[QUE/ME-08010] ME-PROBLEM

A conical pendulum moves in a circular path of radius \(a\) and string making an angle \(\alpha\) with vertical.

• Working in the inertial frame, draw a diagram showing the forces acting on the pendulum and prove that the angular frequency \(\omega\) is given by \[ \omega= \sqrt{\frac{g}{L\cos\alpha}}\]
• Draw the all forces acting on the pendulum as seen from the rotating frame in which the pendulum is at rest. Is the resultant of all forces is zero or not? If it is not zero, how do you explain that the pendulum is at rest in the rotating frame? Give a complete answer.
• Next consider a third frame rotating with angular velocity \(2\omega\), the direction of the angular velocity is the same as that of the pendulum. What is the motion of the pendulum as seen by an observer in this frame? Does the sum of all forces vanish now or not? Explain observed behaviour of the pendulum using the equation of motion as applicable in this frame.

%FigNoNumX{10,-65}{40}{0}{ConicalPendulum}