Hydrodynamics- rotational movement.

[bondmmo]

Hydrodynamics--- rotational movement.

Hi,I am not sure whether my solution is correct. I am not an expert in this area either. Could anyone here help me to check my solution? Thank you

If i hang a block like a cube in water. If we look from the top view, there will be two side A and two side B, see the attached file . The object will be rotated only when current,drag forces, act on the side B. (Suppose the left and right side of side B area are not totally symmetrical and the moment can rotate the cube with very low speed because of small different area in Side B. Also, no moment can cause from side A)

When the object rotates, the force and moment will reduce. This results in non-constant angular acceleration, which I am not sure how to solve it. I calculated angular acceleration using Fxr=I$$\alpha$$.
However, I have done calculation in excel file using X-axis as $$\theta$$degree of rotation and Y-axis is force and moment. I tried to plot angular acceleration, velocity and time vs. the rotational degree. I set $$\theta$$ from 0 to 90 degree, with increase of 5 degrees.

Can i assume to use simply equation of motion to find them? are these following equations used for only a constant acceleration?

1. Can I useFxr=I$$\alpha$$ to find angular acceleration?
2. $$\omega$$^2=$$\omega$$ _o ^2+ 2 $$\alpha$$ $$\theta$$ to find velocity?
3. $$\theta$$ =$$\theta$$o + $$\omega$$*t+ 0.5 *$$\alpha$$*t^2 . Can I solve this equation to find time when the object rotates from 0 to 90 degree?

 

[Achy47]

Hi there,

As a scientist specializing in hydrodynamics, I can help you with your solution. First of all, your approach seems correct. When an object is submerged in water, the drag forces acting on the object will cause it to rotate. And as you mentioned, the rotation will be caused by a difference in the drag forces acting on the two sides of the object (side A and side B).

To solve for the angular acceleration, you can use the equation Fxr=I\alpha, as you have mentioned. However, since the drag forces acting on the object will vary with the rotation, the angular acceleration will also not be constant. This means that you cannot use a simple equation of motion to find the angular acceleration, velocity, and time.

Instead, you will need to use numerical methods to solve for these values. This involves breaking down the rotation into small time intervals and calculating the forces and moments acting on the object at each interval. Then, using the equation Fxr=I\alpha, you can find the angular acceleration at each interval. This process can be repeated to find the angular velocity and time at each interval.

In summary, while your approach is correct, you will need to use numerical methods to solve for the non-constant angular acceleration, velocity, and time. I hope this helps. Let me know if you have any further questions.