Texts: 4. Wait! The Pulley has Mass? Consider the Atwood Machine from Homework #4. Now the pulley has a Mass (M) and Radius (R).
a) Write down an expression for the total mechanical energy of the system of masses and the pulley which depends only on the coordinates x and θ.
b) Obtain the equation of motion for the system by differentiating the equation E = const with respect to time.
c) Show that your equation of motion is the same as what you would obtain by applying Newton's 2nd law to the two masses and the pulley and eliminating the unknown tension from the two resulting equations.