A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from

Question

A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass md = 3.2 kg and radius R = 0.26 m. The rods each have mass mr = 1.4 kg and length L = 0.88 m.

I calculated that the moment of inertai of each rod is 0.361387, the momen of inertia of the disk to be 0.10816, and the total moment of inertia of the whole fan to be 1.915093.

The fan is then turned on and it takes 3.8s to complete 12 revolutions to get to full speed.

i calculated the the angular acceleration is 10.360664 and the final angular speed of the fan is 39.37052 rad/s.

All these calculations are correct, but when i go to calculate the final rotational energy of the fan, i get 1484.233697 J. this answer is incorrect.

What is the final rotational energy of the fan?

Explanation / Answer

or alternative

theta = averag speed*time

12*2*3.14 = (w/2)*3.8

w = (12*2*3.14*2)/3.8

w = 39.6631578 rad/s

-------

alfa = (2*theta)/t^2 = (2*12*2*3.14)/(3.8*3.8) = 10.437673 rad/s^2

w = alfa*t = 39.6631578 rad/s

KE = 0.5*I*w62 = 0.5*1.915093*39.6631578^2

KE = 1506.3796802 J

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