Moment of a force
Forces in Action - OCR A-Level Physics
Key Definition
Moment of a force
The turning effect of a force about a pivot. Moment = force multiplied by the perpendicular distance from the pivot to the line of action of the force.
The turning effect of a force about a pivot. Moment = force multiplied by the perpendicular distance from the pivot to the line of action of the force.
$$M = Fd$$
$$\text{moment} = F \times d$$
Key Definition
Principle of moments
For a body in rotational equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about that point.
For a body in rotational equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about that point.
Common Mistake
MEDIUM
Students often: Don't use the distance along the beam or rod instead of the perpendicular distance to the line of action of the force.
Instead: The distance in the moment equation MUST be the perpendicular distance from the pivot to the line of action. If the force is at an angle theta to the beam, use $moment = Fd \sin(\theta)$.
Instead: The distance in the moment equation MUST be the perpendicular distance from the pivot to the line of action. If the force is at an angle theta to the beam, use $moment = Fd \sin(\theta)$.
Worked Example [4 marks]
A uniform beam of length 4.0 m and weight 200 N is supported at its centre. A 50 N weight is placed 1.5 m from the left end. Where must a 30 N weight be placed to balance the beam?
Show Solution
1
The beam is supported at its centre (2.0 m from each end). The beam's weight acts at the pivot, so it produces no moment
[1]2
$The 50 N weight is 2.0 - 1.5 = 0.5 m to the left of the pivot. Anticlockwise moment = 50 \times 0.5 = 25 \text{ N m}$
[1]3
For equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹..
$clockwise moment = anticlockwise moment. So 30 \times d = 25$
[1]4
$d = \frac{25}{30} = 0.83 \text{ m to the right of the pivot} = 2.0 + 0.83 = 2.83 \text{ m from the left end}$
[1]Answer
The 30 N weight must be placed 2.83 m from the left end (0.83 m to the right of the pivot).