How to know when to break up equilibrium problems into components, vs torque

[Mdhiggenz]

Homework Statement

I am a bit confused on when to break up static equilibrium problems into their linear components, vs just jumping straight into angular torque without breaking the linear forces into their respective components. For example:

A uniform plank of mass 30kg and length 2.0m is attached to the side of a building using the diagramed contraption with a rope making an angle 40 degrees above the board.

In this problem they don't break up the linear forces into any components they just jump straight into torque. while in this one

What is the maximum distance x from a smooth frictionless wall you can put a 100N uniform ladder of length 5.0m on a floor where the coefficient of static friction is 0.40?

They break the forces up into their respective components.

Thank you

Homework Equations

The Attempt at a Solution

 

[PhanthomJay]

You have to look at the problem and see which approach is easiest. When the angle between the force and position vector is known, T = rFsin theta works good. Otherwise, it is usually best to break up the force into its force components and calculate the sum of the moments of each component using T = Fd, where d is the perpendicular distance from the line of action of the force to the point about which you are summing moments. Often you have to break up the force into its components in either case to solve for other forces, so often it is best to use the 'force times perpendicular distance' method.