Tips for drawing components of forces in A-level Maths mechanics

Hi, does anyone have any tips/efficient ways of drawing the components of forces in mechanics? Mainly when you have to find the components horizontal and perpendicular to the plane of a friction force acting on the bottom of a plank resting against a wall in equilibrium. I always end up wasting time drawing a small diagram which makes it hard to tell where the angle should go. Any help appreciated. Thanks.

A sketch is usually the way to go. Are you unsure about which of the two complementary angles in the right force component triangle is equal to the original one? I generally just think about what happens when the original angle is small (~0), then the angle that goes to zero in your right force triangle is that one and the parallel/perpendicular for sin/cos is straightforward.

Of course doing a small amount of angle chasing is really the way to proceed.

Ok thank you that is helpful. I mostly meant the ones where you have a plank at rest against a wall and you need to take moments around the point in contact with the vertical wall, how you go about finding the component that is perpendicular to the plank to find the moment but I think sketching will help

Hi, does anyone have any tips/efficient ways of drawing the components of forces in mechanics? Mainly when you have to find the components horizontal and perpendicular to the plane of a friction force acting on the bottom of a plank resting against a wall in equilibrium. I always end up wasting time drawing a small diagram which makes it hard to tell where the angle should go. Any help appreciated. Thanks.

One method I find very helpful is to visualise what must happen to the force component if the angle in question was increased or decreased, or taken to its logical conclusion, what would happen to the force component if the angle was decreased to 0 or increased to 90.

If it's clear that the force component must increase as the angle is increased, then the component is Fsin@. (An example is the component of a particle's weight acting down a slope inclined at @).

If it's clear that the force component must decrease as the angle is increased, then the component is Fcos@. (An example is the normal reaction to a particle's weight on a slope inclined at @).

If in doubt about this, consider the shape of the sine and cosine curves between 0 and 90deg. The same line of thought can be applied to moments.

Ok thank you that is helpful. I mostly meant the ones where you have a plank at rest against a wall and you need to take moments around the point in contact with the vertical wall, how you go about finding the component that is perpendicular to the plank to find the moment but I think sketching will help