physics

1. Classical Mechanics
By, Geevee RK
Geevee RK 1

2. Atwood’s Machine
Geevee RK 2
By, Geevee RK

3. Masses m and 2m are connected by a light
inextensible string which passes over a pulley of mass
2m and radius a. Write the Lagrangian and find the
acceleration of the system.
Geevee RK 3

4. Geevee RK 4

5. Solution
Geevee RK 5
The system has only one degree of freedom, and x is
taken as the generalized coordinate. The length of the
string be l and the centre of the pulley is taken as zero
for potential energy.

6. Geevee RK 6

7. Geevee RK 7
Substitution of these derivatives in Lagrange’s equation gives the equation of motion: