Translational and Rotational Equilibrium

Vocabulary flashcards covering translational equilibrium, component resolution, force calculations, and rotational equilibrium/torque from physics lecture notes.

Translational Equilibrium

The condition of a system where the net external force is zero ($F_{\text{net}} = 0$), resulting in zero acceleration ($a = 0$) and satisfying both $\Sigma F_x = 0$ and $\Sigma F_y = 0$.

Equilibrium Components Method

A problem-solving method where all applied forces are resolved into perpendicular horizontal ($x$) and vertical ($y$) components so that $\Sigma F_x = 0$ and $\Sigma F_y = 0$ can be solved algebraically.

Sine Law Method (Equilibrium)

A trigonometric method applied to three concurrent forces in equilibrium that relates the magnitude of each force vector to the sine of its opposite interior angle in a closed force triangle.

Gravitational Force ($F_g$)

The downward force exerted on an object by gravity, calculated by $F_g = mg$, where $g = 9.81\,\text{m/s}^2$.

Tension ($F_T$)

The pulling force transmitted axially through a string, rope, cable, or chain when subjected to external loading.

Torque ($\tau$)

A vector quantity created by applying a force at some distance away from a pivot point, measured in Newton-meters ($\text{N}\cdot\text{m}$) and calculated as $\tau = F_\perp r$.

Fulcrum

The pivot point or point of rotation for a lever system; applying a force directly at this point produces zero torque and no rotation.

Perpendicular Force ($F_\perp$)

The component of an applied force that acts at a right angle to the lever arm to generate rotational force.

Distance from Fulcrum ($r$)

The distance from the point of rotation or fulcrum to the location where an external force is applied, measured in meters ($\text{m}$).

Rotational Equilibrium

The state of a system where the net torque is zero ($\Sigma \tau = 0$), satisfied when total clockwise torque equals total counterclockwise torque ($\tau_{cw} = \tau_{ccw}$).

Counterclockwise Torque ($\tau_{ccw}$)

A torque that tends to cause rotation in the direction opposite of clock hands, conventionally assigned a positive ($+$) sign.

Clockwise Torque ($\tau_{cw}$)

A torque that tends to cause rotation in the same direction as clock hands, conventionally assigned a negative ($-$) sign.