3. Tensioning creates friction against rollers and within winding rolls.
A tensioned web pulled over a cylinder exerts pressure over the contact area equal to the tension (in force per width) divided by the cylinder radius. The friction developed between a web and roller will be equal to the coefficient of friction (μ) x pressure (P) x area (A). (Theta, θ, is wrap angle in radians, which equals 2*Pi for a layer of a wound roll.)
Friction = μPA = μ(T/r)(rwθ = μTwθ = μFTwθ
4. Tension is potential energy that can be released to drive idler rollers or keep wound rolls tight.
Idler rollers (i.e., undriven rollers) require force to overcome bearing drag and offset inertia drag during speed changes. Tension from the web delivers these forces to idler rollers as needed and available. If a series of rollers requires 100N to turn, this will take 100N out of the web. If the tension is 500N, there is sufficient tension to give to the idlers and have 400N leftover; however, if the tension is 80N, there is insufficient tension to give 100N to the rollers and some roller will not turn with the web.
Winding rolls rely on the friction of outer layers squeezing down on inner layers to create the friction that holds a roll together (except self-wound adhesive coated web that can stick roll layers together without tension). Over time, some rolls will loosen due to web relaxation, wound-in air escaping the roll, or core shrinkage. Without sufficient tension from winding, these dimensional changes in the roll may relieve all the tension in the roll and it will be lack the friction for transporting or unwinding.