so i need to calculate the moment of inertia of the pulley and the angular

acceleration of the pulley.

mass A = 9kg
Mass B = 15kg
Inner pulley= Mass 3kg R= 6cm
Outerpulley= mass 7kg R=12cm
both are disks glued together.
it is a composite pulley with two masses hanging. Mass A on the outer pulley held by a tension on the left side, and another Mass B on the inner pulley held by a tension on the right side.

For inertial i did I= 1/2mr^2+ 1/2mr^2

then for alpha i did
RT2-RT1= Ialpha

Body diagram to find T of both then plug into equation and solve for alpha

is this corect?

Your overall approach is correct, but there are a few corrections and additional steps needed to accurately calculate the moment of inertia and angular acceleration of the pulley.

To calculate the moment of inertia of the pulley, you need to consider its composite structure. Since the inner and outer pulleys are glued together, you need to treat them as a single system. The moment of inertia of a solid disk is given by the formula (1/2)mr^2, where m is the mass and r is the radius. Therefore, for the composite pulley, the moment of inertia can be expressed as:

I = (1/2)(mass_inner_pulley)(radius_inner_pulley)^2 + (1/2)(mass_outer_pulley)(radius_outer_pulley)^2

So, in your case, the moment of inertia would be:

I = (1/2)(3 kg)(0.06 m)^2 + (1/2)(7 kg)(0.12 m)^2

Next, to find the angular acceleration (α) of the pulley, you can use Newton's second law for rotational motion:

Στ = Iα

where Στ is the net torque acting on the pulley. In this case, the net torque is given by the difference in tension (T) on the left and right sides of the pulley, multiplied by the radius of the pulley. So the equation becomes:

T_left * radius - T_right * radius = I * α

Now, for the body diagram, you need to consider the forces acting on the masses A and B. Since mass A is on the outer pulley, it experiences a tension T_left, and mass B on the inner pulley experiences a tension T_right.

So, the equation for mass A would be:

T_left - mass_A * g = mass_A * acceleration

The equation for mass B would be:

T_right - mass_B * g = mass_B * acceleration

To solve for the tensions T_left and T_right, you can use the fact that they are equal in magnitude. So, you can set T_left equal to T_right and solve the resulting system of equations for acceleration.

Finally, once you have the tensions T_left and T_right, you can substitute them back into the torque equation to find the angular acceleration α.