(Solved):   Calculate the angular acceleration of the cylinder The ropes in the FIGURE 6 below are ea ...

 

Calculate the angular acceleration of the cylinder

The ropes in the FIGURE 6 below are each wrapped around a cylinder, and the two cylinders are fastened together. The smaller cylinder has a diameter of \( 10 \mathrm{~cm} \) and a mass of \( 3.0 \mathrm{~kg} \); the larger cylinder has a diameter of \( 20 \mathrm{~cm} \) and a mass of \( 15 \mathrm{~kg} \). The ends of the ropes are connected to \( 2.5 \mathrm{~kg} \) and \( 4.0 \mathrm{~kg} \) respectively. Calculate the angular acceleration of the cylinders? Assume that the cylinders turn on a frictionless axle.