1. The problem asks to identify which statements about a system of particles are incorrect. 2. Given definitions: $$M = \sum_{i=1}^n m_i, \quad p = \sum_{i=1}^n m_i \dot{x}_i, \quad f^e = \sum_{i=1}^n f_i^e, \quad M \ddot{x} = \sum_{i=1}^n m_i \ddot{x}_i, \quad \pi = \sum_{i=1}^n (x_i - o) \times m_i \dot{x}_i$$ 3. Known physics principles: - The total momentum derivative equals the total external force: $$\dot{p} = f^e$$ (True) - The acceleration of the center of mass times total mass equals total external force: $$M \ddot{x} = f^e$$ (True) - The time derivative of angular momentum $$\dot{\pi}$$ equals the external torque $$\tau^e$$ plus terms depending on the reference point motion. 4. The statements: - $$\dot{p} = f^e$$ is correct. - $$M \ddot{x} = f^e$$ is correct. - $$\dot{\pi} = - M \dot{o} \times \ddot{x} + \tau^e$$ is correct if $$o$$ is moving. - $$\dot{\pi} = \tau^e$$ is generally incorrect unless $$\dot{o} = 0$$. - If moments are taken about the center of mass, then $$\dot{\pi} = \tau^e$$ is correct. 5. Therefore, the incorrect statements are: - $$\dot{\pi} = \tau^e$$ (without specifying the reference point is fixed) 6. Final answer: The only incorrect statement is: - $$\dot{\pi} = \tau^e$$