Rotation and translation of an object

In summary, when 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, the object will both rotate and translate. To obtain only rotation and no translation, equal and opposite forces must be applied off-centre in opposite directions. The net force must be zero in order for there to be no translation, but there can still be rotation if there is a couple of forces. The net force must go through the CM in order for there to be no rotation, but there can still be translation if there is a parallel force.
  • #1
fisico30
374
0
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
 
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  • #2
fisico30 said:
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.
fisico30 said:
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.

fisico30 said:
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.
 
  • #3
"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?
 
  • #4
fisico30 said:
"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.
 
  • #5
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
 
  • #6
fisico30 said:
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.
 
  • #7
DaveC426913 said:
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.
 
  • #8
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
 
  • #9
DaveC426913 said:
Yes. You are transferring kinetic energy to the object that has a directional component to it - the direction you poked it in.

AlephZero said:
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.
 
  • #10
fisico30 said:
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.
 
  • #11
D H said:
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.
 

1. What is the difference between rotation and translation of an object?

Rotation is the movement of an object around an axis or fixed point, while translation is the movement of an object from one location to another without changing its orientation.

2. How do you calculate the amount of rotation and translation an object undergoes?

The amount of rotation can be measured using angles, while the amount of translation can be measured using distance or displacement.

3. Can an object undergo both rotation and translation simultaneously?

Yes, an object can undergo both rotation and translation at the same time. This is known as a compound motion.

4. What are some real-life examples of rotation and translation of objects?

An example of rotation would be the movement of a Ferris wheel, while an example of translation would be the movement of a car on a straight road.

5. How do rotation and translation affect an object's center of mass?

Rotation does not change an object's center of mass, but translation can cause the center of mass to move to a different location.

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