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and a pulley that is rigidly attached to the flywheel, as shown in Figure P10.39. The flywheel is a solid disk with a mass of 80.0 kg and a diameter of 1.25 m. It turns on a frictionless axle. Its pulley has much smaller mass and a radius of 0.230 m. If the tension in the upper (taut) segment of the belt is 135 N and the flywheel has a clockwise angular acceleration of 1.67 rad/s2, find the tension in the lower (slack) segment of the belt.

Hi guys, I've managed to work this question via the method below.

torque about pulley = torque about flywheel

Tensile force x radius of pulley = moment of inertia of flywheel x angular acceleration

(T1 -T2) x radius= 0.5 x mass of flywheel x square of radius of flywheel x angular acceleration

(T1-135) 0.23 = 0.5 x 80 x 0.625^2 x 1.67

T1 =21.5N

However, can anyone explain to me why the torque about the pulley and flywheel would be the same?

Shouldn't the torque about the flywheel be greater due to its greater moment of inertia and similar angular acceleration?