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T
motion); because of friction, T > ; µ = coefficient of static or
1
2
kinetic friction between the belt and the surface of contact; β = angle
of belt to surface contact, measured in radians; e =2.718 … , base of
the natural logarithm.
Note that T is independent of the radius of the drum, and
2
instead it is a function of the angle of belt to surface contact, β . As a
result, this equation is valid for flat belts passing over any curved
contacting surface.

30 Rolling Resistance

When a rigid cylinder rolls at constant velocity along a rigid
surface, the normal force exerted by the surface on the cylinder acts
perpendicular to the tangent at the point of contact, as shown in Fig. 1-
67,a. Actually, however, no materials are perfectly rigid, and therefore
the reaction of the surface on the cylinder consists of a distribution of
normal pressure. For example, consider the cylinder to be made of a
very hard material, and the surface on which it rolls to be relatively
soft. Due to its weight, the cylinder compresses the surface underneath
it, Fig. 1-67,b. As the cylinder rolls, the surface material in front of the

a b c d
Rigid surface of contact Soft surface of contact
Fig. 1-67.

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