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From your question and tag words it sounds like you are talking about centripetal force. This is the force of circular motion where the force is perpendicular to the straight line velocity of the moving object, always pointing to the center of the circle. This is what keeps the object moving in a circular motion and not moving away from the circle tangentially. The general equation for the centripetal force is:
F = mr4pi^2/T^2
where F is the centripetal force, m is the mass of the object, r is the radius of the circle, and T is the time of the period of one revolution around the circle.
In terms of careers that would make use of this, an engineer is the first thing that comes to mind, particularly chemical engineers. Chemical engineers are concerned with the physics behind large chemical reactors that are used to perform chemical reactions on an industrial scale. One item of particular concern to chemical engineers is the high speed stirring of several thousands of pounds of potentially harmful and expensive chemicals. If the reactor and the contents inside are not perfectly balanced while stirring, the centripetal force will not be balanced, thus putting stress on the reactor and its components, possibly leading to a breakdown or even a release of chemicals. This can pose a safety/cleanup risk and will certainly cost the manufacturer money in repairs and lost time. So a chemical engineer is most definitely interested in studying centripetal force.
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