Determining angular velocity radius and velocity of the center of rotation

In summary, the conversation discusses a problem involving the equations va=vr+ ω × rra, vb=vr+ ω ×(rra+rab), and vc=vr+ ω × (rra+rac). The problem involves finding the angular velocity vector, radius rra, and velocity vr of a rigid body given 3 known points. The person is having trouble solving the problem analytically and in MATLAB, and is wondering if there are infinite solutions or if they are doing something wrong. It is also mentioned that the inverse of a cross product may not have a unique solution.
  • #1
Eve_mecheng
2
0
Hey,

I am trying to solve the following problem:

va=vr+ ω × rra
vb=vr+ ω ×(rra+rab)
vc=vr+ ω × (rra+rac)

I know the vectors va, vb, vc, rab and rac and I want to know the angular velocity vector, the radius rra and the velocity vr. Physically it means that I know 3 points on a rigid body and I want to decompose their velocities in an angular and linear component by determing around which point they rotate.

So there are 9 equations and 9 unkowns. But if I try to solve this problem analytically I can not come to any answer. I also put it in MATLAB but this also gives weird results.
My first attempt was subtracting the vectors which eventually gave me a solution for omega. But than I still could not solve the problem.

Does anyone know why this is the case? Is it something with the outer product which I don't understand? Are there infinite number of solution to this problem? Or do I just do something wrong?

Any help would be appreciated since I am already trying things for some days.

Thanks.
 
Physics news on Phys.org
  • #2
Does it have something to do with the fact that the inverse of a cross product does not have an unique solution? So if for v= ω x r I would know v and ω than there are infinite solutions for r.
 

1. What is angular velocity?

Angular velocity is a measure of how fast an object is rotating around a fixed point, also known as the center of rotation. It is typically measured in radians per second or degrees per second.

2. How is angular velocity calculated?

Angular velocity is calculated by dividing the change in the angle of rotation (measured in radians or degrees) by the change in time. The formula for angular velocity is ω = Δθ/Δt, where ω represents angular velocity, Δθ represents change in angle, and Δt represents change in time.

3. What is the relationship between angular velocity and linear velocity?

Angular velocity and linear velocity are directly related through the radius of rotation. The linear velocity of a point on a rotating object is equal to the product of its angular velocity and the radius of rotation. This relationship is expressed by the formula v = ωr, where v represents linear velocity, ω represents angular velocity, and r represents radius of rotation.

4. How do you determine the radius of rotation?

The radius of rotation can be determined by measuring the distance from the center of rotation to any point on the object that is rotating. This distance is known as the radius of rotation. Alternatively, if the linear velocity and angular velocity of the object are known, the radius of rotation can be calculated using the formula r = v/ω.

5. Can angular velocity be negative?

Yes, angular velocity can be negative if the object is rotating in a clockwise direction. This is because the direction of rotation is taken into account when calculating angular velocity. A positive angular velocity indicates a counterclockwise rotation, while a negative angular velocity indicates a clockwise rotation.

Similar threads

Replies
19
Views
1K
Replies
6
Views
2K
Replies
1
Views
396
Replies
15
Views
864
Replies
5
Views
987
Replies
3
Views
1K
  • Mechanics
Replies
3
Views
1K
Replies
3
Views
856
Replies
7
Views
2K
Back
Top