I understand that but the x'-x' axis in the question is parallel to the bar and not perpendicular?Orodruin said:
Exactly, and the moment of inertia relative to that axis is zero, as shown in the solution.influx said:
Orodruin said:
Because the problem you are solving is idealising the rod as infinitely thin - i.e., having negligible diameter.influx said:
Orodruin said:
influx said:
So you need a negative angle to counter that offset. The y-axis is pointing into the screen so a positive rotation would typically be clockwise.influx said:
The inertia matrix of a bar is a mathematical representation of its resistance to changes in rotational motion. It contains information about the bar's mass distribution and shape.
The inertia matrix is calculated by multiplying the mass matrix (a diagonal matrix with the bar's mass along the diagonal) by the square of the transformation matrix, which describes the orientation of the bar in space.
The inertia matrix provides information about how difficult it is to change the rotational motion of the bar. It includes the moments of inertia, which indicate how the mass is distributed around the rotation axis, and the products of inertia, which show how the mass is distributed off the rotation axis.
The inertia matrix determines the bar's resistance to changes in rotational motion. A higher inertia matrix means that it will be more difficult to change the bar's rotation, while a lower inertia matrix means it will be easier to change its rotation.
Yes, the inertia matrix of a bar can change if its mass distribution or shape is altered. For example, if weights are added to one end of the bar, the inertia matrix will increase, making it more difficult to change the bar's rotation.