I want to calculate the minimum force $F$ required to tip the above shape about the pivot point (orange dot). Assume the mass of the vertical portion is negligible compared to the base. Assume that the center of mass is where the purple dot is.
I know the torque of due to the center of mass is $\tau_{com} = m g r$$\tau_{\text{com}} = m g r$, but I'm having trouble conceptualizing the torque due to $F$, since it is off-axis. My guess is that it's either $\tau_F = F L$, or $\tau_F = F \sqrt{(L+h)^2 + r^2} \cdot sin(180-tan^{-1}(\frac{L+h}{r})$$\tau_F = F \sqrt{(L+h)^2 + r^2} \cdot \sin(180-\tan^{-1}(\frac{L+h}{r})$.
Is it one of those, or am I completely wrong?
