Motion of a rectangular rod in free space

[BLOBIFY]

Hello physicsForum..

I am trying to make a 2d physics engine for my game all on my own but I am stuck in the very basic problem. My problem is this..

If there is a rectangular body (with negligible depth since i am working on 2d) is present in free space as in attached file and a force of 'F' Newton is applied along the edge, how will it move?

I am guessing it will rotate about its center of mass but I need to know why it rotates around center of mass and not any other axis... Also, please tell me about the nature of the translational motion of the object as well...

 

[tiny-tim]

Welcome to PF!

Hello BLOBIFY! Welcome to PF!

I am guessing it will rotate about its center of mass but I need to know why it rotates around center of mass and not any other axis... Also, please tell me about the nature of the translational motion of the object as well...

Its centre of mass will move as if the force was directed through the centre of mass.

It will also rotate, with an angular acceleration α determined by τ = Iα, where τ is the torque and I is the moment of inertia.

In that sense, yes it will rotate about its centre of mass (however, the centre of mass is not the official centre of rotation … which has to be stationary … since it is itself moving).

 

[BLOBIFY]

Thanx for reply tiny tim... But I do not understand how the center of mass itself will move if the force is applied on the edge of the rectangular rod...

How does the translational motion of body vary along the distance? I know that translational motion will be maximum if force is applied along center of mass (and thus zero rotation) and translational motion will be zero if force is acting along the edge (as in the attachment above).. I want to know how the translational motion occur in the middle between these two extremes..

I know i am asking dumb qstns but I am not able to get my head around it.. :|

 

[tiny-tim]

… I do not understand how the center of mass itself will move if the force is applied on the edge of the rectangular rod...

It just does …

the centre of mass always moves as if the net force is directed through the centre of mass.

If you don't want to just accept this, you'll need to read a book (or watch a youtube video) on rigid body motion. ​

 

[BLOBIFY]

give some link please.. I am doing 2d physics engine u know.. need to be convincing if not accurate.. please share some links for rigid body videos..

 

[tiny-tim]

dunno!

try google ​

 

[BLOBIFY]

I have tried google.. It hasn't specifically helped.. :)
I understand I acted naive in my questions.. I will ask again..

Let the force 'F' act as shown in attachment at a distance of 'a' from center of mass.. Let the duration of impact be 'T'... I want to know the eqns of translational and rotational motion... I want to know how one can determine positions x,y and angle tita given any time.. Plz explain me the physics involved.. Give me a hint, I will derive it myself!

 

[tiny-tim]

The (linear) acceleration of the centre of mass is d²x/dt² = F/m.

The angular acceleration is d²θ/dt² = 12F.a/m(L² + w²), where w is the width of the rectangle.

 

[BLOBIFY]

Thanx for eqns.. It is my job to derive it on my own!
But according to first eqn, the linear acceleration does not depend on where the force is applied along the rectangle.. But I cannot understand how? If I place a pen on the flat surface and strike it along the edge, it just rotates and if i strike it at the center it moves but hardly rotates... But the first eqn suggests otherwise! How is this possible?? Is it because I am conducting this "pen" experiment not in free space?

 

[haruspex]

according to first eqn, the linear acceleration does not depend on where the force is applied along the rectangle.. But I cannot understand how? If I place a pen on the flat surface and strike it along the edge, it just rotates and if i strike it at the center it moves but hardly rotates

It may seem like you're applying the same impulse in each case, but in practice that's hard to do. If you strike it in the middle with your finger, it puts up much more resistance to movement than when struck at one end, so you can't help delivering a bigger impulse. You could try hitting it with a projectile, but then you would run into another issue. A strike in the middle would transfer more of the energy from the projectile to the pen. To do a proper comparison you need an inelastic impulse.

 

[BLOBIFY]

So in ideal case, taking same impulse time, the translation will be same regardless of where the pen is hit right?

 

[tiny-tim]

right