A1.4kg block and a 2.7kg block are attached to opposite ends of a light rope. the rope hangs over a solid, frictionless pulley that is 27cm in diameter and has a mass of 0.78kg .when the blocks are released, what is the acceleration of the lighter block?

Explanation:

27 cm = 0.27 m

As the blocks are hanging on 2 sides of the pulley, their difference in mass would generate a net force toward the heavier side:

Let g = 9.81 m/s2

F = g(2.7 - 1.4) = 9.81*1.3 = 12.753 N

This force would generate a torque at 0.27 m moment arm

T = F*r = 12.753*0.27 = 3.44 Nm

The moment of inertia of the solid disk:

Where m = 0.78 kg is the disk mass and R = 0.27 m is the radius of the disk.

So the angular acceleration of the torque is

So the linear acceleration is its angular component times radius

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