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.

Question

1. Find an expression for the tension T in the string.
(Express your answer in terms of the variables L, m, r and appropriate constants.)

2. Find an expression for the ball's angular speed (omega).
(Express your answer in terms of the variables L, r and appropriate constants.)

3. What is the tension for a 500g ball swinging in a 20 cm radius circle at the end of a 1.0 m-long string?

4. What is angular speed (in rpm) or a 500g ball swinging in a 20-cm-radius circle at the end of a 1.0-m-long string?

Answer 1

1. mg/(cos(sin^-1(r/L)))

Answer 2

1) T = m*g*L / sqr^ L^2 - r^2