Determining angular velocity radius and velocity of the center of rotation

AI Thread Summary
The discussion revolves around solving a problem involving the angular velocity vector, radius, and linear velocity of a rigid body based on known vectors for three points. The user has established nine equations with nine unknowns but struggles to find a solution analytically or through MATLAB, leading to confusion about the role of the outer product and potential infinite solutions. The user questions whether the issue stems from the non-uniqueness of the inverse of a cross product, suggesting that knowing velocity and angular velocity could yield multiple radius solutions. Despite attempts to isolate variables, the user has not achieved a satisfactory resolution. Assistance is sought to clarify these concepts and find a way forward in solving the problem.
Eve_mecheng
Messages
2
Reaction score
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
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.
 

Thread '1:1 versus 2:1 Mechanical Advantage debate'

The rope is tied into the person (the load of 200 pounds) and the rope goes up from the person to a fixed pulley and back down to his hands. He hauls the rope to suspend himself in the air. What is the mechanical advantage of the system? The person will indeed only have to lift half of his body weight (roughly 100 pounds) because he now lessened the load by that same amount. This APPEARS to be a 2:1 because he can hold himself with half the force, but my question is: is that mechanical...
View full post »

Thread 'Average velocity as a weighted mean'

Hello everyone, Consider the problem in which a car is told to travel at 30 km/h for L kilometers and then at 60 km/h for another L kilometers. Next, you are asked to determine the average speed. My question is: although we know that the average speed in this case is the harmonic mean of the two speeds, is it also possible to state that the average speed over this 2L-kilometer stretch can be obtained as a weighted average of the two speeds? Best regards, DaTario
View full post »

Thread 'Newton's first law?'

Some physics textbook writer told me that Newton's first law applies only on bodies that feel no interactions at all. He said that if a body is on rest or moves in constant velocity, there is no external force acting on it. But I have heard another form of the law that says the net force acting on a body must be zero. This means there is interactions involved after all. So which one is correct?
View full post »

Similar threads

I Confusion about adding angular velocities
Replies
4
Views
2K
I Velocity transformation between frames rotating relative to one another
Replies
1
Views
2K
I Question about a Rotating system with mass moving inwards
Replies
19
Views
2K
What is the angular velocity in the center of a rotating disc?
Replies
6
Views
2K
I How can angular displacement be larger than 2pi?
Replies
20
Views
2K
Angular momentum and when center of rotation is changed
Replies
3
Views
2K
I A rod that falls while rotating from the end of a table
Replies
2
Views
1K
Calculate the change of angular velocity
Replies
5
Views
2K
Angular veolcity in rotating frame
Replies
3
Views
2K
I Energy of spinning objects as axis of rotation moves
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top