Torque on a Rigid Body: Explained

[miss photon]

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is it true that when the net force on a rigid body is zero, the torque about any line perpendicular to the plane of the forces is equal?

it is known that angular velocity, and hence angular acceleration about any line is the same for a given rotating rigid body.
implies,$$\alpha$$ is same about all lines.
$$\tau$$=I$$\alpha$$
if we accept the above statement to be true, then I comes out to be equal about every axis, which we know is not true. so what's the explanation?

 

[radou]

is it true that when the net force on a rigid body is zero, the torque about any line perpendicular to the plane of the forces is equal?

Perhaps I misunderstood something, but in general all the forces need not act in the same plane.

 

[Shooting Star]

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is it true that when the net force on a rigid body is zero, the torque about any line perpendicular to the plane of the forces is equal?

it is known that angular velocity, and hence angular acceleration about any line is the same for a given rotating rigid body.

When only two equal anti-parallel forces act on a body it’s called a couple. This just rotates the body about the CM in the plane containing those forces. The torque of these two forces is independent of the choice of origin, and the answer to your first Q is yes.

(But there need not be exactly two forces as long as the resultant force is zero. Then also, the net result is a couple.)

Your 2nd statement about ang mom is not true. The ang mom of a body around any axis is the sum of the ang mom of the body about the CM and the ang mom of the CM about that axis considering the whole mass to be residing in the CM.