Question

a fan is rotating at 90rpm.it is then switched off. it stops after 21 revolutions.calculate the time taken by it to stop assuming that the frictional torque is constat​

Answer 1

Topic :- Rotational Dynamics

$\maltese\:\underline{\sf AnsWer :}\:\maltese$

We are given Initial frequency as 90 rpm. First we need to convert this Initial frequency to rps :

$:\implies \tt Initial \: frequency = 90 rpm$

$:\implies \tt Initial \: frequency = \dfrac{90}{60}$

$:\implies \tt Initial \: frequency = \dfrac{9}{6}$

$:\implies \underline{ \boxed{ \tt Initial \: frequency = 1.5 \: rps}}$

As the fan will switched off the final frequency will be 0 rps.

• Number of revolutions = 21
• Initial frequency = 1.5 rps
• Final frequency = 0 rps
• Time taken = ?

$\dashrightarrow\:\:\tt Number \: of \: revolutions = \bigg(\dfrac{Initial \: frequency - Final \: frequency}{2} \bigg)\times Time$

$\dashrightarrow\:\:\tt 21 = \bigg(\dfrac{1.5 - 0}{2} \bigg)\times Time$

$\dashrightarrow\:\:\tt 21 = \bigg(\dfrac{1.5}{2} \bigg)\times Time$

$\dashrightarrow\:\:\tt 21 \times 2 = 1.5 \times Time$

$\dashrightarrow\:\:\tt 42 = 1.5 \times Time$

$\dashrightarrow\:\:\tt Time = \dfrac{42}{1.5}$

$\dashrightarrow\:\: \underline{ \boxed{\tt Time = 28 \: seconds}}$

Answer 2

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♧Question♧

• A fan is rotating at 90rpm.it is then switched off. it stops after 21 revolutions.calculate the time taken by it to stop assuming that the frictional torque is constat

♧Answer♧

• ☆First we have 90rpm by 60 to change into 90rps.
• ➠90/60
• ➠9/6
• ➠1.5rps

Given data:-

• Initial frequency = I.F= 1.5rps
• Final frequency= F.F = 0rps ( it is 0 because the fan is stop after some time )
• Number of revolution= N.R = 21

To find:-

• Time = t = ?

Solution:-

☆We will use this formula,

[ N.R = ((I.F - F.F)/2) × t ]

• Put values in the formula,
• ➠21 = ((1.5 - 0)/2) × t
• ➠21 = ( 1.5/2 ) × t
• ➠21 × 2 = 1.5 × t
• ➠42 = 1.5 × t
• ➠4.2/1.5 = t
• ➠t = 28 seconds Ans

☆So the fan will take 28 seconds to stop assuming that the frictional torque is constat.

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