Spinning objects and angular acceleration

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Sundown444
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I believe I know that when an object, in terms of linear motion, accelerates, it is being resisted by inertia, thus creating so called fictitious forces. Now, that said, how does angular acceleration affect spinning objects like say, a gymnast, when they spin around the axis of rotation? Do they feel resistance and fictitious forces the same way accelerating objects in linear motion do?
 
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Yes. Here is a clear example of a fictitious force generated by rotational motion. Imagine a small package on the back seat of your car. As long as you move in a straight line at constant speed, the package is at rest relative to you. When you steer the car into a left turn, you see the package slide across the seat from left to right. You conclude that a force is suddenly acting on the package otherwise why would it start moving? A gymnast may not spin fast enough to experience an appreciable fictitious force, but the majority of amusement park rides offer fictitious force thrills.
 
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