Circular motion and inertial mass

Higher tier: an object moving in a circle is always accelerating, even at a steady speed. Inertial mass tells you how hard it is to change an object's velocity.

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Changing velocity at a steady speed

Velocity is speed in a given direction. In a circle the direction changes all the time, so the velocity changes even if the speed is constant.
A change in velocity is an acceleration, so there must be a resultant force.

Centripetal force

The resultant force on an object moving in a circle acts towards the centre of the circle. It is called the centripetal force.
It is not a new kind of force; it is supplied by a real force:
Tension in a string (a ball whirled on a string, a hammer thrower).
Friction between tyres and road (a car going round a bend).
Gravity (the Moon orbiting the Earth, satellites).
If the force stops, the object carries on in a straight line (along a tangent).

Inertial mass

Inertia is the tendency of an object to keep moving at the same velocity (or stay at rest).
Inertial mass measures how hard it is to change an object's velocity:
inertial mass = force ÷ acceleration (m = F ÷ a)
A bigger inertial mass needs a bigger force for the same acceleration.
Worked example

A force of 600 N gives an object an acceleration of 1.5 m/s2. What is its inertial mass?

  1. m = F ÷ a
  2. = 600 ÷ 1.5

Answer: 400 kg

Key idea

In circular motion the speed can be constant but the velocity changes, so there is an acceleration and a resultant force towards the centre (centripetal force) from tension, friction or gravity. Inertial mass = force ÷ acceleration.

Key words
Velocity
Speed in a stated direction. A vector.
Acceleration
The rate of change of velocity: change in velocity ÷ time. Unit m/s^{2}.
Resultant force
The single force that has the same effect as all the forces acting on an object together.
Friction
A force that opposes motion between surfaces in contact.
Time
1 hour = 3600 s. Convert minutes and hours to seconds before using P = E ÷ t or Q = I × t.

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Extra practice

2 more questions

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  1. A force of 900 N gives an object an acceleration of 2.5 m/s2. Calculate its inertial mass.

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    Answer: 360 kg

    m = F ÷ a = 900 ÷ 2.5 = 360 kg

  2. A ball on a string is whirled in a horizontal circle at constant speed. Which is true?

    1. It is not accelerating
    2. It is accelerating outwards
    3. Its speed is changing
    4. It is accelerating towards the centre
    Show the answer

    Answer: It is accelerating towards the centre

    Changing direction means changing velocity, so it accelerates towards the centre.

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Sources and references

Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.

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