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Non-Uniform Circular Motion

If there is a force angled inwards acting on the object in circular motion counterclockwise, and the force is split into 2 components, the tangential and the radial, how does each component force affect the motion of the object?

From problems I've done, it appears that only the tangential component of the force is affecting the motion of the object, and that is used to calculate the tangential acceleration of the said object. Why can the radial component of the force be ignored?

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    $\begingroup$ "Why can the radial component of the force be ignored?" - you've stipulated that the object is in (not necessarily uniform) circular motion. Think about the implication of that stipulation for the radial component. $\endgroup$ – Alfred Centauri Sep 22 '17 at 22:14
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The radial component of force just keeps the particle moving in a circle (as opposed to a straight line, which it would do otherwise).

In a typical circular motion problem, something in the premise of the problem allows you to take for granted that there will be the right amount of radial force to keep the particle moving in a circle. For example, if the particle is confined to a circular track, the track applies whatever radial force is needed. That's why you can ignore it in calculations.

Of course, there are some problems where you can't take for granted that the particle is moving in a circle at all. In those cases, you may have to calculate the radial component of force, and if it's not the right amount required to maintain the circular motion, the particle will go off along some different trajectory.

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