Will a Jet-Powered Rigid Link Reach a Steady State?

[DrBwts]

I have a mass (m) at the end of a rigid link of length r, pivoted at the red circle (below).

m is acted on by a force (F) which is always normal to the surface shown (thrust from a jet say).

My question is will this system reach a steady state, ie will it have constant angular velocity or will the angular acceleration just carry on increasing?

Thx Nic

 

[UltrafastPED]

Here's a thought: the gravitational field at the surface of the Earth is nearly constant - so if you drop a rock does it continue to gain speed as it falls?

Note that if air resistance is to be taken into account you there is a terminal velocity.

 

[Nugatory]

My question is will this system reach a steady state, ie will it have constant angular velocity or will the angular acceleration just carry on increasing?

Angular acceleration and angular velocity are different things. If we ignore air resistance and friction at the pivot, the angular acceleration will be constant and the angular velocity will keep on increasing without limit until something breaks.

If you consider air resistance, it is possible that the system will reach a steady state before something breaks. That force increases with speed, so as the speed increases will eventually be striping enough to counteract the applied force. (as UltrafastPED points out, this situation is analogous to the terminal velocity reached by a falling object in air).

 

[DrBwts]

OK thanks both. This is what I thought (sorry about the velocity/acceleration mix up).

Puzzling thing was, I ran this simulation in a well known CAD software & after an initial transitory increase in velocity it hit a steady state with no further acceleration!

 

[PJC01]

The system you have described is a classic example of rotational motion and can be analyzed using principles of dynamics and Newton's laws. In order to determine whether the system will reach a steady state or continue to increase its angular acceleration, we need to consider the forces acting on the mass (m) and the moment of inertia of the rigid link.

First, let's consider the forces acting on the mass. The only force acting on the mass is the thrust from the jet, which is always normal to the surface. This means that the force will always act perpendicular to the radius (r) of the rigid link. As a result, the torque created by this force will always be zero, and there will be no change in angular momentum.

Next, we need to consider the moment of inertia of the rigid link. The moment of inertia is a measure of an object's resistance to change in its rotational motion. In this case, the moment of inertia will depend on the shape and mass distribution of the rigid link. If the moment of inertia is constant, then the system will reach a steady state with a constant angular velocity. However, if the moment of inertia is not constant, then the angular acceleration will continue to increase.

In conclusion, the system will reach a steady state if the moment of inertia is constant. However, if the moment of inertia is not constant, then the angular acceleration will continue to increase. This can be seen in real-life scenarios, such as a spinning top, where the moment of inertia is not constant and the top's angular velocity continues to increase until it reaches a maximum. I hope this helps answer your question.