When a ceiling fan is switched off its angular velocity reduces to 50% while it makes 36 rotations. How many more rotation will it make before coming to rest (Assume uniform angular retardation)
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By using equation \(\omega^{2} = \omega_{0}^{2} - 2 \alpha \omega\)
\(\left|\frac{r_0}{2}\right|^2 - w_6^c \cdot 2u(2\pi m)\) ⇒ ⇒ \(r < -\frac{3}{4} \frac{r_0^2}{4.7 \times 36}\) , ( n = 36) ..(i)
Now let fan completes total n ¢ ¢ revolution from the starting to come to rest
\(0 = m \dot{x}^2 - 2 \lambda (2m)\) ⇒ ⇒ \(p' = - \frac{(\rho v)^2}{4 \kappa \tau}\)
substituting the value of a from equation (i)
\(n = \frac{c \nu_2^2}{4 \tau} \frac{4.7 \times 36}{3 \mu_0^2} = 48\) revolution
Number of rotation = 48 – 36 = 12
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