Clarification on Torque/Angular Momentum in Case of Accelerating Center of Mass

[breez]

My textbook says the following:

"If the center of mass of the system is not accelerating relative to an inertial frame, that origin can be any point. However, if the center of mass of the system is accelerating, the origin can be only at that center of mass. As an example, consider a wheel as the system of particles. If the wheel is rotating about an axis that is fixed relative to the ground, then the origin for applying Eq. 11-29 can be any point that is stationary relative to the ground. However, if the wheel is rotating about an axis that is accelerating (such as when the wheel rolls down a ramp), then the origin can be only at the wheel’s center of mass."

Can someone explain to me why we must calculate torque and angular momentum with respect to the center of mass if the center of mass is accelerating?

 

[rbj]

i think it's because, if you have a body floating around in space, far from anything, if you apply a force to that body that is not in line with the center of mass, you can model that with an equivalent force going through the center of mass and, in the accelerated frame of reference, you have that force and you have D'Alembert's principle which says, in that accelerated frame of reference, that you have to have a force acting on the center of mass, which is equal to, and opposite direction of the net force acting on the body that you see in any inertial or unaccelerated frame of reference.

i dunno, but that's what i think they're talking about in your textbook.

 

[arildno]

Look closely at the assumptions and derivation of Eq. 11.29, and see why these fail in the case of an accelerating frame.