determine the angular velocity if 11.3 revolutions are completed in 3.9 seconds
11.3 revs/39 sec
= 11.3(2π)radians / 39 seconds
= (113/195)π radians/s or appr 1.82 rad/s
To determine the angular velocity, we need to convert the number of revolutions completed into radians and divide it by the time taken.
1 revolution is equal to 2π radians.
Given that 11.3 revolutions are completed in 3.9 seconds, we can calculate the angular velocity as follows:
Number of revolutions completed = 11.3 revolutions
Time taken = 3.9 seconds
Convert revolutions into radians:
1 revolution = 2π radians
11.3 revolutions = 11.3 * 2π radians
Angular velocity = (11.3 * 2π radians) / 3.9 seconds
Now, we can calculate the angular velocity.
To determine the angular velocity, we need to use the formula:
Angular velocity = (Angle covered) / (Time taken)
In this case, we are given that 11.3 revolutions are completed in 3.9 seconds. Since 1 revolution is equal to 360 degrees, we can convert the given angle to degrees:
Angle in degrees = 11.3 revolutions * 360 degrees/revolution
Angle in degrees = 4072 degrees
Now, we can substitute the values into the formula to find the angular velocity:
Angular velocity = 4072 degrees / 3.9 seconds
Simplifying this expression, we get:
Angular velocity ≈ 1045.13 degrees per second
Therefore, the angular velocity is approximately 1045.13 degrees per second.