Moments and Stability
Understanding turning effects, equilibrium, and center of mass
Moments determine how forces cause rotation around a pivot
A moment (also called torque) is the turning effect of a force around a pivot point. The moment depends on both the size of the force and how far it acts from the pivot. The formula is M = F × d, where M is the moment (in Newton-meters, N·m), F is the force (in Newtons), and d is the perpendicular distance from the pivot (in meters).
The principle of moments states that for an object in equilibrium (balanced), the sum of clockwise moments equals the sum of anticlockwise moments. This principle explains how seesaws balance and is used to calculate unknown forces or distances in lever systems. For example, a heavier person must sit closer to the pivot to balance a lighter person sitting further away.
The center of mass is the point where an object's entire weight appears to act. For uniform objects, it's at the geometric center. For irregular shapes, we can find it using the suspension method: hang the object from different points and mark vertical lines - they intersect at the center of mass.
Stability depends on two factors: the height of the center of mass and the width of the base. Objects are more stable with a lower center of mass and wider base. This is why racing cars are low and wide (very stable), while double-decker buses are relatively unstable. An object tips over when the vertical line from its center of mass falls outside its base.
Explore turning effects, equilibrium, and stability
Moment (Torque)
25.0 N·m
M = F × d = 50 × 0.50
Key Formula: Moment = Force × Perpendicular distance from pivot (M = F × d). Larger force or greater distance creates a larger turning effect.
Term
Moment (Torque)
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Example 1: Seesaw Balance
A child weighing 400 N sits 1.5 m from the pivot. Where must an adult weighing 600 N sit to balance?
Clockwise moment = Anticlockwise moment
F₁ × d₁ = F₂ × d₂
400 N × 1.5 m = 600 N × d
600 N·m = 600d
d = 1 m
The adult must sit 1 m from the pivot.
Example 2: Wrench Comparison
Compare the turning effect of a 10 cm wrench vs a 30 cm wrench, both with 50 N force.
Short wrench: M = 50 N × 0.1 m = 5 N·m
Long wrench: M = 50 N × 0.3 m = 15 N·m
The longer wrench gives 3× more turning effect!
Example 3: Mechanical Advantage
A crowbar has an effort arm of 1 m and load arm of 0.1 m. What load can be lifted with 100 N effort?
Mechanical Advantage = effort arm ÷ load arm
MA = 1 m ÷ 0.1 m = 10
Load = Effort × MA = 100 N × 10
Load = 1000 N (can lift 10× the effort force)
Calculate the moment when F = 50 N and d = 0.5 m