# Why does rotation occur?

Sorry if this sounds like a dumb question, but I can't understand why something would rotate. Ex. with a two particles connected by a rod, if a force is applied anywhere other than its center of mass, the same force would cause both translation and rotation.

Also, how come if the same force is acted onto the center of mass of the object described above, it would move at the same rate linearly as if the force was applied anywhere else, so it seems the rotational motion doesn't require any work, what's the explanation for this?

Thanks.

## Answers and Replies

I know about torque and moment but that's not what I'm getting at. I'm trying to understand the physics behind the concept of rotation, like what's actually going on physically not a concept that scientists invented to describe it. For example, what kind of internal interaction are going on to make something rotate?

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Think of the rod as a bunch of individual masses connected by springs. Your initial force pushes on one of the masses. You can see that it wants to drag its neighbors, pulling in a direction associated with that spring's connection. If you model that, you'll see that rotation and overall movement both emerge from the initial push.

Doc Al
Mentor
Also, how come if the same force is acted onto the center of mass of the object described above, it would move at the same rate linearly as if the force was applied anywhere else, so it seems the rotational motion doesn't require any work, what's the explanation for this?
The center of mass may move the same, but the point of contact will move more if the force is off-center. It's the same force acting through a greater distance that provides the extra work for the rotation.

Your assumption is the original post is incorrect....as Doc Al explains....why would you assume rotation requires no energy but translation motion does??

Ever try to crank an engine by hand? or, equivalently, that's why you have a battery (electrical energy) to start your car....work is required to rotate the engine....and work is required in all rotations. Or think about windmill power generation...those huge blades all over the place don't turn by themselves...the wind does work to cause them to rotate and produce electrical power.....no wind and they sit motionless, right??

In a system with the combined translational and rotational movement, there is KE in both the both movements......the rotational velocity is v = wr and so if you can visualize velocity v requiring energy it's clear the w also does.

Sorry if this sounds like a dumb question, but I can't understand why something would rotate. Ex. with a two particles connected by a rod, if a force is applied anywhere other than its center of mass, the same force would cause both translation and rotation.

Also, how come if the same force is acted onto the center of mass of the object described above, it would move at the same rate linearly as if the force was applied anywhere else, so it seems the rotational motion doesn't require any work, what's the explanation for this?

Thanks.

Actually, it would not move at the same rate linearly as if the force were applied off-center. You're putting energy into the two-particle system. If you hit it center of mass, it'll move with the greatest linear velocity possible, but if you hit it off-center, it'll move with less velocity. The remaining energy is transformed into angular momentum (spin).

Thanks for the responses.
The center of mass may move the same, but the point of contact will move more if the force is off-center. It's the same force acting through a greater distance that provides the extra work for the rotation.

Sorry I didn't really quite get what you mean, can you expand on that?

Actually, it would not move at the same rate linearly as if the force were applied off-center. You're putting energy into the two-particle system. If you hit it center of mass, it'll move with the greatest linear velocity possible, but if you hit it off-center, it'll move with less velocity. The remaining energy is transformed into angular momentum (spin).

So if I hit the rod off center, then I can't simply get its linear acceleration based on the applied force divided by mass of rod? How would I determine the linear acceleration of this system then knowing only the duration and magnitude of the applied force and the mass of the rod?

Your assumption is the original post is incorrect....as Doc Al explains....why would you assume rotation requires no energy but translation motion does??

Ever try to crank an engine by hand? or, equivalently, that's why you have a battery (electrical energy) to start your car....work is required to rotate the engine....and work is required in all rotations. Or think about windmill power generation...those huge blades all over the place don't turn by themselves...the wind does work to cause them to rotate and produce electrical power.....no wind and they sit motionless, right??

In a system with the combined translational and rotational movement, there is KE in both the both movements......the rotational velocity is v = wr and so if you can visualize velocity v requiring energy it's clear the w also does.

Yeah I realize that now, thanks. I initially assumed that the applied force would cause the same linear acceleration no matter where it is applied (at the CoM or off-center), which led to my confusion.

So if I hit the rod off center, then I can't simply get its linear acceleration based on the applied force divided by mass of rod? How would I determine the linear acceleration of this system then knowing only the duration and magnitude of the applied force and the mass of the rod?

You must also know something about the distribution of mass throughout the rod in order to use the equations of rotational http://en.wikipedia.org/wiki/Dynamics_(mechanics)" [Broken] required to calculate the resulting motion (both linear and rotational) of the rod after you push on it.

http://en.wikipedia.org/wiki/Rigid_body_dynamics" [Broken]with the equations and information you will require to comput both rigid body linear momentum as well as rigid body angular momentum.

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Doc Al
Mentor
Actually, it would not move at the same rate linearly as if the force were applied off-center. You're putting energy into the two-particle system. If you hit it center of mass, it'll move with the greatest linear velocity possible, but if you hit it off-center, it'll move with less velocity. The remaining energy is transformed into angular momentum (spin).
If you apply the same force to a body, its center of mass will have the same linear acceleration regardless of where that force is applied, off-center or not. That's just Newton's 2nd law.

Doc Al
Mentor
Sorry I didn't really quite get what you mean, can you expand on that?
What determines the work done is not simply the applied force, but the movement of that applied force through some distance. If you push something off-center, the motion of the point of contact will be greater than if you pushed it on-center. That means more work is required to sustain that motion; that extra work goes into rotational energy.

So if I hit the rod off center, then I can't simply get its linear acceleration based on the applied force divided by mass of rod?
Sure you can.

Yeah I realize that now, thanks. I initially assumed that the applied force would cause the same linear acceleration no matter where it is applied (at the CoM or off-center), which led to my confusion.
No, that's not the source of your confusion. You were correct about that!

What determines the work done is not simply the applied force, but the movement of that applied force through some distance. If you push something off-center, the motion of the point of contact will be greater than if you pushed it on-center. That means more work is required to sustain that motion; that extra work goes into rotational energy.

Ah okay, thanks for clearing that up; I'm always confused when energy is involved.

So the same force acting at a different position would add more energy to the system (however the work needed for its linear motion is the same) and I can calculate the rotational work by using Ek= 1/2Iw^2?

Also, the point of contact may move forward more, but other part of the rod also moves backwards due to the same force, how come the motion of those parts don't need to be considered?

Lastly back to my original question, how does the particles that make up the rigid body interact when the force is applied off center to make it rotate?

Think of the rod as a bunch of individual masses connected by springs. Your initial force pushes on one of the masses. You can see that it wants to drag its neighbors, pulling in a direction associated with that spring's connection. If you model that, you'll see that rotation and overall movement both emerge from the initial push.

I think I'm getting the general idea, but how come they follow a circular motion instead of just moving in the direction of the applied force?

Read about center of percussion at

http://en.wikipedia.org/wiki/Center_of_percussion

This describes how an off-center impulse causes both linear acceleration and rotation.

Bob S

I actually have an additional question regarding the article, on the diagram, the article mentions that the beam hanging off the wire would rotate about the center of gravity? Why would it not pivot around the connection point between the wire and the beam? Is there a definition that would help us identify the pivot in a rotating object?

I actually have an additional question regarding the article, on the diagram, the article mentions that the beam hanging off the wire would rotate about the center of gravity? Why would it not pivot around the connection point between the wire and the beam? Is there a definition that would help us identify the pivot in a rotating object?
In the diagram in the article, the beam is "suspended from a wire by a U-bolt so that it can move freely along the wire."
Bob S

In the diagram in the article, the beam is "suspended from a wire by a U-bolt so that it can move freely along the wire."
Bob S

Sorry but I still don't see why the beam would rotate around its center of gravity instead of the connection point.

loseyourname
Staff Emeritus
Gold Member
Sorry but I still don't see why the beam would rotate around its center of gravity instead of the connection point.

Because the "connection point" in this case can move. It isn't an anchor to one position on the wire. When you push your clothing aside in your closet, any rotation is caused by friction between the hangar and the dowel it hangs on, causing the hangar to stick a bit until you push hard enough to overcome the stickiness. In the absence of friction, the movement would just be translational. Well, since clothing isn't rigid, some of the movement would just distort the clothing, but you get the point.

Because the "connection point" in this case can move. It isn't an anchor to one position on the wire. When you push your clothing aside in your closet, any rotation is caused by friction between the hangar and the dowel it hangs on, causing the hangar to stick a bit until you push hard enough to overcome the stickiness. In the absence of friction, the movement would just be translational. Well, since clothing isn't rigid, some of the movement would just distort the clothing, but you get the point.

But if this connection point isn't a pivot, then that means that point have to be able to follow a rotational/circular path but in this case I don't see how it can move in such a fashion around the center of gravity because the point only able to travel on the pre-defined line.