# I Doubt with rotating body and force

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1. Jun 28, 2017

### carlitos_30

Hello.

Let's image a bar. In one side is attached to a body so the bar can rotate over this axis. There is no friction between the two bodies. The system is at rest in t=0. A force acts forming a 90° angle with the bar. The bar moves and begin to rotates. The force dissapear.

There is no force acting on this system, but I think that the bar doesn´t keep moving forever since its changing his direction every moment, hence there is an acceleration present, but if there is an acceleration present a force should be acting in the system which contradicts the assumption.

¿How this can be?

2. Jun 28, 2017

### rumborak

Do you think you can create a pic? I'm not sure of the setup.

3. Jun 28, 2017

### carlitos_30

Justo imagine there is no Gravity or another force.

Something like this:
The dashes represent the bar.

I----------------

4. Jun 28, 2017

### SlowThinker

If I understand you correctly, it is a cylinder that rotates along its axis and no other movements are going on.

If that's the case, every point of the cylinder is accelerating at right angle to its direction of motion (aka centripetal acceleration). In this special case, the speed is preserved. But yes, forces are present. If the cylinder rotates too fast, it will fall apart.

5. Jun 29, 2017

### A.T.

Where is the joint axis? Where is the froce?

In any case:
- If you exert a net force, the whole thing will start moving, and will keep moving after the force is gone.
- If you exert a net torque, at least some parts will start spinning, and will keep spinning after the torque gone.

6. Jun 29, 2017

### pixel

I think OP is asking this: if an object is rotating, in this case at constant angular velocity after the initiating force is removed, then each point on the object is constantly changing direction, so is accelerating. What force is providing the acceleration?

7. Jun 29, 2017

### A.T.

In that case it would be internal forces. Without external forces the center of mass of the whole thing has no acceleration.

Last edited: Jun 29, 2017
8. Jun 29, 2017

### carlitos_30

Moving at constant speed?

In this example, a force is applied and the wrench start to move. When is moving, the 200 N force isn't applied any more? Is just applied at the beginning? Or I have to assume that the 200 N force is applied every instant the wrench is moving?

9. Jun 29, 2017

### carlitos_30

The center of mass would be at the center of the bar and I imagine is moving every instant, changing the velocity vector, hence there is an acceleration in the center of mass.

10. Jun 29, 2017

### A.T.

I was talking about net force and net torque. Are the 200N the only force acting on the wrench?

I was talking about the center of mass of the whole isolated system, not just the wrench.

11. Jun 29, 2017

### carlitos_30

Something like this:

It will keep moving forever?

12. Jun 29, 2017

### carlitos_30

Yes.

To keep the wrench rotating or anything rotating with no friction, the 200 N force has to be applied every instant or only at the beginning?

13. Jun 29, 2017

### pixel

The following assumes there is no friction: If 200N is the net force, it will cause angular acceleration. As long as a net force is applied, the angular velocity will continue to increase. If the force is removed and the net force is 0, the wrench will continue to move with a constant angular velocity, equal to what it was when the force was removed.

For a particle, Newton's second law says F = ma, net force equals mass times acceleration. As long as there is a net force, there will be acceleration, or an increase in the velocity. If the net force F is zero, the acceleration is zero and the velocity is constant.

For rotational motion of a rigid body, there is an analogous law: T = Iα, the net torque, T, equals the moment of inertia, I, times the angular acceleration, α.

14. Jun 29, 2017

### A.T.

Really? The screw exerts no forces on the wrench?

15. Jun 29, 2017

### carlitos_30

Yes, outward the wrench due to Newton third law.

May I conclude safely that the ridig body will keep rotating forever when only centripetal and the reaction to this force in the pivot(centrifugal?) are acting in the body?

16. Jun 29, 2017

### CWatters

A wrench turning a bolt has friction so a force (torque) is needed to keep it turning. If you remove the torque the friction will cause it to slow down a and stop.

An object floating in space has no friction. A torque has to be applied to start it spinning but it will keep spinning after the torque is removed.

The general case is...

Torque = moment of inertia * angular acceleration

Or

Angular acceleration = Torque / moment of inertia

Where Torque is actually the net torque (eg the applied torque - friction torque).