I have been looking at some of my old A level books with example answers to questions regarding acceleration of a block on non-smooth inclined plane. But they all show the friction force as if it is being applied through the COM just like the youtube video frame image below.
Can anyone explain why textbooks ignore the fact that friction is an eccentric force and will also cause a couple about the block's COM?
You’re right the friction force doesn’t act through the COM. It acts parallel to the surface. But the net effect of the force is to act through the COM of the block.
What’s missing from the diagram, as you pointed out, is a force couple to account for the counter clockwise torque produced by the friction force about the COM. The reason it is ignored is it doesn’t affect the solution. It increases the normal force on one side of the COM and decreases it on the other side by an equal amount.
Hope this helps.
It is not unusual at a relatively elementary level to deal with point masses rather than extended bodies and this is the case in this example.
As you have pointed out, if the block is taken to have finite dimensions the forces would need to be re-positioned which would detract from the objective of the problem which was draw a simple free body diagram with all the forces acting at the centre of mass, consider component forces and use Newton's second law.
The acceleration of the COM doesn't care where the force is being applied, it moves as if all forces are being applied to it. Even if the object was not rigid. See here. It does ,matter if you are considered motion beyond what happens to the center of mass, such as if there is also a rotation about the COM.
