A ceiling fan starting from rest reaches an angular velocity of 30 rev/sec in 5 sec. What is the angular displacement of the fan during these 5 sec?

Can you show me the steps need to figure this question out?

Thanks!

φ=ω₀t±εt²/2

ω=ω₀±εt
ω=2πn
ω₀=2πn₀=0

φ=εt²/2
2πn= εt
ε=2πn/t
φ=εt²/2=2πn t²/2t= πn t=3.14•30•5=...(rad)

Sure! To find the angular displacement of the fan during the 5-second interval, we can use the formula:

angular displacement = initial angular velocity * time + 1/2 * angular acceleration * time^2

First, let's find the initial angular velocity:

The angular velocity of the fan starting from rest is 0 rev/sec.

Next, let's find the angular acceleration:

angular acceleration = (final angular velocity - initial angular velocity) / time

Plugging in the given values, we have:

angular acceleration = (30 rev/sec - 0 rev/sec) / 5 sec

angular acceleration = 6 rev/sec^2

Now, let's calculate the angular displacement using the formula:

angular displacement = 0 rev/sec * 5 sec + 1/2 * 6 rev/sec^2 * (5 sec)^2

angular displacement = 0 + 1/2 * 6 * 25

angular displacement = 0 + 75 rev

Therefore, the angular displacement of the fan during the 5-second interval is 75 revolutions.