Solving for Speed of Blocks in Uniform Pulley System

[Littlemstrouble]

Homework Statement

A pulley is a uniform cylindrical disk of mass m and radius r. The strings are massless and there is no friction. If the system is initially at rest, find the speed of the blocks (m1 and m2) after they have moved a distance d.

m1----------0
**********l
**********l
**********l
**********m2

Homework Equations

The Attempt at a Solution

The answere should be v = square root(4gd/5)

 

[Dick]

You'll need to look at the change in the gravitational potential energy of m1 and m2 and equate that to the kinetic energy of m1 and m2 plus the rotational kinetic energy of the disk. I don't believe your answer unless there is a special relation between m1, m2 and m.

 

[chaoseverlasting]

If there is no friction, then tension in the string is constant and the speed of m1=m2. Now, v(m1)=v(m2)=rw where r is the radius of the disk and w is the angular velocity.