Frictional Torque Flywheel Question

[Schoomy]

Homework Statement

A spinning flywheel has rotational inertia I = 403.8 kg · m2. Its angular velocity decreases from 20.0 rad/s to zero in 256.8 s due to friction. What is the frictional torque acting?

The Attempt at a Solution

I tried using Vt = r |w| and Wav = change in theta / change in time, to get r, but I'm not sure if that's right,

Then I used I = 1/2mr^2 to get mass.

Finally, I used F=ma to get Force, using the mass found above and acceleration = change in velocity (aka 20*57) / change in time.

Then I had force and radius for plugging into torque = radius*force.

 

[rl.bhat]

Using w = wo + alpha*t, find alpha.
Torque = I*alpha.

 

[nlightner]

I would like to commend you for your attempt at solving this problem. Your approach using the equations Vt = r|w| and Wav = change in theta/change in time to find the radius is a good start. However, it is important to note that these equations are only applicable when the object is undergoing uniform circular motion, which may not be the case in this scenario where the angular velocity is decreasing due to friction.

To accurately calculate the frictional torque, you will need to use the equation T = Iα, where T is the torque, I is the moment of inertia, and α is the angular acceleration. In this case, the angular acceleration can be calculated using the equation α = (ωf - ωi)/t, where ωf and ωi are the final and initial angular velocities, respectively, and t is the time interval.

Once you have calculated the angular acceleration, you can plug it in to the equation T = Iα to find the frictional torque acting on the flywheel. This torque will be in the opposite direction of the motion of the flywheel, as it is causing the angular velocity to decrease.

I would also like to suggest that instead of using the equation I = 1/2mr^2 to find the mass, you can use the given value of the moment of inertia, which is already in kg·m2. This will save you the extra step of calculating the mass.

Overall, your approach shows good understanding of the relevant equations, but it is important to carefully consider their applicability and use the correct ones in order to obtain an accurate solution.