# Intuitive idea behind the moment of inertia, torque

I'm not sure what idea I have of the concept of twisting moment, moment of inertia. The moment of inertia of a particle is $$mr^2$$. The torque indicates how much force $$F$$ applied at a distance d from the axis of rotation to obtain a change in angular acceleration. The greater the distance from the axis of rotation, with the same force, the greater its torque will be. Instead the law torque=inertia*acceleration links the moment of inertia (distribution of mass with respect to an axis of rotation) and angular acceleration. The greater the moment of inertia, the greater the force to be exerted to obtain a certain angular variation. So the torque can be imagined as an "angular" force? Only this idea seems wrong to me because it does not depend only on the force but also on the distance from the axis in which it is applied. So when I have a high torque, we are in both cases.

1. the particle requires a high "angular" force to obtain a certain acceleration variation
2. the particle requires a large distance from the axis of rotation to obtain a certain change in angular acceleration. What I say is wrong, can you suggest me other ideas to understand this concept even more deeply?
• Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer.
– Community Bot
May 19, 2023 at 17:53
• A way to think about it is that it applies to a conceptual "rotating body" (this is not necessarily an established term, just a way to think about things, for your benefit). Bodies with different shape, mass distribution and rotation axis can be considered different "rotating bodies". A degenerate case of that would be a single particle (point mass), so two particles at different distances from the axis can be seen as different "rotating bodies". But of course, when you're dealing with particles, you can also shift your perspective and look at how rotation laws are related to translation laws May 20, 2023 at 18:19