Turning Effects of Force

A force applied to a body that is free to rotate does not simply push it — it turns it. How much turning effect you get depends on two things: how hard you push, and how far from the pivot you push.

This is why a door handle is fitted on the edge furthest from the hinges. Push near the hinge and almost nothing happens; push at the far edge with the same force and the door swings easily. It is also why a long spanner undoes a tight nut that a short one cannot.

The word perpendicular in the definition is not decoration. The distance must be measured at right angles from the pivot to the line of action of the force. Push along a line that passes straight through the pivot and the perpendicular distance is zero, so there is no turning effect at all, however hard you push.

moment

turning effectN m

F

forceN

d

perpendicular distancem

Slide the masses and watch the two moments. Balance is reached when the clockwise total equals the anticlockwise total — a small mass far out can balance a large mass close in, which is the whole principle of a lever.

When an object is balanced and not rotating, the turning effects in the two directions must cancel exactly. This is the principle of moments: for a body in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that same point.

The phrase "about any point" is genuinely useful. You may take moments about whichever point you like, and a well-chosen pivot makes a hard problem easy — pick the point where an unknown force acts, and that force disappears from the equation because its distance is zero.

Setting these problems out neatly saves marks. List the clockwise moments on one side, the anticlockwise on the other, set them equal, and solve. Muddling the two directions is the commonest error, and it is always visible in a tidy layout.

Every particle of an object has weight, but for the purposes of a calculation all of that weight can be treated as acting at one point. For a uniform object of regular shape that point is at its geometric centre — the middle of a uniform metre rule, the centre of a uniform sphere.

For an irregular flat shape it can be found experimentally. Suspend the shape freely from a point, hang a plumb line from the same point and mark the vertical. Repeat from a second point. The centre of gravity lies where the two lines cross, because a freely suspended object always hangs with its centre of gravity directly below the point of support.

A third suspension point is normally used as a check. If all three lines meet at one place, the result is reliable.

An object topples when its centre of gravity moves outside its base. That single sentence answers most stability questions, and everything else follows from it.

Tilt an object and its weight acts vertically down through the centre of gravity. While that line still falls inside the base, the weight produces a moment that turns the object back upright — it is stable. Tilt it further, past the point where the line falls outside the base, and the same weight now turns it over instead.

So an object is made more stable in two ways: give it a low centre of gravity and a wide base. Both increase the angle it must be tilted through before the line of the weight escapes the base.

This is why a racing car is low and wide, why a Bunsen burner has a heavy base, and why a double-decker bus is tested for stability with passengers only on the upper deck. It is also why you instinctively spread your feet and crouch on a moving bus.