Question

A flywheel rotates at 7200 rpm when the power is suddenly cut off. The flywheel decelerates at a constant rate of 2.1 rad/s2 and comes to rest 5 min later. How many revolutions does the flywheel make before coming to rest?

Answer 1

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

Answer 2

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

$\theta = \omega_0 t + \alpha t^2/2$

$\theta = 754 * 300 - 2.1 * 300^2/2 = 131700 rad$

Again we can convert this to number of revolution

131700 rad * (1/2π) (rev/rad) = 20960.7 rev