A roll of a toilet paper of radius r is hanged on a toilet paper holder as shown. The flap of the toilet paper holder has a form of an arc of radius R and its weight W is applied at the contact point between the flap and the paper roll. The roll of the paper has a radius r and is tangent to the vertical line passing through the flap's hinge. Notice that R = r(1+2). The toilet paper is mounted so that the in one case the free end of the paper is facing the user, while in the other case it is facing the wall. Assuming that the coefficient of friction between the toilet paper and the holder flap is u determine in which case a larger force P can be applied to the free end of the toilet paper before the roll starts to rotate. Solution: P = W -(2-1) -> P W + (2-1) - 450 R - W 45 R