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Hello there.

I have some difficulty in understanding the condition for a rigid body standing still (or rotating).

If we have a body, let's say a yoyo which is somehow pierced through the center and attached in a way that it's center of mass can't move, but the yoyo can rotate if we apply a torque.

If we pull the yoyo rope, it will exert a torque which will make the yoyo start rotating, but there will be a force of same size but opposite direction acting on the center of rotation. This force won't exert a torque (since it acts on the rotation axis) but it will prevent translation movement of the center of mass since all forces applied on the body are zero.

Now let's observe this image:

[PLAIN]http://img524.imageshack.us/img524/4026/kuglananagibu.gif [Broken]

And let's suppose

[tex]k mg Cos{\alpha}-mg Sin{\alpha}=0[/tex]

The resultant torque is:

[tex]k mg Cos{\alpha} R=J \alpha[/tex]

(R is the radius and alpha in this case is the angular acceleration)

So in the end we have a rolling body which has a translational acceleration of the center of mass, without any resultant force acting on the body.

I know that can't be, i just don't know what I'm I doing wrong.

Please help

I have some difficulty in understanding the condition for a rigid body standing still (or rotating).

If we have a body, let's say a yoyo which is somehow pierced through the center and attached in a way that it's center of mass can't move, but the yoyo can rotate if we apply a torque.

If we pull the yoyo rope, it will exert a torque which will make the yoyo start rotating, but there will be a force of same size but opposite direction acting on the center of rotation. This force won't exert a torque (since it acts on the rotation axis) but it will prevent translation movement of the center of mass since all forces applied on the body are zero.

Now let's observe this image:

[PLAIN]http://img524.imageshack.us/img524/4026/kuglananagibu.gif [Broken]

And let's suppose

[tex]k mg Cos{\alpha}-mg Sin{\alpha}=0[/tex]

The resultant torque is:

[tex]k mg Cos{\alpha} R=J \alpha[/tex]

(R is the radius and alpha in this case is the angular acceleration)

So in the end we have a rolling body which has a translational acceleration of the center of mass, without any resultant force acting on the body.

I know that can't be, i just don't know what I'm I doing wrong.

Please help

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