As in Figure P10.57, toppling chimneys often break apart in mid-fall because the mortar between the bricks

Question:

As in Figure P10.57, toppling chimneys often break apart in mid-fall because the mortar between the bricks cannot withstand much shear stress. As the chimney begins to fall, shear forces must act on the topmost sections to accelerate them tangentially so that they can keep up with the rotation of the lower part of the stack. For simplicity, let us model the chimney as a uniform rod of length l pivoted at the lower end. The rod starts at rest in a vertical position (with the frictionless pivot at the bottom) and falls over under the influence of gravity. What fraction of the length of the rod has a tangential acceleration greater than g sin θ, where θ is the angle the chimney makes with the vertical axis?

As in Figure P10.57, toppling chimneys