Question

When a fan is switched on, it produces an angular acceleration of 10 rad/s*2 . Find the time it would take to reach an angular velocity of 50 rad/s. How many revolutions will the fan make before reaching this speed?

Answer 1

Answer:

1st case:

We can write the equation of motion for circular motion as:

ω

2

=ω

0

2

+2aθ

n

Now, ω=

2

ω

0

,θ=36×2π (given)

So,

4

ω

0

2

=ω

o

2

+2α×36×2π

So, α=

4×144π

−3ω

0

2

2nd case:

0=

4

ω

0

2

−2×

4×144π

3ω

0

2

×θ

So, θ=24π

So, number of rotations made by the fan before coming to rest =

2π

24π

=12

Answer 2

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