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Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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A uniform disk of mass 2M and radius a can roll along a rough horizontal rail. A particle
of mass m/2 is suspended from the centre C of the disk by a light inextensible string of
length b. The whole system moves in the vertical plane through the rail. Take as generalised
coordinates x, and θ the angle between the string and the downward vertical.
(a) Write the Lagrangian for the system.
(b) Obtain Euler-Lagrange equations.
(c) Identify the cyclic coordinate and find the corresponding conserved momentum (say px).
(d) Is px the horizontal linear momentum of the system?

Transcribed Image Text:2. A uniform disk of mass 2M and radius a can roll along a rough horizontal rail. A particle
of mass m/2 is suspended from the centre C of the disk by a light inextensible string of
length b. The whole system moves in the vertical plane through the rail. Take as generalised
coordinates x, and 0 the angle between the string and the downward vertical.
(a) Write the Lagrangian for the system.
(b) Obtain Euler-Lagrange equations.
(c) Identify the cyclic coordinate and find the corresponding conserved momentum (say pa).
(d) Is pr the horizontal linear momentum of the system?
а
•8
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