a 1.5 kg is connected by a rope across a 50cm diameter Solution the tension in t

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Explanation / Answer

the tension in the rope connected to the 1.5 kg block is T - mg = -ma where m is mass and a is linear acceleration (since a will accelerate down, mg >tension on the other side, we set a as a negative number) the pulley, assumed to be a disk, experiences a torque due to the difference in tension on either side of the pulley; this tension difference is (T-10), and the torque it generates is (T-10)R where R isthe radius of the pulley (0.25m) torques cause angular accelerations according to: torque = I alpha where I is the moment of inertia of the pulley and alpha is the angular acceleration the moment of inertia of a disk is 1/2 MR^2; M=pulley mass angular acceleration is related to linear acceleration via a=R alpha or alpha = a/R so we have torque = (T-10)R = 1/2 MR^2 (a/R) the R's cancel, leaving T-10 = 1/2 Ma

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