Circular motion — common mistakes

A very common mistake is to add an extra force labelled 'centripetal force' to a force diagram. Do not do this! Instead, identify all the real forces acting on the object and find their resultant force towards the centre of the circle. This resultant force is the centripetal force.

For problems involving 'losing contact' or a string going 'slack', the key is to set the relevant contact force (Normal Reaction R or Tension T) to zero. This gives you the boundary condition for that event occurring.

Acceleration is the rate of change of velocity. Velocity is a vector quantity, having both magnitude (speed) and direction. In circular motion, the direction of the velocity vector is continuously changing, even if its magnitude (speed) is constant. This change in direction constitutes an acceleration, known as centripetal acceleration.

No, it is not. Centripetal force is a 'net force' or a 'resultant force'. It is the sum of all real, physical forces (like tension, gravity, normal force, friction) that act towards the centre of the circular path. You should never add a 'centripetal force' arrow to your force diagram.

Centripetal force is the real, net force directed towards the centre of a circle that is required for an object to move in a circular path. We analyse problems from an inertial (non-accelerating) frame of reference. Centrifugal force is an apparent or 'fictitious' force that seems to push an object outwards from the centre. It only appears when you analyse the motion from within the rotating (non-inertial) frame of reference. For A-Level Further Mathematics, you should always work in an inertial frame and only use centripetal force.

Both formulae are equivalent since v = rω. Use the one that is most convenient for the information given in the problem. If the question gives or asks for linear speed (v), use F = mv²/r. If it gives or asks for angular velocity (ω), use F = mrω².