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).

 

[quicknote]

I would first like to clarify that the term "unstable" can have different meanings in the context of a ladder and a thin wheel. In the case of the ladder, the man may be feeling physically unsteady or unsafe due to the height and potential for the ladder to shift or slip. This could be caused by a variety of factors such as uneven ground, the ladder not being properly secured, or the man's own balance and coordination.

In terms of the change in center of mass, this could also play a role in the man's stability on the ladder. As he climbs higher, his center of mass shifts higher up the ladder, making it more difficult for him to maintain his balance. Additionally, if the man is carrying any objects with him, this could further impact his center of mass and stability.

As for the thin wheel staying upright on its rim while rolling but falling down when it stops, this is due to the concept of rotational inertia. When the wheel is rolling, its rotational inertia keeps it upright and stable. However, when it stops, the rotational inertia is no longer present and the wheel will fall down due to the force of gravity. This can be demonstrated by spinning a top - it stays upright while spinning due to its rotational inertia but will eventually fall down when it stops spinning.

In summary, both the man's stability on the ladder and the thin wheel's behavior can be explained by principles of physics such as center of mass and rotational inertia. Understanding these concepts can help us better understand and predict the behaviors of objects and people in different scenarios.