Does it take energy to move something in a circle?
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Work can be calculated by $W = Fdcostheta$ where $theta$ is the angle between the force $F$ and the displacement $d$ Let's say there's a ball and a (physically ideal - no friction etc.) robotic arm situated in otherwise empty space. The arm takes the ball, moves it around in a circle, and then returns it exactly to where it started. The arm also returns to its starting position. In this case, there is no displacement overall. The ball and the robot arm are in the exact same positions as when they began. Thus, $W = Fcdot 0 cdot costheta = 0$ So no energy was required to move the ball in a circle. However, this disagrees with my intuition, because if I were to make a robot arm that would do this, I feel like I would need to give it an energy source (for example, a battery), and that