Rotation and translation of an object

[fisico30]

Hello Forum,
if a force is applied to an object along a direction that passes through the center of mass, the object will translate without rotation.

If the force acts along a line that does not pass through the CM, will the object both rotate and translate?

Where and how does the force need to applied to cause the object to only rotate and not translate?
I am assuming the object is not constrained but free to move in any direction...

To obtain translation does the force need to always have a component along a direction that goes through the center of mass?
thanks,
fisico30

 

[DaveC426913]

If the force acts along a line that does not pass through the CM, will the object both rotate and translate?

Yes. You are transferring kinetic energy to the object that has a directional component to it - the direction you poked it in.

Where and how does the force need to applied to cause the object to only rotate and not translate?
I am assuming the object is not constrained but free to move in any direction...

You would have to apply equal and opposite forces. For example, poking it off-centre from opposite directions simultaneously.

To obtain translation does the force need to always have a component along a direction that goes through the center of mass?

No. Two parallel or somewhat parallel pokes off-centre could sum up to translational movement with no rotational movment.

 

[fisico30]

"Two parallel or somewhat parallel pokes off-centre could sum up to translational movement with no rotational movment..."

True. So the translation is not only caused by forces directed through the center of mass.
The net force, sum of the two force, goes through the CM, does it?

 

[haruspex]

"Two parallel or somewhat parallel pokes off-centre could sum up to translational movement with no rotational movment..."

True. So the translation is not only caused by forces directed through the center of mass.
The net force, sum of the two force, goes through the CM, does it?

Yes, in the sense that there is zero net moment about the CM. So e.g. you could have a force of 2N missing the CM by 1m on the left, and a parallel force of 1N missing it by 2m on the right. For just two forces, the lines of action and the CM would all have to be in one plane.

 

[fisico30]

Thank you.

So, to be general, maybe we should discuss the possibility (or lack of it) of translation of rotation in terms of net torque about the center of mass and net force about the center of mass:

1) zero net torque about CM implies no rotation of the object, even if translation may present.
In the example of two parallel forces with same direction, applied on either side of the CM at equal distance, the net torque is zero. The net force is not zero, but does it really act through the center of mass? How do we prove that?

2) zero net force about the CM implies no translation of the object, but possibly rotation (a couple of forces)

thanks
fisico30

 

[haruspex]

1) zero net torque about CM implies no rotation of the object, even if translation may present.
In the example of two parallel forces with same direction, applied on either side of the CM at equal distance, the net torque is zero.

No, not necessarily at equal distances. That would only be true if the forces have equal magnitude. In general, the forces would be in inverse proportion the distances of their lines of action from the CM. Perhaps you meant to write "with equal magnitude".

The net force is not zero, but does it really act through the center of mass? How do we prove that?

From the fact that there is no rotation! (How else would you define it?)

2) zero net force about the CM implies no translation of the object, but possibly rotation (a couple of forces)

Not happy with your use of "about" there. That implies moments. "Through" perhaps. Otherwise, yes.

 

[AlephZero]

Yes. You are transferring kinetic energy to the object that
has a directional component to it - the direction you poked it in.

Just in case that statement confuses anybody: Kinetic energy (or any other sort of energy) is a scalar quantity. It doesn't have a direction.

Sure, sometimes you can resolve a velocity into components, find the KE corresponding to each component, but you have to be careful what you mean by "velocity" if the body is rotatinng!

Don't confuse energy and momentum (which is a vector). They are two different things.

 

[fisico30]

Hello Haruspex,

The net force is not zero, but does it really act through the center of mass? How do we prove that?

You mention from the fact the rotation is absent. That means that the net torque is zero.
But, vectorwise, there must be a net force through the CM due to the two forces...
How do we prove that there is going to be a net force? How does it relate to those two forces causing torques that cancel each other?

fisico30

 

[DaveC426913]

Yes. You are transferring kinetic energy to the object that has a directional component to it - the direction you poked it in.

Just in case that statement confuses anybody: Kinetic energy (or any other sort of energy) is a scalar quantity. It doesn't have a direction.

Thank you. Sorry if I wasn't clear that I was taking a scalar and combining it with a direction to get a vector.

 

[D H]

zero net torque about CM implies no rotation of the object, even if translation may present.

Not quite right. Zero net torque does not imply no rotation. It implies no change in angular momentum. If an object is already rotating this means it will continue rotating in the absence of an external torque.

In the example of two parallel forces with same direction, applied on either side of the CM at equal distance, the net torque is zero. The net force is not zero, but does it really act through the center of mass? How do we prove that?

Better said, the system center of mass moves exactly as would a point mass with mass equal to the total mass of the system acted upon by the sum of the external forces acting on the system.

How to prove this? Two ways. One is via Newton's laws, the other via the conservation laws. Every undergraduate physics classical mechanics text will proves this in one of the opening chapters of the text.

zero net force about the CM implies no translation of the object, but possibly rotation (a couple of forces)

Once again this is not quite right. Zero net force does not imply no translation. It implies no change in linear momentum. Think Newton's first law.

 

[DaveC426913]

It implies no change in angular momentum.

It implies no change in linear momentum.

OP likely assumed a stationary and rotationless starting state. But good to be explicit.