What is the need to know the linear net acceleration?

[ehabmozart]

When we talk about rotational motion. I know what is the purpose of angular acceleration. We can get tangential acc. which accelerated the v tangential. Fine. Again, centripetal or radial acceleration for the change in direction but WHAT IS THE NEED TO KNOW THE LINEAR NET ACCELERATION? Take an example of a small ball connected to a horizontal fan. We can know tangential and rADIAL acc but when it looses contact, the only acc is g... Thanks to whoever contributes

 

[bp_psy]

When the fan is spinning the ball will apply a force on the blade equal to its weight. Due to Newton's third law the fan will also apply an equal opposite force on the ball therefore the ball will be static along the vertical axis. The net linear acceleration will then be only along the plane of rotation.