How Do You Calculate the Moment of Inertia of a Ceiling Fan?

AI Thread Summary
To calculate the moment of inertia of a ceiling fan, first determine the angular acceleration using kinematics, given the fan's initial angular speed of 2.40 rad/s and a stopping time of 6.65 seconds. The frictional torque of 0.227 Nm can then be used in conjunction with Newton's second law for rotation to find the moment of inertia. The equation K = 1/2 I ω^2 is not directly applicable without a radius, but understanding the relationship between torque, angular acceleration, and moment of inertia is key. By applying these principles, the moment of inertia can be deduced effectively. This approach successfully led to the correct answer in the web assignment.
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Homework Statement



When a ceiling fan rotating with an angular speed of 2.40 rad/s is turned off, a frictional torque of 0.227 Nm slows it to a stop in 6.65 s. What is the moment of inertia of the fan?


Homework Equations





The Attempt at a Solution



In almost all of the moment of inertia equations, they involve a radius. there is no radius given in the problem. i tried to use K= 1/2 I w^2. I am really stuck and don't know what to do next.
 
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You don't have the data to compute the moment of inertia directly. Instead, deduce the moment of inertia by applying Newton's 2nd law for rotation. Hint: First compute the angular acceleration using kinematics.
 
Thanks so much! i just got it right on the webassign
 
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