Rotational Speed/Linear Speed help, need confirmation

[Elysian]

Homework Statement

A 4 kg block, 10m above the ground is attached to a long cord which is wrapped around a 1050 g iron disc of radius 40 cm. The system is originally at rest, afterwards the block is let go and allowed to fall. From the time the block is let go to when the block crashes with the ground, calculate the speed of the block as it hits the ground
the number of revolutions the disc makes

Homework Equations

energy equations

The Attempt at a Solution

For the linear speed as it hits the ground i used

mgh = .5m1v² + .5Iω²

Where I = 1.050*.4²*.5
m1 is the mass of the disc + the block, so 1.050+5kg = 5.050 kg
I replaced ω with v/r, to have the equation

mgh = .5mv² + .5I(v/r)²

Is this correct?

For the revolutions, I would probably use

θ = ωt + .5αt², where t = (ωf - ωi)/α

is this part correct?

Thanks

 

[Spinnor]

The m in your mgh should be 4 kg as that is the mass that falls to the ground? I'm confused with the number you wanted to use for m.

 

[Elysian]

Oh god my bad sorry, I meant the m in .5 mv^2 should be 4+1.050, so 5.05, idk where i got 1.5 from, i replaced m1 with the mass in .5mv^2, and mgh has a mass of 4 as you said. Sorry for the confusion