Calculating Tension in a Flywheel Drive Belt

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To calculate the tension in the lower belt of a flywheel drive system, the difference in tension between the upper and lower belts is crucial for determining the net torque responsible for the flywheel's angular acceleration. Given the upper belt tension of 135N and an angular acceleration of 1.67 rad/s², the net torque can be derived from the flywheel's radius of 0.230m. The resulting calculations reveal that the tension in the lower belt is 21.5N. Understanding the relationship between tension, torque, and angular acceleration is essential for solving similar problems in mechanical systems. Properly drawing the forces and radii can aid in visualizing and solving the equations involved.
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An electric motor turns a flywheel through a drive belt that joins a pulley on the motor and a pulley of the flywheel. The flywheel has a mass of 80 kg and a diameter of 1.25m. Its pulley has a much smaller mass and a radius of .230m. the tension in the upper (taut) part of the belt is 135N and the flywheel has a clockwise angular acceleration of 1.67 rad/s2. Find tension in lower belt.

The answer is 21.5N but I can't figure out the equations to get the answer.
 
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The difference in tension between the upper and lower belts will provide the net torque that causes the clockwis angular acceleration. Draw a drawing of the forces and radii, etc., and see where you get to...
 

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