n.12 - pulley

The pulley in Figure has a moment of inertia of 5.0 kg ∙ m² and a radius of 0.50 m. The cord supporting the masses m₁ and m₂ does not slip, and the axle is frictionless. (a) Find the acceleration of each mass when m₁ = 2.0 kg and m₂ = 5.0 kg. (b) Find the tension in the cable supporting m₁ and the tension in the cable supporting m₂. [Note: The two tensions are different].

m_2 a = m_2 g -T_2

I alpha = T_2 R - T_1 R

m_1 a = T_1 - m_1 g

m_2 a = m_2 g -T_2

I a / R = T_2 R - T_1 R

m_1 a = T_1 - m_1 g

m_2 a = m_2 g -T_2

I a / R^2 = T_2  - T_1 

m_1 a = T_1 - m_1 g

sommo: a = (m_2 - m_1)g/(m_1+m_2+I/R^2)