# Rotating Rod As a conical pendulum

Consider A Rigid Rod hinged at its top point Whirled around in a circle (similar to a conical pendulum). It is given that the angular velocity (and thus the semi-vertical angle) is constant. I am trying to analyse this sytem:

1. From the rotating frame, the rod is at rest. Thus, The net torque must be zero. We have to consider Pseudo forces as well. Consider a mass element $$dm$$ of length dx at a distance x from the hinge point. It rotates in a circle of radius $$xsin(\theta)$$ so it exerts a torque: $$(dm)(\omega^2)(xsin\theta)(xcos\theta)$$ about the suspension point. This must be balanced by the Torque of weight=$$dmgxsin\theta$$. Equating Both these integrals gives a relationship between $$\omega$$ and $$\theta$$.
2. However, from the ground frame , It is clear that there will be a Net torque (due to weight) about the suspension point, which made me question the fact that $$\omega$$ is constant. However, if you consider the axis of rotation,$$mg$$ cant produce a torque, since its parallel to the axis! So is that why $$\omega$$ is constant? What then , is the significance of the Net torque being non zero about the suspension point?
3. An (unsolved) illustration in my textbook asks for the " rate of change of angular momentum" of the rod. Since this is equal to the "torque", what should I consider? Torque about the suspension point? or about the axis? and why?
• You forgot to add tension of the rod – maverick Apr 23 '20 at 7:37
• @maverick Wont that always pass through the Point of suspension and axis? It shouldnt produce a torque – satan 29 Apr 23 '20 at 7:44
• yes about suspension point there wont be torque due to tension, but it can be useful to balance forces which are in equilibruim – maverick Apr 23 '20 at 7:48