Does Centripetal Acceleration Result in a Higher Velocity for a Released Mass?

[vector22]

I wondered what would happen to a steel mass that was spun around an axis in a circular motion and then suddenly released. What would happen to the velocity of the mass? Would it be the same as the tangent velocity? What about the direction of the mass as it heads off in in a new direction. After some number crunching I found the new velocity of the mass would be:

$$v = \sqrt {2 V_t ^2$$

Where $${V_t$$ is the tangent velocity.

Not only that but the kinetic energy of the mass as it rotates about the axis is

$${m V_t^2$$
exactly twice what you would expect

The most amazing thing is that the new velocity is higher than the tangent velocity and at the moment of release of the mass, it did not accelerate to the new speed!
is the math correct?

 

[matiasmorant]

I wondered what would happen to a steel mass that was spun around an axis in a circular motion and then suddenly released. What would happen to the velocity of the mass?

I don't think this is quite clear. what is the shape of the mass you are talking about? about what axis is it spun?

if its a particle in a radius r from the axis, it will move with a velocity equal to the tangential velocity when its released. if it is a bar of steel rotating about its center, it will keep rotating after is released. in either case, kinetic energy and angular momentum will be conserved. how did you get your results?

 

[AlephZero]

Show us your work, then we'll try and explain you where you went wrong, or what you are misunderstanding.

If you think the KE suddenly doubled you are certainly misunderstanding something, but we aren't mindreaders, so we can't guess what it is.

 

[vector22]

Im sorry I should have been more specific

I agree that a tethered mass rotating about an axis at a distance r when released will have a velocity equal to the tangent velocity and in the direction of the tangent vector. I wonderd what would happen if the mass has a velocity in the direction of the redius vector as well as the tangent vector. I think the resultant velocity would be a vector sum.

The centripetal acceleration is a hard concept to imagine because there does not seem to be any measurable acceleratio to a tethered mass since tangent velocity is constant.

What happens if the direction of the mass is limited to the radius vector only. That could be achievd by allowing the mass to rotate inside a hollow tube with the tube being in the direction of the radius vector

Say the mass is at 1r in the tube and the tube is 2r in length. A pin at 1r through the tube prevents the mass from travleing radialy. Let the mass be rotating at a steadt tengent velocity so that the kinectic energy of the mass is constant.

Then pull the pin and at the same time keep the kinetic energy os the system constant this would mean the angular velocity would tend to zero. By the time the mass exits the tube the angular velocity is zero and the kinetic energy of the mass is still the same as when the mass what positioned at 1r (before the pin was pulled) The mass travel in the direction of the radius vector. SO we see the mass has accelerated from 1r to 2r (ihope that distance is correct) and it should be the same value as the centripetal acceleration.

That implies a translation of kinetic energy from tangent vector to radius vector.

Anyway I need peer review on this...

 

[Doc Al]

The centripetal acceleration is a hard concept to imagine because there does not seem to be any measurable acceleratio to a tethered mass since tangent velocity is constant.

Something moving in a circle does not have a constant velocity. The speed might be constant, but not the velocity. It's constantly changing direction, which is what gives the centripetal acceleration.