Saved Bookmarks
| 1. |
Demonstrate that in the reference frame rotating with a constant angular velocity omega about a stationary axis a body of mass m experiences the resultant (a) centrifugal force of inertia F_(cf)=momega^2R_C, where R_C is the radius vector of the body's centre of inertia relative to the rotation axis, (b) Coriolis force F_(cor)=2m[v_C^'omega], where v_C^' is the velocity of the body's centre of inertia in the rotating reference frame. |
|
Answer» Solution :For a point mass of mass `dm`, looked at from C rotating frame, the equation is `dmoverset(RARR')w=vecf+dmomega^2overset(rarr')r+2dm(OVERSET(rarr')vxxvecomega)` where `overset(rarr')r`=radius vector in the rotating frame with respect to rotation axis and `overset(rarr')v`=VELOCITY in the same frame. The total centrifugal FORCE is CLEARLY `vecF_(cf)=sumdmomega^2overset(rarr')r=momega^2vecR_c` `vecR_c` is the radius vector of the C.M. of the body with respect to rotation axis, also `vecF_(cor)=2moverset(rarr')v_cxxvecomega` where we have used the definitions `mvecR_c=sum dmoverset(rarr')r` and `moverset(rarr')c=sumdmoverset(rarr')v` |
|