Question

When a ceiling fan rotating with an angular speed of 2.20 rad/s is turned off, a frictional torque of 0.225 n · m slows it to a stop in 25.5 s. what is the moment of inertia of the fan?

Answer 1

Here, check this out.

Answer 2

The moment of inertia of the fan is 2.60 kg-m²

Step-by-step explanation:

Given that,

Angular speed = 2.20 rad/s

Torque = 0.225 N-m

Time = 25.5 sec

We need to calculate the moment of inertia of the fan

Using formula of torque

`\tau=I* \alpha`

We know that,

The angular velocity is

`\Delta \omega=\alpha t`

`\alpha=(\Delta\omega)/(t)`

Put the value of
`\alpha` in to the formula of torque

`\tau=I**(\Delta\omega)/(t)`

`I=(\tau* t)/(\Delta\omega)`

Put the value into the formula

`I=(0.225*25.5)/(2.20)`

`I=2.60\ kg-m^2`

Hence, The moment of inertia of the fan is 2.60 kg-m²