Determine the angular speed.. please?
Use conservation of energy to determine the angular speed of the spool after the 3.00 kg bucket has fallen 4.75 m, starting from rest. The light string attached to the bucket is wrapped around the spool and does not slip as it unwinds.
What about the moment of inertia of the spool? And what about it radius?
E_ini = E_fin
E_ini = m g h
E_fin = (1/2) m v^2 + (1/2) I omega^2
omega = v/R
where
E_ini and E_fin are the initial and final energy, respectively
v the final speed of the bucket
m it mass
I the moment of inertia of the spool
R its radius
omega the final angular velocity of the spool
Then
m g h = (1/2) m omega^2*R^2 + (1/2) I omega^2
and
omega = sqrt[(2mgh)/(mR^2+I)]
If you want the numerical value of omega, you should provide R and I. Even assuming I is negligible (m R^2 >> I), we need the radius.