TUTORIAL – CENTRIPETAL FORCE
This work covers elements of the syllabus for the Engineering Council
Exam D225 – Dynamics of Mechanical Systems C103 Engineering
This tutorial examines the relationship between inertia and acceleration.
On completion of this tutorial you should be able to
• Explain and define centripetal and centrifugal acceleration.
• Explain and define centripetal and centrifugal force.
• Solve problems involving centripetal and centrifugal force.
• Derive formulae for the stress and strain induced in rotating
• Solve problems involving stress and strain in rotating bodies.
• Analyse problems
overturning on bends.
It is assumed that the student is already familiar with the following
• Newton’s laws of Motion.
• Coulomb’s laws of friction.
• Stiffness of a spring.
• The laws relating angular displacement, velocity and acceleration.
• The laws relating angular and linear motion.
• Basic vector theory.
• Basic stress and strain relationships.
All the above may be found in the pre-requisite tutorials.
ACCELERATION AND FORCE
Centripetal acceleration occurs with all rotating bodies. Consider a point P rotating
about a centre O with constant angular velocity ω (fig. 1).
The radius is the length of the line O-P. The tangential velocity of P is v = ωR. This
velocity is constant in magnitude but is continually changing direction.
Let’s remind ourselves of the definition of acceleration.
Velocity is a vector quantity and a change in direction alone is sufficient to produce a
change. It follows that a point travelling in a circle is continuously changing its
direction, velocity and hence has acceleration.
Next let’s remind ourselves of Newton’s second Law of Motion which in its simplest
Force = Mass x acceleration.
It follows t