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406-L: Vertical Circles 1: Constant Speed

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406-L: Vertical Circles 1: Constant Speed

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These problems involve a person swinging a mass vertically. Vertical circles are good practice for understanding the nature of the centripetal force, because in a vertical circle, the centripetal force is not always equal to the same force. For practice, note that these problems are very similar to elevator problems.

Principles

The magnitude of centripetal force:

For an object to move in a circle at a constant speed, the magnitude of centripetal force must equal the value:

F_c = \frac{m v^2}{r}

Forces

In a vertical circle, there are only two forces acting on the mass:

More notes can be accessed here.

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