Turning Effect Of Forces Notes

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Chapter 5 Notes Turning Effect of Forces

Turning Effect of Forces

• The turning effect of a force about a point is the product of the force and the perpendicular distance from the point to its line of action of the force

○ Also known as ‘ moment’ or ‘ torque’

• Moment = F x d

○ d refers to its perpendicular distance!

• Clockwise vs. Anti-Clockwise Moments
• Unit is Nm (newton meter)

How to find the moment

• Draw the line of action of force
• Connect it to the pivot
• Make sure it’s perpendicular

Principle of Moments

 When an object is in equilibrium, the sum of clockwise moments about a point = the sum of anticlockwise moments about same point  Conditions for Equilibrium of an Object

• Resultant force acting on it is zero
• Resultant moment about a pivot is zero

Mega Lecture Chapter 5: Turning Effect of Forces

Example 1:

Example 2:

The masses of P, Q, and R are such that the rods are horizontal. What are their possible masses?

• R: 2x distance from pivot → ½ mass of Q - P: 2x distance from pivot → ½ mass Q+R

Object R falls off. Describe what happens to rod N.

• Only Q left on rod N, creating an anticlockwise moment about pivot, so rod N rotates anticlockwise about its pivot

Example 3:

Describe how the largest moment about the pivot can be produced at A.

• With force at A, perpendicular distance of line of action of force from pivot is greatest
• Using formula ‘moment = F x dh’, this generates largest moment about pivot

Mega Lecture Chapter 5: Turning Effect of Forces

Centre of Gravity

• The point through which its whole weight appears to act
• An object will only balance in equilibrium if the point of balance is directly below the center of gravity
• For any uniform/regular object, the C.G. is located at its geometrical center
• If you place the pivot at any point that is NOT C.G., sum of clockwise moments will not be = sum of anticlockwise moments

Mega Lecture Chapter 5: Turning Effect of Forces

Example 1: The front of a helicopter tilts down, while its CG stays at the same height. How?

• Lift force from front rotor decreased, while lift force from back rotor increased

Example 2: Where is the CG of the object?

Most of mass is on right of knife, so CG is to right of it → Exerts clockwise moment to counter anticlockwise moment caused by suspended weight

Stability

• Definition: Measure of a body’s ability to maintain its original position

(after being tilted)

• For something to be stable, the line of action must fall within the base

area

• Stability can be increased by lowering center of gravity +

increasing base area

• An object with a lower CG and a larger base area has to be tilted at a larger angle before the line of action falls outside base area, so it is more stable

Mega Lecture Chapter 5: Turning Effect of Forces

Types of Equilibrium

• Stable Equilibrium : Object returns to original position after being displaced slightly
• Limiting Equilibrium: Maximum orientation of an object before it topples
• Unstable Equilibrium: Object continues to move away from original position
• Neutral Equilibrium: Object remains where it is displaced (new position)
• Currently in neutral equilibrium position (ramp) → Tilted further, line of action of weight outside base area → Resultant clockwise moment about right wheel → Tilts over

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