Belts
When a belt slides on a surface, the friction
between the belt and the surface makes the tension in the belt change. If the
belt is sliding on a cylindrical surface, the tension will depend on the
contact angle and the coefficient of friction between the belt and the
cylinder.
To show this we can draw the free body
diagram of a segment of the belt
The equilibrium equations for this segment
are
Substitution of 
, using the small angle
approximations, and taking a limit yields
Combining the two equations to eliminate N
yields
Integrating this over the interval of contact
yields
The relation between tension on one side of
the contact and on the other side can be then calculated from the equation
where 
is the contact angle in radians
and 
is the
coefficient of friction.
ã Mehrdad Negahban and the
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Department of Engineering Mechanics,