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.