Let
be a certain radius vector of a point rotating with an angular velocity vector
. Let the unit vector in the direction of be
. Let us choose and x,y,z Cartesian coordinate system such that the z-axis aligns with the angular velocity vector and the point rotates in the x,y plane. Then we have,
In Eqn (1) w is the magnitude of the angular velocity vector. Let r be the magnitude of
, then we have,
Differentiating once again,
When seen from the rotating frame both these acceleration appear as pseudo forces with a negative sign. Now consider a infinitesimally small piece of the rotating body of mass dm. The centrifugal force and the Coriolis force experienced by this mass are respectively given by,
No comments:
Post a Comment