A flywheel rotating at 5.3 revolutions per second has an angular retardation of 4/5 radian per second per minute.calculate:(i)its angular velocity after 45 seconds(ii),the number of revolutions it makes in 1 minute, and in coming to rest.
To calculate the angular velocity and the number of revolutions, we need to use the formula for angular acceleration:
angular acceleration (α) = change in angular velocity (Δω) / change in time (Δt)
Given:
Initial angular velocity (ωi) = 5.3 revolutions per second
Angular retardation (α) = 4/5 radian per second per minute
Time (t) = 45 seconds
(i) Calculate Angular Velocity:
To find the final angular velocity (ωf) after 45 seconds, we need to convert the initial angular velocity to radians per second:
Initial angular velocity (ωi) = 5.3 revolutions per second
(1 revolution = 2π radians)
So, ωi = 5.3 * 2π radians per second
Now, we can calculate the change in angular velocity (Δω):
Δω = α * Δt
= (4/5 radian per second per minute) * (45 seconds)
Next, add the change in angular velocity to the initial angular velocity:
ωf = ωi + Δω
Substitute the values and calculate ωf.
(ii) Calculate the number of revolutions:
To find the number of revolutions in 1 minute (60 seconds), we can use the formula:
Number of revolutions (N) = ω * t / (2π)
Substitute the values and calculate N.
To find the number of revolutions it takes to come to rest, we need to find the time it takes for the flywheel to stop. We can use the formula:
Final angular velocity (ωf) = 0
Rearrange the formula to solve for time (t), and substitute the values to calculate t. Then use the formula above to calculate the number of revolutions.
Following these steps, you should be able to find the angular velocity, the number of revolutions in 1 minute, and the number of revolutions it takes for the flywheel to come to rest.