Question

A table-top fan has radius of 0.5 m. It starts to rotate from rest to 800 rpm within 30 seconds. Determine: 1) the angular momentum 2) how many revolutions have it gone through after 2 minutes? 3) If the rotational inertia of each blade around the center is 0.3 kg.m^ 2, what is the magnitude of the torque provided by the motor of the fan, assuming no friction?

Answer 1

Part a)

L = 25.13 kg m^2/s

Part b)

N = 3200 rev

Part c)

torque = 0.837 Nm

Step-by-step explanation:

Part a)

As we know that angular frequency is given as

`\omega = 2\pi f`

`\omega = 2\pi(800/60)`

`\omega = 83.77 rad/s`

now the angular momentum is given as

`L = I\omega`

`L = (0.3)(83.77)`

`L = 25.13 kg m^2/s`

Part b)

angular acceleration of fan is given as

`\alpha = 2\pi(800/60)/(30)`

`\alpha = 2.79 rad/s^2`

total number of revolutions are

`N = (1)/(4\pi)\alpha t^2`

`N = (1)/(4\pi)(2.79)(120^2)`

`N = 3200 rev`

Part c)

Torque is given as

`\tau = I\alpha`

`\tau = (0.30)(2.79) = 0.837 Nm`