How to go from angular to linear velocity.

What is the earliest point in the universe that we can observe? why can’t we see back further than this?

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.

In one or two sentences, describe how you did in the balancing game. in a few more sentences, explain one strategy you learned for balancing more complex equations.