Final answer:
Angularity in a planar surface in physics involves three equilibrium conditions that reduce to torques only in the x- and y-dimensions when rotation occurs around the z-axis. Conservation of angular momentum is crucial, which holds true when net external torque is zero. The direction of angular momentum is perpendicular to the plane containing the lever arm and linear momentum.
Step-by-step explanation:
When angularity is applied to a planar surface, certain equilibrium conditions must be satisfied. In the context of physics and specifically regarding planar equilibrium problems with rotation, the equilibrium conditions for a system can be reduced to three. A chosen axis, the z-axis, would typically be the axis of rotation, making the net torque have only a z-component. Forces with non-zero torques would lie in the xy-plane, and therefore, torques arise only from the x- and y-components of these external forces.
Moreover, the conservation of angular momentum is a fundamental principle that applies to systems in equilibrium. Angular momentum is analogous to linear momentum, described as L = Iw, where I is the moment of inertia and w is the angular velocity. For angular momentum to be conserved, the net external torque must be zero, analogous to the conservation of linear momentum when the net external force is zero.
It's also important to note that the direction of the angular momentum is chosen to be perpendicular to the plane containing the lever arm and momentum, which parallels the convention of the torque direction being perpendicular to the plane formed by the lever arm and the force.