For example my water bottle can be quite hard to open with bare hands but if I wrap my shirt around it, it becomes very easy to open.
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By wrapping something around the bottle, you’ve essentially increased it’s diameter. By increasing it’s diameter you can apply more torque (rotational force) on the bottle top. Torque is measured by a force applied at a radius from the center point (T = F x r). This is where you get foot-pounds of torque in a car. Feet of the radius, pounds of the force applied at that radius. In smaller applications like a bottle top you’d measure ounce-inches of torque but the same thing applies. Think about using a wrench on a bolt. The longer the wrench, the more force you apply to the bolt head. By wrapping the towel around the bottle, the “wrench” is just a little bit longer and it helps get that little bit more you need.
There are several reasons. It’s true that the cloth could improve grip and or leverage. But mostly its because it cushions your hand, so the item you are trying to twist dose not stretch and pull your skin causing discomfort. You can exsert ALOT more effort if whatever you are working with is not also causing you pain.
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