The moment of inertia of Pulley is 8.89 kgm².
Angular acceleration of the pulley
The angular acceleration of the pulley is calculated as follows;
[tex]\alpha = \frac{\omega_f - \omega _i}{t}[/tex]
where;
- ωi is the initial angular velocity = 0
- ωf is the final angular velocity = 17 rev/min
- t is the time of motion
Final angular velocity in radian per second is calculated as
[tex]\omega _f = 17 \frac{rev}{\min} \times \frac{2\pi \ rad}{1 \ rev} \times \frac{1\min}{60 \ s} = 1.78 \ rad/s[/tex]
Now, solve for angular acceleration
[tex]\alpha = \frac{1.78-0}{5} \\\\\alpha = 0.36 \ rad/s^2[/tex]
Moment of inertia of the pulley
The the moment of inertia of Pulley is determined using the formula for torque.
Iα = Fr
I = Fr/α
I = (16 x 0.2)/(0.36)
I = 8.89 kgm²
Thus, the moment of inertia of Pulley is 8.89 kgm².
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