The dynamics of rotational motion

When considering the kinematics of the rotational movement of an IRB, we had to introduce some new characteristics elemental angular displacement, angular velocity and angular acceleration. These values are identical to the whole rotating body, whereas the linear characteristics for all the body s MPs differ. 

In rotational motion other dynamic characteristics are also required, such as a force moment (torque) with regard to a motionless axis, a moment of inertia (MI) and an angular momentum, being in some respect analogous to the characteristics of linear motion (mass, force, momentum). 

These models do not exhaust the whole description of problems concerning rotational motion, but cover a wide range of phenomena with which the chemist may be confronted. Ignoring the logic of physics for the sake of simplification, we will start from the description of the rotation of an IRB relative to a motionless axis. We will then generalize the results obtained and apply them to the motion of an MP around a pole. 

Since all the body s points are at different distances from the axis of rotation their linear velocities and, correspondingly, their momentums are different. In order to find a body s rotation characteristics let us draw at a moving point, a mass element dm = pdV, where p is the body s density. The value 

That is, the angular momentum of a body relative to a motionless axis is the product of the moment of inertia and the angular velocity of a body s rotation relative to the same axis. (This definition according to its structure is equivalent to the definition momentum of the translational movement is a product of its mass and their velocity. ) 

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