The fan blades on a jet engine make one thousand revolutions in a time of 87.6 ms. What is the angular frequency of the blades?
Well, let's start by doing some math. To find the angular frequency, we need to divide the number of revolutions by the time it takes. So, by using a calculator or your brain power (if you're feeling ambitious), we can calculate that the angular frequency of the blades is approximately 11,415.525 radians per second. That's pretty "revolving" if you ask me! Keep on spinning, jet engine!
To find the angular frequency of the blades, we can use the formula:
Angular frequency = 2π / Time period
First, let's find the time period. The time period is the time it takes for one revolution.
Time period = 87.6 ms / 1000 revolutions
= 0.0876 ms / revolution
Now, we can calculate the angular frequency.
Angular frequency = 2π / Time period
= 2π / (0.0876 ms / revolution)
≈ 71.885 radians/ms
Therefore, the angular frequency of the blades is approximately 71.885 radians/ms.
To find the angular frequency of the fan blades, we need to know the number of revolutions made by the blades per unit time.
Angular frequency is a measure of how fast an object is rotating in radians per unit of time. In this case, we are given the number of revolutions and the time it takes to complete those revolutions.
To find the angular frequency, we can use the following formula:
Angular frequency = (2π * Number of revolutions) / Time
In this case, the number of revolutions is 1000 and the time is 87.6 ms.
First, convert the time to seconds:
Time = 87.6 ms = 87.6 * 10^-3 s = 0.0876 s
Now, substitute the values into the formula:
Angular frequency = (2π * 1000) / 0.0876
Calculating:
Angular frequency ≈ 22732.972 rad/s
Therefore, the angular frequency of the fan blades is approximately 22732.972 rad/s.
Freq. = 1000rev/0.0876s = 11,416rev/s =
11,416 cycles/s = 11,416 Hz.