# Rotational Speed/Linear Speed help, need confirmation

1. Jan 30, 2012

### Elysian

1. The problem statement, all variables and given/known data

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

2. Relevant equations

energy equations

3. 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

Last edited: Jan 30, 2012
2. Jan 30, 2012

### 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.

3. Jan 30, 2012

### 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