TUTORIAL – COUPLED BODIES
This work covers elements of the syllabus for the Edexcel module
21722P HNC/D Mechanical Principles OUTCOME 4.
On completion of this tutorial you should be able to do the following.
• Predict the common speed when two freely rotating bodies
are suddenly coupled together.
• Calculate the energy lost that occurs when two freely
rotating bodies are suddenly coupled together.
It is assumed that the student is already familiar with the following
• Angular motion.
• Moment of inertia.
• Angular momentum.
• Angular kinetic energy.
• Conservation of momentum.
All these above may be found in the pre-requisite tutorials.
This short topic is about angular momentum and the way it is used to predict what
happens when two rotating machines are coupled together. To do this you need to
understand the law of conservation of momentum.
CONSERVATION OF MOMENTUM
In the tutorial on linear momentum, the law of conservation of momentum was
applied to bodies that collide or become joined. The law stated that “The total
momentum before the event is equal to the total momentum after the event”. In this
tutorial we will apply the same law to rotating bodies that become joined (coupled).
Angular Moment is the product of angular velocity ω and moment of inertia I. The
momentum of a flywheel is hence Iω.
Consider two flywheels, initially rotating independently, that are connected by
engaging a clutch.
Total initial total momentum I1ω1+ I2ω2
After connection they will have a single moment of inertia I3 and a single speed ω3
and the final momentum will be I3ω3.
Because momentum is conserved we may equate the initial and final momentum.
I1ω1 + I2ω2 = I3ω3.
And it follows that I3 = I1+ I2
Although momentum is conserved, energy is not and there will be a loss of energy
during the coupling. This is due to friction in the clutch as the plates slip. The only
energy involved here is