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 Homework Statement

'm trying to calculate moment of inertia of a pulley connected to a shaft mounted on bearing by using free fall method. A load (270 g) is tied to a string and the string is wrapped around pulley.
The load is dropped from 1,6 m height then i measure rotation speed of pulley when the load is going down, plot the data and get acceleration from the slope (α up). I also measure rotation speed after the load is already on the ground until it is stopped and get the deceleration (α down).
 Homework Equations
 Στ=Iα
On speeding up:
τload  τfriction = Iαup
On speeding down:
τfriction = Iαdown
If i substitute τfriction from speeding down to speeding up equation, i get moment of inertia:
I = (τload)/(αup+αdown)
But, is this allowed? Does friction torque in speeding up is equal to friction torque in speeding down?
Additional info: the speeding up range from 0 to 38 rad/s and the speeding down from 38 rad/s to 0 rad/s.
τload  τfriction = Iαup
On speeding down:
τfriction = Iαdown
If i substitute τfriction from speeding down to speeding up equation, i get moment of inertia:
I = (τload)/(αup+αdown)
But, is this allowed? Does friction torque in speeding up is equal to friction torque in speeding down?
Additional info: the speeding up range from 0 to 38 rad/s and the speeding down from 38 rad/s to 0 rad/s.
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