Rotational motion

As we already mentioned in the Introduction, the motion of a rigid body can be very complex, but in these pages we will approach it in a simplified way.

Throughout these pages we will focus only on two cases:

  • A rigid body rotates with respect to a fixed axis.
  • A rigid body rotates with respect to an axis that passes through its center of mass and moves.

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In the first case the equation that describes the motion is Newton’s second law for rotation:

With the help of the above equation we will determine the angular acceleration of the solid and its movement will be completely described.

In the second case we will need two equations to describe the movement of the solid. The first one is Newton’s second law for rotation, but calculating the torques of the forces with respect to the center of mass:

With the help of this equation we will determine the angular acceleration of the rigid body in its rotational motion with respect to an axis that passes through its center of mass.

The translational motion of the center of mass of the rigid body is described by the second law of Newton applied to it:

From the above equation we obtain the linear acceleration of the center of mass, which behaves as if the whole mass of the solid was concentrated at that point.

Note that to correctly apply both equations it is necessary to determine the external forces acting on the solid.

 

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