Question

A fan KS rotating with angular velocity 100 rev/ sec
Then after switched off it takes 5mins to stop.

Find the total number of revolution made before it stops..

Answer 1

Correct question:

A fan is rotating with angular velocity 100 rev/ sec

Then after switching it off it takes 5mins to stop.

Find the total number of revolution made before it stops.

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Given:

• $\dfrac{N}{t}$ = 100 rev/ sec
• Final Angular velocity = ω = 0 rev/sec
• Time = t = 5mins

━━━━━━━━━━━━━━━

Need to find :

• Number of revolutions =?

━━━━━━━━━━━━━━━

Solution:

Time = 5mins

→ Time = 5 × 60 secs

→ Time = 300 secs

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$\implies \omega\: o = \dfrac{2\pi \: N}{t}$

$\implies \omega\: o= 2\pi \times ( \dfrac{N}{t} )$

$\implies \omega\: o = 2\pi \times 100$

$\implies \omega\:o = \: 200\pi$

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we know,

$\theta = \dfrac{ \omega + \omega \: o}{2} \times t$

$\implies \theta = \dfrac{0 + 200 \: \pi}{2 } \times 300$

$\implies \theta = 3 \times {10}^{4} \pi$

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Also we know,

$N= \dfrac{ \theta}{2\pi}$

$\implies N = \dfrac{3 \times {10}^{4} \pi}{2\pi}$

$\implies N = \dfrac{3 \times {10}^{4} }{2}$

$\red{\bold{\large{\boxed{\implies N=15000\: revolutions}}}}$

Answer 2

Given:

\dfrac{N}{t}

t

N

= 100 rev/ sec

Final Angular velocity = ω = 0 rev/sec

Time = t = 5mins

━━━━━━━━━━━━━━━

Need to find :

Number of revolutions =?

━━━━━━━━━━━━━━━

Solution:

Time = 5mins

→ Time = 5 × 60 secs

→ Time = 300 secs

━━━━━━━━━━

i

\implies \omega\: o= 2\pi \times ( \dfrac{N}{t} )⟹ωo=2π×(

t

N

)

\implies \omega\: o = 2\pi \times 100⟹ωo=2π×100

\implies \omega\:o = \: 200\pi⟹ωo=200π

━━━━━━━━━━

we know,

\theta = \dfrac{ \omega + \omega \: o}{2} \times tθ=

2

ω+ωo

×t

\implies \theta = \dfrac{0 + 200 \: \pi}{2 } \times 300⟹θ=

2

0+200π

×300

\implies \theta = 3 \times {10}^{4} \pi⟹θ=3×10

4

π

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Also we know,

$\implies N = \dfrac{3 \times {10}^{4} \pi}{2\pi}⟹N= </p><p>2π</p><p>3×10 </p><p>4</p><p> π$

.

$N= \dfrac{ \theta}{2\pi}N= </p><p>2π</p><p>θ$

⟹N=

.

⟹N=15000revolutions