Revise Turning effects of forces for Cambridge 9702 (4.1)

Every object has a special point where its entire weight seems to act – this is its Centre of Gravity (CoG). Imagine balancing an object; the CoG is the point you'd try to support. For uniform objects (like a perfectly symmetrical ruler), the CoG is usually at its geometric centre.

Closely related is the Centre of Mass (CoM), which is the average position of all the mass in an object. While distinct in theory, in typical Cambridge Physics scenarios (where the gravitational field is considered uniform), the CoG and CoM are located at the exact same point. So, for most calculations, you can treat them as identical.

For an irregular shape, like a piece of cardboard, the CoG can be found experimentally. By suspending the object from a point and hanging a plumb line from the same point, you can trace the vertical line where the CoG must lie. Repeating this from a different suspension point gives a second line. The CoG is where these two lines intersect.

The moment of a force quantifies its ability to cause rotation about a specific point, called the pivot. Think of it as the turning power. A larger force or a greater distance from the pivot will create a larger moment, making it easier to rotate the object.

$M = F \times d_{\perp}$

For an object to be in rotational equilibrium – meaning it's either stationary or rotating at a constant angular velocity (not accelerating angularly) – the turning effects in one direction must perfectly balance the turning effects in the opposite direction. This is the Principle of Moments.

Sometimes, two specific forces combine to produce a pure turning effect without any linear movement. This arrangement is called a couple. A couple consists of two forces that are equal in magnitude, opposite in direction, parallel to each other, but act along different lines. Examples include turning a steering wheel with both hands or using a key to open a lock.

The turning effect produced by a couple is called torque (often represented by $\tau$). Unlike the moment of a single force, the torque of a couple is the same regardless of where you choose your pivot point. It causes rotation only.

$\tau = F \times d$

For an object to be in complete equilibrium, it must satisfy two conditions simultaneously: it must not be accelerating linearly, and it must not be accelerating rotationally. This means no overall push/pull and no overall turning effect.

The stability of an object is its ability to return to its original position after being slightly displaced. It is determined by the position of its Centre of Gravity (CoG). An object is most stable when its CoG is as low as possible and its base area is as wide as possible. There are three types of equilibrium: