A Level Maths Notes: M2 - Bodies on Slopes - Toppling
The triangular prism above is on a slope which makes an angle %theta with the horizontal. If a horizontal force is applied to the left at the top of the triangle, assuming the plane is rough enough so that the prism will topple before it slips, it will begin to topple when the vertical through the centre of gravity C passes through A.
The distance from the top of
the triangle to the centre of the base is
and
the distance from C to the centre of the base is one third of this:![]()

Angle CAB is then![]()
The prism has to move
through the extra angle
and
obviously as
increases up to the toppling angle, this extra angle will decrease,
making the prism easier to topple.