Question

struggling with how to set this one up. any ideas? I've done the incline plane and pully problems before but I don't know how to tie in the radius/weight of the pully

Answer 1

The sum of torque experienced by the pulley
\[\sum\tau = I\alpha\]
where \(I\) is the moment of inertia of the pulley,

and \(\alpha\) is the angular accereration.

Answer 2

the torque is coming from the tension (T\) in the string,
where the radius of the pulley is \(r\)
\[\tau = tT\]

Answer 3

the moment of inertia \(I\), of a rotating cylinder (the pulley) of mass \(m\),and radius \(r\),is
\[I = \tfrac12mr^2\]

Answer 4

whoops **

\[\tau = rT\]

Answer 5

So how do I use that to find the acceleration of m1?

Answer 6

\[\alpha = a/r\]

Answer 7

so the acceleration of the pully/the radius gives me the answer?

Answer 8

assuming the string stay at tension, the acceleration of the blocks will be equal, and proportional to the angular acceleration of the pulley.

Answer 9

so theta and the masses of the blocks play no part in the calculations? I feel like that's a lot of values not being used.

Answer 10

what are your free body diagrams for the masses ?

Answer 11

I am extremely lost.....