A wheel spins on a horizontal axis, with an angular spped of 140rad/s and with its angular velocity pointing east. Determine the magnitude of the angular velocity after an angular acceleration of 35 rad/s^2, pointing 68 degress west of north, with a time of 4.6 seconds. I found that the magnitude of the angular velocity is 61 rad/s, but how do i determine the direction of its angular velocity west of north in degrees.
What does Drwls mean by "Apply the vector equation
dw/dt = a
where w is the angular velocity and a is the angular acceleration.
a has components -21.55i (which points west) and 13.11 j (which points north).
w starts out at 140 i. After 4.6 seconds
w (t=4) = 40.87 i + 60.31 j
The magnitude does not agree with your answer. The direction tangent can be obtained from the ratio of the components.
Magnitude = 72.9 "
especially when he says the direction tangent can be obtained from the ratio of the components"
I get 27degrees west of north?
To determine the direction of the angular velocity west of north in degrees, you can use the ratio of the components of the angular velocity.
In this case, Drwls provided the components of the angular acceleration: -21.55i (which points west) and 13.11j (which points north). These components indicate the change in the angular velocity in the x and y directions, respectively.
You also have the final angular velocity components: 40.87i and 60.31j.
To find the direction tangent, you can use the ratio of the components:
tangent(theta) = (change in y) / (change in x)
Using the provided values:
tangent(theta) = (60.31) / (40.87)
You can use the inverse tangent (arctan) function to find the angle:
theta = arctan(60.31 / 40.87)
Calculating this, you should get theta ≈ 56.47 degrees.
However, keep in mind that Drwls mentioned that the magnitude is 72.9, not 61 as you calculated. It's possible that there was an error in your calculations or assumptions. Make sure to double-check your work to ensure accuracy.