 #1
TomK
 69
 14
 Homework Statement:
 The correct answer is '2g/7r'.
 Relevant Equations:

torque = inertia x angular acceleration
angular acceleration = linear acceleration / radius (of curved trajectory)
torque = force x perpendicular distance (between a chosen point and line of force direction)
Note: the working (taken from iWTSE website) refers to inertia as the symbol ‘J’ (incase there was any confusion).
I found equations of motion for mass m and 2m which were ‘T1 = ma + mg’ and ‘T2 = 2mg – 2ma’, respectively. I know they are connected particles with the same acceleration ‘a’.
I have not been taught about moment of inertia, but I watched videos and read about it online. I had some questions:
In this problem, do we assume the circular pulley is a thin ring with inertia = (1/2)mr2? I looked up the inertia of different shapes, and it seems like a solid disk would, instead, be (1/4)mr2. I’m assuming the problem wants me to think of the pulley as a hollow ring.
How can we prove that a hollow ring has inertia = (1/2)mr2?
Why does this video (at 5:35) say that a wheel had moment of inertia = mr2? If this is correct, what shape is the wheel (in the video) meant to represent (is it a solid disk, a hollow ring, or something else)?
I want to clarify why the working shows a net force of 'T2 – T1', in the ‘torque = Fr’ equation. Is it because T2 is pointing down and the pulley is going to rotate in a clockwise direction?