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"If an object is tilted it will topple over if a vertical line from its centre of gravity falls outside its base"

http://www.schoolphysics.co.uk/age11-14/Mechanics/Statics/text/Stability_/index.html

What does it mean by outside its base, and why does that affect stability? Also how does torque relate to this?

Thanks!

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You need to consider the torque about the point of contact between the wheel and ground.

This is an image from your link.

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If the torque about the point of contact will rotate the vehicle anti-clockwise then the vehicle does not right itself (left car and right bus) whereas if the torque about the point of contact is clockwise and the vehicle will right itself (right car and left bus).
If the vehicle will right itself then the line of action of the weight of the vehicle passes through an area which the vehicle covered, aka "the base", when it was upright ie the line of action of the weight is to the right of the point of contact between the tyre and the road and so the torque is clockwise.

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