[PHY] Chapter 5 - Moments

DARRELL ER (COPYRIGHTED) © TOPIC 5: MOMENTS DARRELL ER (COPYRIGHTED) ©

CHAPTER ANALYSIS THE ABOUT MASTERY EXAM WEIGHTAGE DARRELL ER (COPYRIGHTED) ©

PRINCIPLE OF MOMENTS CENTER OF GRAVITY STABILITY KEY CONCEPT DARRELL ER (COPYRIGHTED) ©

Principle of Moments When an object is at equilibrium, the sum of clockwise moments about any pivot is equal to the sum of anticlockwise moments about the same pivot. For an object to be in equilibrium, 1) Resultant forces must be zero 2) Resultant moment must be zero MOMENTS DARRELL ER (COPYRIGHTED) © Moment Moment of a force is defined as the product of a force and the perpendicular distance from the line of action of the force to the pivot. Units: Nm Formula: Moment = F x d where d is the perpendicular distance

Principle of Moments (Example 2) A uniform rod AB of weight 100 N and length 2 m is supported by two vertical strings at its ends and carries a load of 20 kg as shown in the diagram below. Determine the tensions in the strings. Answer: Let the tension of the string at A be T1 the tension of the string at B be T2 Taking moments at A, 100 x 1 + 200 x 0.5 =T2 x 2 T2 = 100 N Sum of upward forces = sum of downward forces T1 + T2 = 200 + 100 T1 = 300 – 100 = 200 N OR Taking moments at B 100 x 1 + 200 x 1.5 =T1 x 2 T1 = 200 N MOMENTS (EXAMPLE 1) DARRELL ER (COPYRIGHTED) ©

CENTER OF GRAVITY For irregular bodies, we can use a plumb line to determine the center of gravity. CENTER OF GRAVITY DARRELL ER (COPYRIGHTED) © Center of gravity is defined as the point through which the entire weight of the object appears to act. A regular body with uniform weight distribution will have its center of gravity in the centroid.

STABILITY Increase base area Lower center of gravity DARRELL ER (COPYRIGHTED) © STABILITY Stability is the measure of a body’s ability to return to its original position after being tilted slightly. To increase stability, Equilibrium Diagram Stable equilibrium - when object is displaced, the cg of the object is raised - the line of action of the cg still falls within its base area - the weight generates a moment about the pivot causing the object to return to its original position Unstable equilibrium - when object is displaced, the cg of the object is raised - the line of action of the cg falls outside its base - its weight generates a moment about the pivot causing the object to topple over Neutral equilibrium - when object is displaced, the cg of the object remains at the same horizontal level - the line of action through the cg will always pass through the pivot point - its weight has zero moment about the pivot

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