Answer:
20960.7 revolutions
Explanation:
Convert from revolutions-per-minute to angular speed (rad/s) knowing that each revolution has a 2π angle and each minute has 60 seconds
7200 rpm = 7200 (rev/min) * 2π (rad/rev) * (1/60) (min/sec) = 754 rad/s
We can use the following equation of motion to calculate the angle swept by the flywheel during the deceleration of t = 5 minute = 300 s
[tex]\theta = \omega_0 t + \alpha t^2/2[/tex]
[tex]\theta = 754 * 300 - 2.1 * 300^2/2 = 131700 rad[/tex]
Again we can convert this to number of revolution
131700 rad * (1/2π) (rev/rad) = 20960.7 rev
Answer:
20940.3 revolution
Explanation:
Using,
θ = ω₀t+1/2αt² ................... Equation 1
Where θ = number of revolution made by the flywheel, t = time, ω₀ = angular initial velocity, α = angular acceleration.
Given: ω₀ = 7200 rpm = 7200(0.1047) = 754 rad/s, t = 5 min = 300 s, α = -2.1 rad/s²( decelerating)
Substitute into equation 1
θ = 754(300)+1/2(-2.1)(300²)
θ = 226200-94500
θ = 131700 rad.
If 1 rad = 0.159 rev,
Then 131700 rad = 0.159×131700 = 20940.3 rev.
Hence the flywheel makes 20940.3 revolution before coming to rest
