quote:

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Original post by rmsgrey
Applying the same net moment or torque to an object will always produce the same angular acceleration.

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That''s not true; inertia depends on the axis of rotation. A given torque will always produce the same increase in angular momentum, not angular acceleration.

Cédric

Cedric,
Why do you say that the force will inevitably add to the linear motion of the object? This is false, because only the amount of the force in the direction of the radius vector will contribute to linear acceleration. Think about a sphere in space with a rocket engine attached to its surface. The sphere will just rotate about its center of mass, not accelerating linearly. It's the same concept behind early steam engines from long ago. It applies force perpendicular to the radius vector, causing the whole system to rotate, but not move linearly. Finally, you can have all or none of the energy go into either the rotational or linear motion of the object in space. It's just dot products and cross products, look it up in your physics books, thats where I have gotten this info.
Brendan

[edited by - Punty50 on December 12, 2002 4:07:54 PM]

quote:

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Original post by Punty50
This is false, because only the amount of the force in the direction of the radius vector will contribute to linear acceleration.

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I disagree. In classical newtonian mechanics, a = F / m = dp / dt

I understand your point of view, as I have already defended it, but now, I am pretty sure that it is false.

If the posts here haven''t convinced you, I don''t know what to say. I''ve already debated this idea one week ago on this forum, and I don''t want to start over again. Sorry.

Cédric

quote:

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Original post by cedricl
Original post by rmsgrey
Applying the same net moment or torque to an object will always produce the same angular acceleration.
That''s not true; inertia depends on the axis of rotation. A given torque will always produce the same increase in angular momentum, not angular acceleration.

Cédric

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Probably a terminology confusion. I''m fairly sure the net moment (also dependent on axis) determines angular acceleration. Use of torque as a synonym is probably inaccurate (but fairly common).

How exactly would you apply a force to a body and only increase its angular momentum without somehow altering its linear momentum as well? You''d have to apply the force at the exact edge completely perpendicular to the radius vector, but if this is the case, would it even alter the angular momentum in the first place? It''s somewhat of a "singularity" in this case (although that''s probably the worst word to use).

quote:

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Original post by rmsgrey
Probably a terminology confusion. I''m fairly sure the net moment (also dependent on axis) determines angular acceleration. Use of torque as a synonym is probably inaccurate (but fairly common).

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alpha = N / I

where alpha is the angular acceleration and N is the torque. Since

N = r X F

N doesn''t take into account the inertia on the axis r X F. You could rotate F without changing the magnitude of the torque, but it would change the axis of rotation, and its associated inertia.

quote:

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How exactly would you apply a force to a body and only increase its angular momentum without somehow altering its linear momentum as well? You''d have to apply the force at the exact edge completely perpendicular to the radius vector

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No. Any force applied for a given time at a given point on an object will cause the object to accelerate by the same value.

A good example of this is a wheel. If the wheel is perfect, then friction is exactly perpendicular to the radius vector. Yet, that''s what makes the car accelerate.

Cédric

quote:

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No. Any force applied for a given time at a given point on an object will cause the object to accelerate by the same value.

A good example of this is a wheel. If the wheel is perfect, then friction is exactly perpendicular to the radius vector. Yet, that's what makes the car accelerate.

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I was still talking about an object in free space. That's a good example, but would it apply in free space (I'm not so sure)? Like you said yourself:

quote:

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The rotation of the object does not affect p because the linear momentum of the mass on one side of the object is cancelled by the mass on the other side of the object (because p is a vectorial quantity).

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I would think that the friction on the bottom would retard the linear momentum tangeant to the bottom, and thus would create a net linear momentum on the top in the "forward" direction, actually causing the wheel to move. But in free space, there wouldn't be this friction. That's where my question came in. How exactly do you apply this force completely tangeant to the object? You can say friction, but I think that friction only causes a de-stabalization of the linear momentum on the sides of the wheel that already exists due to the angular momentum applied by the shaft (I'm not a mechanic, so whatever it's called that turns the wheels ). So without gravity that pulls stuff together, can we say that a force applied completely tangeant to the object at the edge would even affect it? It would have to come from friction, but last I knew, physicists weren't completely sure why friction works. They have a bunch of equations, but they don't really understand how it works.

Sorry if I'm totally wrong, I just like exploring these things a little.

[edited by - Zipster on December 13, 2002 1:12:37 PM]

Applying a force completely tangent to the surface isn't a particular case to deal with. There are many ways to get very close to having a completely tangential force. With a very long rod, you could apply a force at the end. You could also create an object like an inverted circle (sqrt(x) + sqrt(y) = 1, IIRC)

And friction may be complex, but it is usually modelled as a force acting at the point of contact, and opposed to the speed of the object.

Cédric

[edited by - cedricl on December 14, 2002 11:13:17 AM]

Aw, heck, just give him some code.

As you know, torque = r x F. In other words, the part of the force which angularly accelerates the object in free space varies as the sine of the angle between the force vector and the vector from the point of contact to the center of mass.

Similarly, the part of the force that acts toward linear acceleration varies as the cosine of angle between those two vectors, or in other words will use the dot product r . F.

This code is cut right out of my physics engine. I assume basic understanding of inertial moments and so forth.


void Cb3dPhysicsObject::ApplyForce(D3DXVECTOR3 vPos, D3DXVECTOR3 vForce)
{
float fForce = D3DXVec3Length(&vForce);

//based on Torque=I*alpha and F=MA
//assuming mass and inertial moment constant

D3DXVECTOR3 vTorque;
D3DXVECTOR3 vR = vPos-GetCenterOfMass();//vector from point of contact to center of mass
float fR = D3DXVec3Length(&vR);

D3DXVec3Cross(&vTorque, &vR, &vForce);

m_vRotationalVelocity += vTorque/GetInertialMoment()*g_pB3DEngine->GetDeltaTime();

float f = fabs(D3DXVec3Dot(&vR, &vForce)/fR/fForce);// = |cos(theta)|

m_vTranslationalVelocity += f*vForce/GetMass()*g_pB3DEngine->GetDeltaTime();
}




~BenDilts( void );

And now... for my shortest post... EVER

http://www-2.cs.cmu.edu/~baraff/pbm/pbm.html