What is the need to know the linear net acceleration?

AI Thread Summary
Understanding linear net acceleration is crucial in analyzing the motion of objects in rotational systems. In the example of a ball connected to a horizontal fan, while tangential and radial accelerations can be identified, the linear net acceleration becomes significant when the ball loses contact with the fan. At that point, the only acceleration acting on the ball is gravitational acceleration. The interaction between the ball and the fan illustrates Newton's third law, where the forces exerted are equal and opposite, maintaining the ball's position vertically. Ultimately, linear net acceleration helps in predicting the ball's trajectory once it detaches from the fan.
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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
 
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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.
 
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