# Tangential force applied on a disc

#### ebelviranli

Hi,

I need to find an answer for the following question:

What happens when you apply a tangential force instantenously to a disc laying on a frictionless surface? Does it rotate, translate or both?

Here is an illustration for a better explanation.
http://cs.bilkent.edu.tr/~belviran/circle.PNG [Broken]

Please note that there is no axis or other forces applied to the disc. Also note that the disc is uniform and the center of mass is at the center of the disc.

Thanks

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#### Doc Al

Mentor
What do you think? Hint: Consider Newton's 2nd law for both translation and rotation.

#### vdogamr

No really, what's the answer to their question? I have been reading physics books for days trying to figure this out.

I know the answer is both, but I want to know why and by how much. If it wasn't both then physics books wouldn't make it a point to mention the Couple force.

All the math I find says that Torque is R x F, and since the cross product is "sin * mag(R) * mag(F)", and since sin(90) is 1, then all of this force is applied to the torque. But none of this force is in the direction of the center of mass, so how much of the force is translational.

And if you tell me that the disk only rotates then I am going to ask what if you apply the two forces: (0,1) (0,1) to the points (-r,0) (r,0) respectively (assuming the center is at (0,0))? I know the disk does not sit still because these two rotational forces cancel out. The disk would move in teh +Y direction, but what is the math to prove it?

Any help would be appreciated. Thank you.

#### Doc Al

Mentor
All the math I find says that Torque is R x F, and since the cross product is "sin * mag(R) * mag(F)", and since sin(90) is 1, then all of this force is applied to the torque. But none of this force is in the direction of the center of mass, so how much of the force is translational.
All of it. The translational acceleration of the center of mass is given by Newton's 2nd law. You may be thinking that a given force is either 'rotational' or 'translational'. Not so. The full applied force creates both rotational and translational acceleration. While the torque about the center of mass depends on the point of application and direction of the force, the translational acceleration does not.

And if you tell me that the disk only rotates then I am going to ask what if you apply the two forces: (0,1) (0,1) to the points (-r,0) (r,0) respectively (assuming the center is at (0,0))? I know the disk does not sit still because these two rotational forces cancel out. The disk would move in teh +Y direction, but what is the math to prove it?
Just apply Newton's 2nd law to find the translational acceleration. The net force is (0,2), so the acceleration of the center of mass is in the +Y direction.

"Tangential force applied on a disc"

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