Physics Blog 8

Last night, before I went to sleep, I turned on the light switch to see (obviously).  But because, the light in my room has an integrated fan, when I turned on the light switch, both the fan and the light came on.  Because it was really cold, I turned on my lamp and then proceeded to turn off the light switch.  As I walked over to the wall, I realized that the fan had a moment of inertia which is what we just studied in physics.  Moment of inertia, I, is generally equal to mr^2.  However, for the fan, I is different.  The fan has five blades and each blade has an I of 1/3mL^2.  This means in the system, the moment of inertia is the sum of those blades so I=5 (1/3mL^2).  One blade has a length of around 1 meter and the mass is approximately 2.2046 kg.  Therefore, I= 3.67433333 kg*m^2.  On the lowest setting, the ceiling fan takes around 25 seconds to get to its top speed of 5.66052731 rad/s. From this information we can find net torque because rotational acceleration= net torque/ I.  Alpha = change in rotational velocity/ time.  5.66052731/25= 0.226421092 rad/s ^2.  Net torque = I* Alpha so Net torque = 0.831946565Nm.