Relative velocities of rigid bodies

In summary, the conversation discussed a triangular body that changes orientation as its supporting links rotate. At a specific moment with given values for theta, theta_dot, and beta, the task was to determine vA and the angular velocity of the body. The equations used were vB = vE + w x rB/E and vB = vA + w x rB/A, with additional information about fixed points E and D, as well as the angles theta and beta. The conversation ended with a question about the diagram and how it would impact the solution.
  • #1
kdm06
14
0

Homework Statement



A triangular body changes orientation as the suspporting links rotate. At the moment shown, theta = 90 deg, theta_dot = 5 rad/s, and beta = 45 deg. Determine vA and the angular velocity of the triangular body.
rB/C = 2j cm and rB/A = 5i cm

Points E and D are fixed. theta is the angle made between horizontal and BE. beta is angle made between horizontal and AD.

Homework Equations



vB = vE + w x rB/E
vB = vA + w x rB/A

The Attempt at a Solution



vB=vE + w x rB/E
vB=0 + 5k x 2[]j[/b]
vB=-10i

vB=vA + w x rB/A
-10i = vA + w x 5j


I am stuck at this point because I am not sure if I should use theta_dot for this w because AD is at a different angle (beta). And if I do need to use a different w (which would be beta_dot how would I find it without knowing the length of AD.
 
Last edited:
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  • #2
Where's the diagram?
 
  • #3
Shooting star said:
Where's the diagram?

ya.. please if diagram is to be provided.. do not omit it.
 

FAQ: Relative velocities of rigid bodies

What is meant by relative velocities of rigid bodies?

Relative velocities of rigid bodies refer to the motion of one body in relation to another body, taking into account their individual velocities and directions of motion.

How is the relative velocity of a rigid body calculated?

The relative velocity of a rigid body is calculated by subtracting the velocity of one body from the velocity of the other body. This takes into account the direction of motion and the magnitude of the velocities.

What are some real-life applications of understanding relative velocities of rigid bodies?

Understanding relative velocities of rigid bodies is crucial in fields such as engineering, physics, and transportation. It is used in designing structures, predicting collisions, and calculating the speed and direction of moving objects.

Can relative velocities of rigid bodies change over time?

Yes, relative velocities of rigid bodies can change over time as the velocities of the individual bodies change. This can happen due to external forces, changes in direction, or changes in the velocities of the bodies themselves.

How does the concept of relative velocities of rigid bodies differ from that of relative velocities of non-rigid bodies?

The concept of relative velocities of rigid bodies differs from that of non-rigid bodies in that rigid bodies do not deform or change shape during motion. This allows for simpler calculations and more accurate predictions in cases where the bodies are considered to be rigid.

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