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Mechanics
 
Centripetal Force
The forces acting on the mass M are in equilibrium, so we can say (considering magnitudes only)
where Te is the tension in the string
The force causing the centripetal acceleration is the horizontal component of the tension in the string.
Therefore, we can write
It is clear from the diagram that
As shown here the centripetal force Fc is given by
So we have
or
 
This means that, if a graph of ω2 against M is a straight line passing through the origin, we have verified the relation between centripetal force and angular speed (assuming we keep L constant).
 
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