A disk starts at rest and accelerates with a constant angular acceleration α. After the disk completes one complete revolution, what is its angular velocity?
ang.acc. = (ang.v. squared) / angle
w = sqrt(angle x ang.acc.) = sqrt (2pi x ang.acc)
However, the test shows that this answer is wrong..
V^2 = Vo^2 + 2a*d = 0 + 2a*2pi = 4a*pi
V = 2*sqrt(pi*a) = 2*1.772*sqrt a =
3.54*sqrt a
To find the angular velocity of the disk after completing one revolution, we can start by using the equation for angular acceleration:
ang.acc. = (ang.v. squared) / angle
Let's rearrange this equation to solve for the angular velocity (ang.v.):
ang.v. squared = ang.acc. * angle
Taking the square root of both sides, we get:
ang.v. = sqrt(ang.acc. * angle)
Next, we substitute the given values for the angle of one complete revolution, which is 2π radians (assuming the disk is rotating in radians):
ang.v. = sqrt(ang.acc. * 2π)
However, you mentioned that the test shows this answer as incorrect. There could be a few reasons for this discrepancy:
1. Incorrect value for angular acceleration (α): Double-check the value given for α. If the angular acceleration is incorrect, it will affect the calculated angular velocity.
2. Inadequate units: Check that all values are in the correct units. Make sure to use radians for the angle and rad/s² for the angular acceleration.
3. Precision and rounding errors: Ensure that you are using sufficient precision in your calculations. Rounding errors can accumulate and affect the final result.
If you have verified all the above factors and the calculated angular velocity still does not match the expected answer, there might be additional information or context missing in the problem statement.