Question

A ceiling fan having moment of inertia 2 kg metre square attains its maximum frequency of 60 RPM in 25 seconds. What is its angular acceleration?​

Answer 1

Answer:

moment of inertia =2kgmeter square

maximum frequency=60rpm

time =25sec

initial frequency v0 =0rps

final frequeny. v1=60rpm convert into rps=1rps

initial angular velocity=w=2πv0=0rad/sec

final angular velocity w1=2πv1 =2π*1=2πrad/sec

angualr acceleration =(w1-w)/t

=2π/25rad/sec square

Answer 2

Given:

A ceiling fan having moment of inertia 2 kg metre square attains its maximum frequency of 60 RPM in 25 seconds.

To find:

Angular acceleration?

Solution:

First of all, let's convert RPM to rad/s :

$60 \: rpm = \dfrac{60 \times 2\pi}{60} = 2\pi \: rad/s$

• Now, let angular acceleration be $\alpha$.

$\alpha = \dfrac{ \omega2 - \omega1}{t}$

$\implies \alpha = \dfrac{ 2\pi - 0}{25}$

$\implies \alpha = \dfrac{ 2\pi}{25} \: rad/ {s}^{2}$

So, angular acceleration is 2π/25 rad/s².