Mechanical Equilibrium
High-Yield Summary
- A Free Body Diagram isolates an object and shows every force acting on it as a labeled arrow.
- Mechanical equilibrium means no net force or torque — the object is at rest or moving at constant velocity.
- Translational equilibrium (∑F = 0) and rotational equilibrium (∑τ = 0) are independent conditions.
- Torque (τ = rF sin θ) depends on force magnitude, lever arm length, and the angle between them — maximized at 90°, zero at 0°.
Drawing a Free Body Diagram
- 1Isolate the object — consider it independently from its environment.
- 2Sketch the object as a simple shape (dot or rectangle).
- 3Identify all forces acting on it — gravity, normal force, friction, tension, applied forces.
- 4Draw each force as an arrow, direction and length showing direction and magnitude.
- 5Label each force with a clear symbol (Fg, FN, Ff, FT).
Translational vs. Rotational Equilibrium
| Translational Equilibrium | Rotational Equilibrium |
|---|---|
| ∑F = 0 | ∑τ = 0 |
| No linear acceleration | No angular acceleration |
| At rest or constant velocity | Stationary or constant angular velocity |
Torque
τ = rF sin θ
- τ = Torque
- r = Lever arm / moment arm — perpendicular distance from pivot to force application
- F = Magnitude of the applied force
- θ = Angle between the force and the lever arm
Common MCAT Trap
- Translational and rotational equilibrium are independent — an object can satisfy one without the other (e.g., spinning in place with zero net force but nonzero net torque is impossible, but a net-zero-force object can still be under a net torque and start rotating).
- Torque is zero when force is applied parallel to the lever arm (θ = 0°), even if the force is large — direction relative to the lever arm matters, not just magnitude.
Quick Recall
What are the two independent conditions for mechanical equilibrium?
At what angle is torque maximized, and at what angle is it zero?