Rotation of a body around which axis

[jd12345]

When i apply torque on a body, it will rotate around whcih axis? I guess its the axis along centre of mass but i don't know why?

Also if the answer is centre of mass what will be the orientation of the axis- I mean there are infinite lines passing through a single point so which of those axis will be the one around which body rotates?

 

[mfb]

You can always describe the movement of a rigid body as a rotation around its center of mass (with a certain orientation of the angular momentum) plus a velocity of the center of mass (in some direction).

If you apply a torque without any net force (which means that the sum of forces (not torques!) is 0) to an unmoved object, it will begin to rotate at the position where it was before. If you apply a torque with a net force (for example, kick one side of the object), it will do a combination of rotation and global movement in the direction of the kicking force.

what will be the orientation of the axis

The same as the axis of your torque (F x r).

 

[phyzguy]

The same as the axis of your torque (F x r).

This statement is not true in general. An irregularly shaped body is described by a tensor of inertia, which means that the body will not necessarily rotate around the axis defined by the torque. The two axes will only coincide if the torque is applied along one of the principle axes. Otherwise, the angular momentum will be along the axis of the torque, but the angular velocity will be around a different axis, as described by the equation L = I w.

 

[mfb]

I meant the axis of angular momentum with this reply.
Maybe I should have said this explicitly.

 

[PJC01]

The rotation of a body around an axis is determined by the direction of the applied torque and the location of the axis of rotation. When torque is applied to a body, it causes a rotational motion around an axis. The axis of rotation is the line around which the body rotates.

In the case of a body rotating around its centre of mass, the axis of rotation will be along the line passing through the centre of mass. This is because the centre of mass is the point where the mass of the body is evenly distributed, and therefore, the point where the torque will have the greatest effect on the rotation of the body.

As for the orientation of the axis, it will depend on the direction of the applied torque. The axis will be perpendicular to the direction of the torque, and the rotation will occur in the same direction as the torque.

It is important to note that there are indeed infinite lines passing through a single point, but the axis of rotation is not just any arbitrary line passing through the centre of mass. It is the specific line that is perpendicular to the direction of the applied torque and passes through the centre of mass. This is the axis around which the body will rotate when torque is applied.