A conical pendulum is formed by attaching a ball of mass \( m \) to a string of length \( L \), then allowing the ball to move in a horizontal circle of radius \( R \).(a) Find an expression for the tension in the string in terms of \( m \), \( L \), and \( R \). , (b) Derive an expression for the period of the pendulum in terms of \( m \), \( L \), and \( R \). :

\(T = \frac{mg}{\sqrt{1 – \frac{R^{2}}{L^{2}}}}\) \(P = 2\pi \sqrt{\frac{L\sqrt{1 – \frac{R^{2}}{L^{2}}}}{g}}\)

A conical pendulum is formed by attaching a ball of mass \( m \) to a string of length \( L \), then allowing the ball to move in a horizontal circle of radius \( R \). • Nerd Notes

AP Physics 1

2.9 Circular Motion

AdvancedFRQMathematical21.5k

Figure 1. Conical pendulum showing string, circle radius, angle with vertical, tension, and weight.

A conical pendulum is formed by attaching a ball of mass \( m \) to a string of length \( L \), then allowing the ball to move in a horizontal circle of radius \( R \).

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