State that, when there is no resultant force and no resultant moment, an object is in equilibrium
1.5.2 Turning Effect of Forces
What is a Turning Effect?
A turning effect, or moment, is produced when a force is applied at a distance from a pivot point. It tries to rotate the object. The magnitude of a moment is given by:
$$\tau = F \times d \times \sin\theta$$
where $F$ is the force, $d$ is the perpendicular distance from the pivot, and $\theta$ is the angle between the force and the lever arm.
Equilibrium Conditions
- For an object to be in static equilibrium, the sum of all forces must be zero: $\sum \mathbf{F} = 0$.
- And the sum of all moments about any point must also be zero: $\sum \tau = 0$.
Analogy: The Balance Scale
Think of a balance scale. If the two pans are at equal distances from the centre and you put equal weights on each side, the scale stays level. The forces (weights) balance each other, and the moments (torques) about the centre are also zero.
⚖️ If you add a heavier weight on one side, the scale tips. The moment on that side becomes larger than the other side, breaking equilibrium.
Practical Example
- Imagine a seesaw (lever) with a child weighing $50\,\text{kg}$ sitting 2 m from the pivot.
- Another child weighing $30\,\text{kg}$ sits 3 m on the opposite side.
- Calculate the moments:
| Child | Weight (kg) | Distance (m) | Moment (N m) |
|---|---|---|---|
| Child A | 50 | 2 | $50 \times 9.8 \times 2 = 980$ |
| Child B | 30 | 3 | $30 \times 9.8 \times 3 = 882$ |
| Net Moment | $980 - 882 = 98$ N m (Clockwise) | ||
Since the net moment is not zero, the seesaw will tip clockwise. To achieve equilibrium, the moments must balance.
Exam Tip 🚀
When you see a problem about equilibrium:
- Identify all forces and their directions.
- Choose a convenient pivot point (often a support or hinge).
- Calculate each moment: $\tau = F \times d$ (use the perpendicular distance).
- Set up the equation: $\sum \tau = 0$ and solve for the unknown.
Remember: Zero net force + Zero net moment = Equilibrium.
Quick Summary
- Moment = Force × Distance (perpendicular).
- Equilibrium requires both $\sum \mathbf{F} = 0$ and $\sum \tau = 0$.
- Use a pivot point to calculate moments.
- Check your units: Force in N, distance in m, moment in N m.
Revision
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