Should I consider Linear Kinetic Energy in this Equation

[Vichakron]

Sorry If the thread name confuse you.
I want to know if I want to find the Torque from deriving Kinetic Energy and the system has Object the Rotate and the rotating cause linear motion(v).
Let's say it a Rolling Disc on the non-slope plane which has angular velocity ω and that ω cause it to move forward at velocity v.

Should I consider Linear Kinetic Energy? which I think will result,
τ=d(½Mv²+½Iω²)/dθ
τ=(I+Mr²)α
or shouldn't I?
τ=Iα.

Sorry if my question wasn't clear or my English was confusing.
Anyways, Thanks in advance.

 

[Baluncore]

Welcome to PF.
A rolling disc has potential, kinetic and rotational energy. You must account for the total.
For a disc it is the centre of rotation that is important. The moment of inertia is a function of mass and section.
You must add the angular KE about the centre to the linear KE of the centre.
Where the height of the centre changes you must also include PE.

 

[Vichakron]

Welcome to PF.
A rolling disc has potential, kinetic and rotational energy. You must account for the total.
For a disc it is the centre of rotation that is important. The moment of inertia is a function of mass and section.
You must add the angular KE about the centre to the linear KE of the centre.
Where the height of the centre changes you must also include PE.

Thank you so much for the answer.