Alzheimer's Disease is a devastating neurological disorder that is increasingly affecting the elderly population. Early and accurate detection of Alzheimer's is crucial for providing effective treatment and support for patients and their families. In this study, we present a novel approach for detecting four different stages of Alzheimer's disease from MRI scan images based on inertia tensor analysis and machine learning. From each available MRI scan image for different classes of Dementia, we first compute a very simple 2 x 2 matrix, using the techniques of forming a moment of inertia tensor, which is largely used in different physical problems. Using the properties of the obtained inertia tensor and their eigenvalues, along with some other machine learning techniques, we were able to significantly classify the different types of Dementia. This process provides a new and unique approach to identifying and classifying different types of images using machine learning, with a classification accuracy of (90%) achieved. Our proposed method not only has the potential to be more cost-effective than current methods but also provides a new physical insight into the disease by reducing the dimension of the image matrix. The results of our study highlight the potential of this approach for advancing the field of Alzheimer's disease detection and improving patient outcomes.