A mass m is free to move without friction in a hoop of radius R, which has no mass. The hoop rotates with a constant angular velocity ω around its vertical diameter (see the figure below). (a) Write the Lagrangian of the system as a function of θ. (b) Find the equation of motion for mass m. (c) Determine the equilibrium angles, that is, the conditions for which ˙θ = ¨θ = 0 . Consider two cases: ω² ≥ g/R and ω² < g/R.
A mass m is free to move without friction in a hoop of radius R, which has no mass. The hoop rotates with a constant angular velocity ω around its vertical diameter (see the figure below). (a) Write the Lagrangian of the system as a function of θ. (b) Find the equation of motion for mass m. (c) Determine the equilibrium angles, that is, the conditions for which ˙θ = ¨θ = 0 . Consider two cases: ω² ≥ g/R and ω² < g/R.
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A mass m is free to move without friction in a hoop of radius R, which has no mass. The hoop rotates with a constant
(a) Write the Lagrangian of the system as a function of θ.
(b) Find the equation of motion for mass m.
(c) Determine the equilibrium angles, that is, the conditions for which
˙θ = ¨θ = 0 .
Consider two cases: ω² ≥ g/R and ω² < g/R.
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