An object (such as a mug of coffee, expensive phone, laptop) is placed on an inclined plane and remains stationary due to friction. After an interval (observed as random) it will begin to move (and hence probably fall off).
Explain this in terms of classical mechanics.
(My guess is that it's due to a tiny amount of vibrational energy reducing the normal moment and hence the frictional force).
I doubt there is single answer for this because I suspect it varies from system to system. However as a general rule this is related to non-Newtonian flow.
If you take a thick fluid like treacle and apply a constant force to it then the fluid will flow, and how fast it flows depends on the thickness of the fluid. There are fluids like pitch that are so thick they appear to be solid, but they do flow if left for long enough. The flow rate is given by Newton's law of viscosity:
$$ \dot\gamma = \frac{\sigma}{\eta} $$
where $\dot\gamma$ is the strain rate and $\sigma$ is the shear stress (effectively flow rate and force respectively) and $\eta$ is a constant called the viscosity that tells us about the thickness of the fluid.
But in some fluids the viscosity isn't a constant. Typically the viscosity decreases as the fluid starts flowing, a behaviour called shear thinning. If you apply a steady force to a shear thinning fluid then at first it will flow only very slowly. However as the fluid flows the flow causes the fluid to get thinner and it flows faster. The increased flow rate causes the fluid to become still thinner and a vicious cycle develops.
Typically the flow rate increases in a roughly exponential manner with time, so the fluid appears at first not to be moving but will at some point suddenly accelerate and flow fast. The obvious example of this is tomato ketchup. I would guess most of us have experienced its tendency not to flow out of the bottle then come out in rush$^1$.
Anyhow, your coffee mug sliding down an inclined plane is not a fluid, but the interface between bottom of the mug and the surface on which it rests can behave in a similar way. That is, if you could look at the contact between the mug and the surface with a super powerful microscope you'd see the molecules at the interface were in motion when the mug was apparently still. This motion reduces the adhesion between the surfaces so the flow rate increases, and as with a shear thinning fluid a vicious cycle develops and the sliding rate increases exponentially.
This tends to happen most with soft materials. I had a polyurethane case for my phone that was particularly prone to doing this, polyurethane having fairly mobile molecules on its surface. With two hard clean surfaces, e.g. glass on glass, it wouldn't happen though in real life all glass surfaces are coated with an adsorbed layer of organic molecules that can flow. So even glass can show this behaviour.
$^1$ strictly speaking the flow of tomato ketchup is more complicated than simple shear thinning as the viscosity is also time dependent. This time dependent behaviour is called thixotropy.
