# Analyzing Action-Reaction between Two Masses in Rotation

• imanator
In summary, the question is about the reaction felt by a rotating mass when another mass collides with it tangentially. The force sensor at the center will not feel the collision itself, but the changed rotation speed will lead to a different radial force. The pivot holding the string will experience a radial force that constantly changes direction as the mass orbits it. If the collision results in the two masses ending up at rest, there will be no tension in the string. However, if the collision changes the tangential velocity, the tension in the string will be affected. The force on the pivot can only ever be radial, along the string.

#### imanator

Hi there, I'm new to the forum, but hopefully this question has a simply answer.

my question is, suppose you have a mass (a) on the end of a string or rod attached to a vertical support which is grounded. The mass is rotating about that support. Now assume you have another mass (b) traveling towards the rotating mass along a path, so that at one point, it is tangential to the radius of mass (a)'s rotation. when mass (b) reaches the rotating mass (a) and collides with it there will be an action reaction. my Question is will the reaction felt by mass (a) be through the centre support and in the same direction as mass (b) was going? or will it just induce a torque at the centre point, in other words if there was a force sensor at the centre point that was directed back (in the direction that mass (b) was coming from, would it register the same reaction force that object (b) felt when it hit object (a)? and what about the momentum of the system?

I hope this question is not too difficult to follow. I Attached a sketch for guidance.

I have done high-school physics and university physics, so I should be able to follow most replies.

Regards.

#### Attachments

• Rotating mass.jpg
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attachment is unreadable even at max magnification

Thanks for that, I uploaded a better one.

A force sensor at the center won't feel the collision itself as there are no radial momentum changes. Afterwards, the changed rotation speed leads to a different radial force.

thanks mfb, not sure what you mean by afterwards the changed speed leads to different radial force though. are you referring to the fact the fact that the rotating mass has slowed down will result in a lower v^2/r value?

imanator said:
thanks mfb, not sure what you mean by afterwards the changed speed leads to different radial force though. are you referring to the fact the fact that the rotating mass has slowed down will result in a lower v^2/r value?
Right.

does everyone else agree with this?

More or less, I think.
The pivot, holding the string will be experiencing a radial force (m vsquared/ radius), which constantly changes direction as the mass orbits it. I assume that the pivot is on a massive enough base to prevent any significant motion (wobble). If the new mass hits the orbiting mass tangentially and the two values of momentum add to zero then the two masses will end up at rest and there will be no tension in the string. If the resulting collision changes the tangential velocity to any other value, the tension in the string will be m newvsquared / radius. This tension will, initially, be at right angles to the path of the arriving mass. The force on the pivot can only ever be radial, along the string.

## 1. How do you determine the magnitude of the action-reaction forces between two masses in rotation?

To determine the magnitude of the action-reaction forces, you can use Newton's Third Law of Motion which states that for every action, there is an equal and opposite reaction. This means that the magnitude of the action force between two masses in rotation will be equal to the magnitude of the reaction force.

## 2. What factors affect the action-reaction forces between two masses in rotation?

The magnitude of the action-reaction forces between two masses in rotation can be affected by the masses of the objects, the distance between them, and the speed at which they are rotating. The forces can also be influenced by external factors such as friction and air resistance.

## 3. How does the direction of rotation affect the action-reaction forces?

The direction of rotation can affect the action-reaction forces between two masses. If the masses are rotating in opposite directions, the action-reaction forces will be in opposite directions as well. If the masses are rotating in the same direction, the action-reaction forces will be in the same direction.

## 4. How can you apply the concept of torque when analyzing the action-reaction forces between two masses in rotation?

Torque, or the measure of a force's ability to rotate an object, can be applied when analyzing the action-reaction forces between two masses in rotation. The torque exerted by one mass on the other will be equal and opposite to the torque exerted by the other mass on the first.

## 5. Are there any real-world applications of analyzing action-reaction between two masses in rotation?

Yes, there are many real-world applications of this concept. For example, it can be used in the design and analysis of rotating machinery such as engines, turbines, and motors. It can also be applied in the study of celestial bodies and their orbits, as well as in the field of sports for analyzing the forces involved in activities like throwing, swinging, and spinning.