30.1 Introduction to Torque and Rotational Dynamics
Consider a rod of mass m, and suppose I apply a force to this rod. Let's say a force like that. So we know that as a result of that applied force, the center of mass of the rod, which we can imagine is right at the center the rod, will translate with some acceleration, such that the vector f is equal to the mass of the rod times the acceleration of the center of mass. Now recall that for a rigid body, this equation will be true regardless of where on the rod I apply the force. So for example, if I draw the rod again over here, and I apply the same force, vector f, but I apply it, let's say, on the right hand side, I'll still have the same f equals ma. All I specify with f is its magnitude and direction. But for a rigid body, no matter where on the body I apply that force, the acceleration of the center of mass will be the same. Now, we know from experience, however, that the motion of the rod is different if I push it at the center at one end or at the other e...