Moments
Section: Motion, Forces & Energy | Syllabus: Cambridge AS Level Physics 9702
Moments A moment describes the turning effect of a force about a pivot point. Moment The turning effect of a force about a pivot or axis. It measures how much a force causes something to rotate. M = F × d Where: \(M\) = moment (N·m), \(F\) = force (N), \(d\) = perpendicular distance from pivot (m) Moment Diagram: Turning Effect of a Force A horizontal beam with a pivot (triangle) at one end.
A downward force arrow (F) acts at a distance (d) from the pivot. The perpendicular distance d is marked with a dashed line. Moment = F × d, causing clockwise rotation. Common Mistake Only the perpendicular distance to the pivot counts - not the slanted or total length of the object.
Equilibrium An object is in equilibrium when all the forces and moments acting on it are balanced. Equilibrium The state when all forces and moments acting on an object are balanced. This means: The resultant force = 0 (no linear acceleration) The resultant moment about any point = 0 (no rotation) Principle of Moments For an object in equilibrium, the sum of clockwise moments = the sum of anticlockwise moments .
Balanced Beam in Equilibrium A horizontal beam balanced on a central pivot (fulcrum). On the left side: a weight W₁ at distance d₁ from pivot (anticlockwise moment). On the right side: a weight W₂ at distance d₂ from pivot (clockwise moment).
For equilibrium: W₁ × d₁ = W₂ × d₂. Centre of Gravity The centre of gravity is the point where an object's entire weight appears to act. Centre of Gravity The point where an object's entire weight appears to act.
For regular, uniform objects, the CG is at the geometric centre For irregular shapes, the CG can be found experimentally Stability Tip An object is more stable if its centre of gravity is low and its base is wide.
Centre of Gravity and Stability Three objects compared: (1) Wide-based cone with low CG - very stable. (2) Narrow-based cone with high CG - unstable. (3) Tilted object showing that if the vertical line from CG falls outside the base, it topples.
Lower CG and wider base = greater stability. Investigating Centre of Gravity To find the centre of gravity of a flat irregular shape: Hang the shape from a pin through one hole Hang a plumb line (string with a weight) from the same point Draw a line along the plumb line Repeat from another hole - the intersection point of the lines is the centre of gravity Finding the Centre of Gravity Experiment An irregular lamina (flat shape) suspended from a pin at one corner.
A plumb line (string with bob) hangs from the same pin. A vertical line is drawn along the string. Process repeated from another corner. The intersection of the two lines marks the centre of gravity. Exam Tip Label your diagram clearly - show the plumb line, pivot point, and intersection marking the CG.
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