Tension and acceleration of a pulley sytem attached to a block

[emmaemma08]

A 10kg block is attached to a massless cord that doesn't stretch or sag which is wrapped around a disc-like wheel for which m=5kg, I=(1/2)mR^2. If the block is allowed to drop straight down held back only by the rotation of the wheel
a) What is the tension in the rope
b) What is the acceleration of the block

I know that the tension isn't just F=mg and so am thinking it is combined with the mass of the block but don't know how to go about it

 

[LowlyPion]

Welcome to PF.

Consider the torque on the wheel.

What equations do you know for Torque?

 

[emmaemma08]

I know that torque = r x F or rFsintheta
i think it needs to use the ones related to angular momentum where torque= dL/dt= Id omega/ dt= I alpha
there was a similar question but it just said the things and didnt really progress or confirm if it was right

 

[LowlyPion]

I know that torque = r x F or rFsintheta
i think it needs to use the ones related to angular momentum where torque= dL/dt= Id omega/ dt= I alpha
there was a similar question but it just said the things and didnt really progress or confirm if it was right

OK. So you have

T = F * R = I * α

m*g*R = 1/2*M*R² * α

but α = a/R

So ... m*g = 1/2*M*a