Question

A bead of mass m slides without friction along a rod, one end of which is pivoted in such a way that the rod can be revolved about the z-axis at a constant angle a, as shown in Fig. 2. The rod is driven with constant angular velocity w about Oz. Use Lagrange method to derive the equation of motion for the bead. Use the distance of m from the origin as generalized coordinate and discuss the motion of the bead. In what circumstances will the head be in equilibrium on the rod? NOTE: The bead is sliding without friction. .. mg Fig. 2.

Answer 1

Sol:- Z (2)926 w Img Sini) mg १ y 4 X As shown in figure red with mass m'an it is in Rotation. motion of Rodi force along rod causing mass to slide Along rod = mg cos(x) {mlar < GM mg Sing) mg RHE Also mass is Acted up Aw by Centripetal force (FC) Fc=mron 'Rv or radius of rotation of mass in at Anly constant Fer Force is provided lay horizental Reaction at support o

force Bead will be in equalibrium Aw rod when net on bead along rod is zero. If frictiow along oud is equal to force due to weight (mg) along rod. Then mass is in equilibrium along rod. So, for equilibrium of dead Aw.rod Friction mg coslo)