceleration.same Fsame Flarger accelerationsmaller accelerationless sand: smaller massmore sand: larger mass
For the same resultant force, a larger mass has a smaller acceleration: greater mass means greater inertia.

To start the pail moving (or to stop it), you must create a resultant force. A heavier (more massive) pail needs a larger force to produce the same acceleration.

D. Seat belts and inertia (common exam explanation)

When a car brakes suddenly, the car slows down, but your body tends to continue moving forward due to inertia.

A seat belt provides the force that changes your motion so you slow down with the car, reducing injury.

4. Common Mistakes

  • Saying “inertia is a force that keeps objects moving” (inertia is not a force).
  • Saying “a moving object needs a force to keep moving” (it needs a force only to change its velocity; without resistive forces it continues at constant velocity).
  • Confusing mass and weight (mass in kg; weight in N).
  • Using a spring balance to “measure mass” (a spring balance measures weight).

5. Exam Tips

  • Use the phrase: “resists change in state of rest or uniform motion”.
  • If a question asks “why does a heavy object accelerate less?”, link inertia to Fᵣₑₛᵤₗₜₐₙₜ = ma.
  • When explaining slowing down, always mention the resultant force (often friction/air resistance).
  • Always give mass in kg before using F = ma.

6. Worked Examples

Modelled example 1

Same force, different masses

Core

Problem

A 12 N resultant force acts separately on trolley A of mass 2.0 kg and trolley B of mass 6.0 kg. Find each acceleration and identify the trolley with greater inertia.
Study the worked solution

  1. Calculate trolley A's acceleration

    Method

    Divide the common resultant force by A’s mass.

    Reason

    For a fixed resultant force, a = F/m.

    Working

    a_A = 12/2.0 = 6.0 m s⁻²

  2. Calculate trolley B's acceleration

    Method

    Repeat with B’s larger mass.

    Reason

    The same force produces less acceleration for greater mass.

    Working

    a_B = 12/6.0 = 2.0 m s⁻²

  3. Interpret inertia

    Method

    Identify trolley B as having greater inertia.

    Reason

    Mass measures inertia, and B has the larger mass.

    Working

    m_B = 6.0 kg > m_A = 2.0 kg

Guided practice 2

Find mass from force and acceleration

About 4 min

Problem

A trolley accelerates at 2.5 m s⁻² when a resultant force of 10 N acts on it. Find its mass.

Rearrange before substituting

Unit: kg

Hints

Hint 1: start from the resultant-force equation
Use Fᵣₑₛᵤₗₜₐₙₜ = ma.
Hint 2: make mass the subject
Divide the resultant force by acceleration.
View solution step by step

  1. Make mass the subject

    Method

    Rearrange before inserting values.

    Reason

    This keeps force, mass and acceleration roles clear.

    Working

    m = Fᵣₑₛᵤₗₜₐₙₜ/a

  2. Calculate mass

    Method

    Substitute the force and acceleration.

    Reason

    The stated force is already the resultant force.

    Working

    m = 10/2.5 = 4.0 kg

Common misconception 3

What happens when the push stops?

Find and correct the mistake

Learner response

A puck slides on nearly frictionless ice. After a short push ends, a student says: “No forward force remains, so the puck must slow to rest.” Locate the error and predict the motion.

Connect zero resultant to velocity

Motion after the push

View solution step by step

  1. Identify the force condition

    Method

    Set the resultant force approximately to zero after the push.

    Reason

    The problem says friction is negligible and the applied push has ended.

    Working

    Fᵣₑₛᵤₗₜₐₙₜ ≈ 0

  2. Apply inertia

    Method

    Predict constant velocity in the same direction.

    Reason

    Zero resultant force means zero acceleration, not zero velocity.

    Working

    Fᵣₑₛᵤₗₜₐₙₜ = 0 ⇒ a = 0 ⇒ v = constant

Examiner practice 4

Same change in velocity, different stopping forces

5 marks

Examination question

A 900 kg car and a 4500 kg truck both travel at 20 m s⁻¹ and stop in 5.0 s. Calculate each resultant stopping force and compare them. [5 marks]

Show the shared acceleration and both forces

View solution step by step

  1. Find the common acceleration

    2 marks

    Method

    Use the velocity change over time.

    Reason

    Both vehicles have the same initial velocity, final velocity and stopping time.

    Working

    a = (0-20)/5.0 = -4.0 m s⁻²

  2. Calculate the car force

    1 mark

    Method

    Multiply the car’s mass by the common acceleration.

    Reason

    The signed resultant force follows F = ma.

    Working

    F = (900)(-4.0) = -3600 N

  3. Calculate and compare the truck force

    2 marks

    Method

    Multiply the truck’s mass by the same acceleration, then compare magnitudes.

    Working

    F = (4500)(-4.0) = -1.8 × 10⁴ N

    Reason

    The truck needs five times the stopping-force magnitude because it has five times the mass.

Challenge 5

Mass versus weight (quick check)

Minimal support

Planetary transfer

An astronaut goes to a planet where gravitational field strength is smaller than on Earth. Which changes: the astronaut’s inertia, mass or weight? Explain.

Separate the property from the force

Hints

Hint 1: identify the property
Mass measures inertia and belongs to the astronaut.
Hint 2: identify the field-dependent quantity
Weight follows W = mg.
View solution step by step

  1. Keep mass and inertia unchanged

    Method

    State that mass and inertia remain the same.

    Reason

    Changing location does not change the astronaut’s amount of matter.

    Working

    mₚₗₐₙₑₜ = m_Earth

  2. Change the weight

    Method

    State that weight is smaller.

    Reason

    The planet has smaller g, so W = mg is smaller.

    Working

    gₚₗₐₙₑₜ < g_Earth ⇒ Wₚₗₐₙₑₜ < W_Earth

7. Mind Stretchers

Mind stretcher 1: Bus passenger “lurching” questionExtension

A bus moves off suddenly from rest. A standing passenger feels as if they are pushed backwards.

Explain using inertia and forces.

Show Answer

When the bus accelerates forward, the passenger’s body tends to remain at rest due to inertia.

The frictional force between the floor and the passenger’s shoes provides the forward force needed to accelerate the passenger. Until this force acts, the passenger’s lower body moves with the bus while the upper body tends to stay at rest, so they appear to lurch backwards.

Mind stretcher 2: Coin-on-card trickExtension

A coin is placed on a card resting on top of a glass. The card is flicked quickly sideways.

Predict what happens to the coin and explain.

Show Answer

The card moves away, but the coin tends to remain at rest due to inertia.

With little friction between coin and card, the coin does not gain much horizontal speed, so it drops into the glass under gravity.

Continue with the next resource in this course.

Course and syllabus information
Course
SEC G3 Physics
Edition
SEC G3 Physics 2027