The applied tension T l o a d ( φ φ ) is a function of the total angle subtended by the rope on the capstan. On the verge of slipping, this is also the frictional force, which is by definition μ μ times the normal force R ( φ φ ) . By simple geometry, the additional normal force δ δ R ( φ φ ) = R ( φ φ + δ δ φ φ ) − − R ( φ φ ) when increasing the angle by a small angle δ δ φ φ is well approximated by δ δ R ( φ φ ) ≈ ≈ T l o a d ( φ φ ) sin ⁡ ⁡ ( δ δ φ φ ) ≈ ≈ T l o a d ( φ φ ) δ δ φ φ . Combining these and considering infinitesimally small δ δ φ φ yields the differential equation