Centripetal Force: What Causes the String to Accelerate?

[IniquiTrance]

If I swing around a mass attached to a string, and then suddenly let go, the mass will fly off in a direction tangent to the circle it was swinging around.

My question is, what will happen to the string? I know it will follow the mass on its tangental path, but how do we explain the behavior of the string? What forces cause it to accelerate behind the mass?

 

[Vanadium 50]

It's attached to the mass, right? Isn't that enough?

 

[A.T.]

What forces cause it to accelerate behind the mass?

The tangential velocity varies along the length of the string. The end of the string attached to the mass doesn't accelerate, it flies off tangentially just like the mass. The rest of the string is accelerated by the force within the string, and follows.

Assuming no gravity and vacuum the string will start rotating around the inertially moving mass.

Interesting follow-up question: Assuming no gravity and vacuum again. And that the mass of the string is not negligible compared to the mass of the rotated body: Will the velocity of the center of mass of body+string after release be less, equal, greater than the tangential velocity of the mass at release?

 

[rcgldr]

Assuming no gravity and vacuum the string will start rotating around the inertially moving mass.

The string was already rotating while the mass was being whirled around, before the moment of release.

A good example of how the string would move is the last hammer throw in the youtube video included in this old thread:

https://www.physicsforums.com/showthread.php?t=291199

 

[sganesh88]

Interesting follow-up question: Assuming no gravity and vacuum again. And that the mass of the string is not negligible compared to the mass of the rotated body: Will the velocity of the center of mass of body+string after release be less, equal, greater than the tangential velocity of the mass at release?

Lesser. Even in the presence of the centripetal force, the COM's velocity should be lesser than that of the mass's. Right?

 

[IniquiTrance]

So the string will rotate around the mass rather than follow it? Will it wrap itself around the mass? How can the motion be described rigorously?

 

[A.T.]

So the string will rotate around the mass rather than follow it? Will it wrap itself around the mass?

No, the mass will spin with the same angular velocity. The mass spins around it's own axis before release with the same rate it orbits the hand.

How can the motion be described rigorously?

On release, switch to the (now inertial) frame of reference of the mass center of mass+string. The rotation you have there will continue, and the whole system moves at tangential velocity the mass center of mass+string had on release. Which is less than the tangential of the mass itself on release (if string mass not negligible), as sganesh88 said.

 

[IniquiTrance]

Thanks for the response. I'm still trying to picture what would happen though.

I understand that the mass-string system will fly off along the line tangent to the COM's orbit, with the COM's orbital speed.

But will all parts of the system be at rest with respect to each other? Will the string be at rest w/r/t the mass at the end?

 

[A.T.]

But will all parts of the system be at rest with respect to each other? Will the string be at rest w/r/t the mass at the end?

Yes it will move like a rigid body.

 

[IniquiTrance]

Ah, ok.

But since, as you said it has an angular momentum, if say we viewed it from above, it was moving CCW before release, the entire rigid body will continue moving CCW after release, translating along its tangential path?