Question

An electric fan rotating at 5 rev/sec is switched off. It comes to rest in 10 sec. The uniform deceleration is?

Answer 1

Answer:

$\huge\bold\green{Given:}$

Revolution/sec = 5 rev/sec

time taken to stop = 10 sec

Deceleration = $\bold{\frac{v\:-\:u}{time}}$

= $\bold{\frac{0\:-\:5}{10}}$

= $\bold{\frac{-5}{10}}$

= $\bold{\frac{-1}{2}}$

$\huge\bold{\boxed{\boxed{Declaration\:=\:-0.5m/s^2}}}$

Answer 2

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Angular\:accleration=-0.5\:rad/sec^{2}}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about an electric fan rotating at 5 rev/sec is switched off. It comes to rest in 10 sec.

• We have to find uniform deceleration.

$\underline \bold{Given : } \\ \implies Initial \: angular \: velocity(\omega_{0}) = 5 \: rad/sec \\ \\ \implies Final \: angular \: velocity(\omega )= 0 \: rad/sec \\ \\ \implies Time(t) = 10 \: sec \\ \\ \underline \bold{To \: Find : } \\ \implies Angular \: acceleration(\alpha) = ?$

• According to given question :

$\bold{Using \: first \: eqn \: of \: circular \: motion : } \\ \implies \omega = \omega_{0} + \alpha t \\ \\ \implies 0 = 5 + \alpha \times 10 \\ \\ \implies 10 \alpha = - 5 \\ \\ \implies \alpha = \frac{ \cancel{- 5}}{ \cancel{10}} \\ \\ \implies \alpha = \frac{ - 1}{2} \\ \\ \bold{\implies \alpha = - 0.5 \: rad \: /{sec}^{2} }$