How Is Angular Momentum Calculated Without Considering Gravity and Viscosity?

In summary, the conversation discusses neglecting gravity and viscosity effects in a problem involving an angled plate and an incoming flow. The main question is about how to compute the cross product in the equation and how to define the r and u vectors. The issue of friction with the plate is brought up, but it is clarified that the problem is idealized and the focus is on the vertical force and torque exerted on the plate.
  • #1
Est120
54
3
Homework Statement
write the macroscopic angular momentum balance for the following problem
Relevant Equations
see image
we neglect gravity and viscosity efects
i really can't understand how does the author managed to get the equation in the image
Bird Angular Momentum Balance.png
 
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  • #2
Not making any sense to me either.
Altitude at ##\frac 12b_1## from where?
##b_1## is at an angle, so ##b_1-b_{2a}## doesn’t seem right.
And what about the force from the plate? We don't know where that is centred, so we can't set the axis so as to eliminate its torque.
 
  • #3
it's an idealized problem, all i need to know is how they compute the cross product , there is no viscosity so there is no friction with the plate
 
  • #4
Est120 said:
how they compute the cross product
For that, I need you to define the r and u vectors in the boxed equation.
Est120 said:
there is no friction with the plate
It's not to do with friction. The incoming flow exerts a vertically downward force ##w_1v_1## on the plate. The reaction from the plate likely has a torque about the chosen axis.
 

Related to How Is Angular Momentum Calculated Without Considering Gravity and Viscosity?

1. What is Angular Momentum Balance?

Angular Momentum Balance is a fundamental principle in physics that states that the total angular momentum of a system remains constant, unless acted upon by an external torque.

2. How is Angular Momentum Balance related to Newton's Laws of Motion?

Angular Momentum Balance is a direct consequence of Newton's Laws of Motion, specifically the Law of Conservation of Angular Momentum. This law states that in the absence of external torques, the total angular momentum of a system will remain constant.

3. What is the formula for calculating Angular Momentum Balance?

The formula for Angular Momentum Balance is L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

4. What are some real-life examples of Angular Momentum Balance?

Some examples of Angular Momentum Balance in real life include figure skaters spinning on the ice, planets orbiting around the sun, and a spinning top maintaining its upright position.

5. How is Angular Momentum Balance used in engineering and technology?

Angular Momentum Balance is used in engineering and technology to design and analyze rotating systems, such as turbines, motors, and gyroscopes. It is also used in spacecraft navigation and control systems.

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