Conditions for Equilibrium (CIE AS Physics)

Revision Note

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Author

Leander

Last updated

16 October 2024

Equilibrium

A system is in equilibrium when all the forces are balanced
- There is no resultant force
- There is no resultant torque
In accordance with Newton's First Law, an object in equilibrium will therefore remain at rest, or at a constant velocity, and will not rotate
The system is in an equilibrium state when applying the Principle of Moments

Worked example

Four beams of the same length, each have three forces acting on them.

Which beam has both zero resultant force and zero resultant torque acting?

Answer:

Step 1: Consider the principle of moments

Zero resultant force and zero resultant torque mean that the beam is in equilibrium
Therefore, for the correct answer:

clockwise moment = anticlockwise moment

Step 2: Calculate the clockwise moments for each answer option

For answer option C
Taking the pivot to be the point at which the 15 N force acts
- Therefore, there is no moment caused by the 15 N force because d = 0

$clockwise moment = 40 \times 0.5 = 20 N m$

Step 3: Calculate the anticlockwise moments for each answer option

For answer option C

$anticlockwise moment = 25 \times (0.5 + 0.3) = 20 N m$

Step 4: Determine if the beam is in equilibrium

$20 N m = 20 N m$

clockwise moment = anticlockwise moment

Therefore, beam C is in equilibrium

Coplanar forces in equilibrium

Coplanar forces can be represented by vector triangles
- For a recap on vector triangles see Scalars & Vectors
Forces are in equilibrium if an object is either
- At rest
- Moving at constant velocity
In equilibrium, coplanar forces are represented by closed vector triangles
- The vectors, when joined together, form a closed path
The most common forces acting on objects are
- Weight
- Normal reaction force
- Tension (from cords and strings)
- Friction

Forming a vector triangle for forces acting on a body in equilibrium

Vector triangle in equilibrium, downloadable AS & A Level Physics revision notes

To form a closed vector triangle, draw a free-body force diagram, then rearrange the force arrows tip to tail maintaining the length and directions of the vectors

Worked example

A mass hangs in equilibrium from a cable at point X. The tensions in the cables are T₁ and T₂ as shown.

WE - Forces in equilibrium question image 1, downloadable AS & A Level Physics revision notes Which diagram correctly represents the forces acting at point X?