Centre of Gravity and Centre of Mass
I was doing some moments problems the other day, and I started considering centre of mass and centre of gravity and have gotten myself rather unsure. My textbook defines centre of mass as "the point through which a single force has no turning effect", which I have an intuitive grasp of. However, it then goes on to talk about how something will topple if the centre of MASS lies outside the base. But in previous studies, the reason for toppling was given as the line of action of weight lying outside the base. But surely that corresponds to the centre of GRAVITY lying outside the base... This has led to me thinking about when a body lies in a non uniform gravitational field and hence the centre of gravity is not in the same place as the centre of mass. I understand the centre of gravity as the point from which the weight can be thought to act. So If you have a body in the aforementioned situation, surely it should rotate as the CoG would cause a moment about the Centre of Mass. Would this body then rotate about the CoM?
I was wondering if someone could define centre of gravity and explain the difference between the two so that i can be sure, and also allowing me to answer some of my puzzling issues.