Man Standing Near Top of Ladder Unstable - Why?

[chound]

A man standing near the top of the ladder fells unstable. Why?
Is it due to the change in centre of mass?
A thin wheel can stay upright on its rim if it is rolled but when it stops it falls down, Why?

 

[Astronuc]

Both problems involve center of mass, or rather the moment about the CM.

When the person ascends a ladder leaning against a wall, the weight moves from the base toward the other end. Over the base, the weight acts on the base, but over the other end, the moment increases. Also geometrically, in a static situation the weight acting downward causes a lateral force at the base which increases as the person moves toward the top.

As for the wheel, the rotation of the mass causes a torque which acts to prevent the wheel from tipping or falling over. The torque is linear proportional to the rotational speed. When the forward speed decreases toward zero, with a concommitant reduction in angular velocity, the torque diminishes toward zero, and at some point, the force of gravity pulls the wheel over (the CM of the well is usually out of the plane of the wheel).