Say we have a fixed cylinder with a radius of R. Looking at any cross section, the shear stress at a radius (r) is given by τ = G γ .
I understand that the particles at the outer radius (R) twist (or elongate) more than those at any inner radius (r) so it makes sense that they would have more stress. However, I was wondering why it is that the outer radius particles twist more than the inner in the first place if the same force is applied at all radiuses.
To make it more clear:
Picture a large circle being twisted due to a shear force F. Why is it that a circle with a smaller radius will twist less due to the same shear force F? What is the reason behind this?