Equilibrium
Scalars & Vectors - OCR A-Level Physics
Key Definition
Equilibrium
An object is in equilibriumResultant force zero; object is stationary or moving at constant velocity. when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector. Measured in $\text{m s}^{-1}$.. By Newton's first law, no acceleration occurs.
An object is in equilibriumResultant force zero; object is stationary or moving at constant velocity. when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector. Measured in $\text{m s}^{-1}$.. By Newton's first law, no acceleration occurs.
Diagram pending
Closed triangle of forces. Three force arrows drawn nose-to-tail: weight $W$ pointing down, tension $T$ along a string at an angle, normal $N$ along a surface. Each arrow's tail starts at the previous arrow's nose, and the third arrow's nose meets the starting point of the first, closing the triangle. Label "closed triangle = equilibrium" beneath.
Will be replaced with a GeoGebra SVG in stream 2.
- For an object in equilibrium under three coplanar forces, the three force arrows drawn nose-to-tail form a closed triangle: the third arrow's nose returns to the first arrow's tail.
- If the triangle does not close, there is a net (resultant) force; the object is NOT in equilibrium and will accelerate.
- Alternatively, resolve all forces into perpendicular components. For equilibrium: sum of horizontal components $\sum F_x = 0$ AND sum of vertical components $\sum F_y = 0$.
- Both conditions are equivalent. The triangle is quicker for scale drawing; the component sums are quicker for calculation.
$$\sum F_x = 0 \qquad \sum F_y = 0$$
Common Mistake
MEDIUM
Wrong: Saying "equilibrium means the object is stationary".
Right: Equilibrium means the resultant force is zero. The object can be stationary OR moving at constant velocity. A skydiver at terminal velocityThe constant velocity reached when the driving force on an object is exactly balanced by resistive forces, so the resultant force is zero. is in equilibrium even though they are moving at $\sim 50 \text{ m s}^{-1}$ downward.
Right: Equilibrium means the resultant force is zero. The object can be stationary OR moving at constant velocity. A skydiver at terminal velocityThe constant velocity reached when the driving force on an object is exactly balanced by resistive forces, so the resultant force is zero. is in equilibrium even though they are moving at $\sim 50 \text{ m s}^{-1}$ downward.
Examiner Tips and Tricks
- For three coplanar forces in equilibrium, either draw a closed force triangle (scale drawing) OR set $\sum F_x = 0$ and $\sum F_y = 0$.
- The component method is more accurate in calculations.
- If the problem mentions "constant velocity", "stationary", "rest", "uniform motion", or "terminal velocity", the object is in equilibrium and you can set the component sums to zero.