Calculate vector of pivoted object

[Brokenhearted]

Hi there, my physics is a bit rusty but here goes:

 

Object A is attached to an axis of rotation, such that if you apply force to it (e.g. a punch), it spins around the pivout / axis that it is attached to.

Example: imagine it is a roundabout in a kids' play area. Give it a push, and it turns about its axis.

 

 

Ok, so imagine Object B strikes Object A at 90 degrees to the radius connecting Object A to the axis.

 

What is the momentum and the velocity of Object A by the time it travels 90 degrees of arc around its pivotal axis? Has Object A done work by the time it travels 90 degrees of arc? A mathematical expression would be fine, as we don't have any actual values to input.

 

Imagine it's a frictionless system.

 

I would have thought that Object A would be doing work even if it's a frictionless system, because it wants to fly off the pivot along the direction Object B is headed, whereas its attachment to the pivotal axis is keeping it equidistant to the pivotal axis the entire time.

 

In otherwords, Person A is sat on a roundabout in a kids play area. Person B collides into Person A at 90 degrees to the radius connecting Person A to the axis of rotation.

Person A wants to therefore move in the same direction as Perseon B, but because the roundabout is of solid construction, Person A instead maintains a constant radius and merely turns in an arc.

Therefore there's going to be some work done, energy lost, by Person A?

[Brokenhearted]

Hello, l have created a diagram to illustrate what l'm asking. The pivoted "object" = Object A, but anyway, whatever you call it, l'd be grateful to get a formula for the momentum of the object, as it turns 90 degrees of revolution, having been punched really hard as per the diagram.

[studiot]

To answer this you would need to settle a few more details.

 

No work would be done if the pivot is indeed frictionless.

The momentum exchange between the impactor and the object would depend upon three things.

1) The masses of the impactor, say M and the object, say m

2) The velocity of impact, say v.

3) Whether we can consider this an elastic or non elastic impact.

[Brokenhearted]

Oh yeah, it's a closed system, elastic impact sum of everything before collision = sum of everything after collision (l had to Google so forgive me if l don't understand elastic properly)

I thought it would have to be elastic wouldn't it? There's nothing else at play here.

I'll try to describe it better, then maybe you can decide for me whether it's elasitc or inelastic:

 

Fist or maybe it's another ball - better if it's another ball because fist has to be connected to something etc etc etc whereas colliding ball is self complete. Let's call it a Fist anyways.

 

Fist collides with Object. Object swivels around in an arc whereas Fist continues moving along its own vector, disappearing off the edge of the paper.

What is the Object's momentum after 90 degrees of anticlockwise ("acw") motion? A formula would do as l don't have any actual data. I would have thought sine waves would come into play, hence l came here to ask because that gets a bit complicated for me.

 

I say "sine wave" because l thought Object would lose energy as it departs further and further from Fist's vector, while it travels in the arc which it is constrained to travel in (it would have prefered to move alone that same vector that Fist is moving in).