Centre of gravity and dynamics

[chandran]

in a dynamics problem the example in a book shows a circular rod rotating about a pin at the end. Now the author says that the
cg of the rod is at a point and he draws an acceleration vector from cg towards the pin and says that it is the normal acceleration and a perpendicular component called tangential acceleration. My question is why these two acceleration vectors should be drawn from cg why not
from any other point in the rod and the problem solved

 

[whozum]

If the acceleration was to be on any part aside from the CM then there would be a torque about the center of mass. An acceleration at the CM gives pure translational accel.

 

[arildno]

in a dynamics problem the example in a book shows a circular rod rotating about a pin at the end. Now the author says that the
cg of the rod is at a point and he draws an acceleration vector from cg towards the pin and says that it is the normal acceleration and a perpendicular component called tangential acceleration. My question is why these two acceleration vectors should be drawn from cg why not
from any other point in the rod and the problem solved

C.G.'s accelerations are directly related to the EXTERNAL forces acting upon the body.
The acceleration of any other point is related to the forces acting at that point (mass), whether those forces are external or internal to the body as a whole.

 

[FredGarvin]

What is the definition of a CG? It's a theoretical point that all of the mass can be thought of existing in an object. If you are looking for forces and only have an acceleration, shouldn't it seem that the accelerations would make the most sense to be applied at the point where all of the mass exists?