A uniform disk of mass 2M and radius a can roll along a rough horizontal rail. A particleof mass m/2 is suspended from the centre C of the disk by a light inextensible string oflength b. The whole system moves in the vertical plane through the rail. Take as generalisedcoordinates 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? 2. A uniform disk of mass 2M and radius a can roll along a rough horizontal rail. A particleof mass m/2 is suspended from the centre C of the disk by a light inextensible string oflength b. The whole system moves in the vertical plane through the rail. Take as generalisedcoordinates 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

The kinetic energy of the disk is, 12Mx˙2+1212Ma2x˙a2=34Mx˙2And the kinetic energy of the particle…

Answered: A uniform disk of mass 2M and radius a…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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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?

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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