Inertia (Mass)

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 Force.
• 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

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

Example 1: Same force, different massesCore

A force of 12 N acts on two trolleys on a smooth track.

• trolley A: m = 2.0 kg
• trolley B: m = 6.0 kg

Find the acceleration of each trolley. Which trolley has greater inertia?

Show Answer

For trolley A:

a = F/m = 12/2.0 = 6.0 m s⁻²

For trolley B:

a = F/m = 12/6.0 = 2.0 m s⁻²

Trolley B has greater inertia because it has the larger mass.

Example 2: Same change in velocity, different stopping forcesCore

A car of mass 900 kg and a truck of mass 4500 kg are both travelling at 20 m s⁻¹. They must both come to rest in 5.0 s.

Compare the required resultant stopping force for each vehicle (neglect resistive forces).

Show Answer

Both have the same deceleration:

a = v-u/t = 0-20/5.0 = -4.0 m s⁻²

Car:

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

Truck:

F = ma = (4500)(-4.0) = -1.8 × 10⁴ N

The truck needs 5 times the stopping force because it has 5 times the mass (greater inertia).

Example 3: What happens when the push stops?Core

A puck slides on ice with negligible friction. A student gives it a short push and then stops pushing.

Describe the puck’s motion after the push.

Show Answer

After the push, the resultant force is approximately zero, so the puck continues moving at constant velocity (same speed and direction) due to inertia (Newton’s first law).

Example 4: Mass versus weight (quick check)Core

An astronaut goes to a planet where the gravitational field strength is smaller than on Earth.

Which changes: the astronaut’s mass or weight?

Show Answer

Mass does not change (it is a property of the body).

Weight changes because W = mg and g is different on the planet.
See Gravitational Field Strength & Weight.

Example 5: Find mass from force and accelerationCore

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

Find the mass of the trolley.

Show Answer

Use F = ma:

m = F/a = 10/2.5 = 4.0 kg

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.

8. Practice, Quiz and Next Step

Close your notes and use Inertia (Mass) in the supplied context below. This requires a constructed explanation or working, not recognition of an option.

Fresh context: A standing passenger lurches forward when a bus brakes suddenly.

1. Retrieve: define inertia and changes of motion in your own words, including units, sign or conditions where relevant.
2. Represent: Draw separate before-and-during diagrams for the passenger and bus, marking velocity and the force that changes the passenger's motion.
3. Apply: Explain the observation using inertia without describing inertia as a forward force.

Check the response before looking back

• The body under analysis is named and only forces on that body are combined.
• Directions, line of action and perpendicular distance are explicit where relevant.
• The conclusion follows from the resultant force or moment, not from motion alone.

If one check fails, name that exact gap, revisit the matching explanation or worked example, and redo the task with different values or a different situation. Then use theO-Level topic checks orpractice browser for an independent re-test.