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A conical pendulum of string length l swings in a horizontal circle with angular velocity omega, the string making angle theta with the vertical. If the string tension is T, which equation is correct?

1. T = m omega² l
2. T sin(theta) = m omega² l
3. T = mg cos(theta)
4. T = m omega² l sin(theta)

Correct answer: T = m omega² l

Solution

Horizontally, T sin(theta) = m omega² r = m omega² (l sin(theta)), so the sin(theta) cancels giving T = m omega² l.

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