1. Consider the Atwood machine below.
y
m?
x
Take the pulley to be a hoop of mass m and radius R (whose moment of inertia is $mR^2$), along
with $m_1 = 2m$ and $m_2 = m$. Take x as your generalized coordinate, with positive x measured
downwards.
(a) Using a Newtonian approach, determine the acceleration of $m_1$.
(b) Find a Lagrangian for the system. Using the Euler-Lagrange equation, determine the
acceleration of $m_1$.
(c) Using the Lagrangian from part (b), find the Hamiltonian of the system. Using Hamilton's
equations, determine the acceleration of $m_1$. Which method is easier?