Moments and Equilibrium

Moments

• The turning effect of a force is called the moment.
• The moment of a force is calculated by multiplying the force by the perpendicular distance from the pivot.
• Forces can cause rotation of an object around a fixed pivot point.
• This rotation can occur either clockwise or anticlockwise.

Moment Equation

• A moment is defined as the turning effect of a force about a pivot.
• The size of the moment is calculated using: moment = force × perpendicular distance from pivot.
• Forces should be perpendicular to the distance from the pivot.
• Increasing the distance from the pivot reduces the amount of force required to achieve the same moment.
• The further from the hinge, the easier it is to open a door, as less force is required.
• Measured in Newton Metres (Nm) .

Principle of Moments

• States that if an object is balanced, the total clockwise moment about a pivot equals the total anticlockwise moment about that pivot.
• For a balanced object, sum of clockwise moments = sum of anticlockwise moments
• In situations where forces and distances of objects on a beam differ but the system is balanced, the principle of moments is applied.
• Clockwise and anticlockwise moments acting on a beam are balanced.

Equilibrium

• In physics, means a state of balance or stability.
• A system keeps doing what it's doing without any change when in equilibrium.
• For objects in equilibrium, the forces must be balanced, there must be no resultant force, clockwise moments must equal the sum of anticlockwise moments and there must be no resultant moment.
• When the forces and moments on an object are balanced, the object will remain in equilibrium.

Investigating Equilibrium

• This experiment aims to demonstrate that there is no resultant moment for an object in equilibrium.
• Independent variables include force (F) and distance (s).
• The dependent variable is moment (M).
• The length of cotton loops should be the same on each side of the beam.
• Equipment needed includes a ruler with a small hole at the center, mass hangers, masses, a clamp stand, optical pin with cork, plasticine and cotton loops.
• Hang unequal loads on either side of the pivot, and adjust the distances of each mass until the beam is balanced and horizontal.
• The mass and distance from the pivot must be recorded and g must be converted to kg while cm must be converted to m to give units of Nm.
• The anticlockwise moment needs to be equal to the clockwise moment when the system is in equilibrium.
• The cotton loops should be added to the ruler when looking straight on to avoid parallax error, and should be measured to ensure they are equal in length.
• Safety goggles should be worn for this experiment, and a G clamp should be used to secure the clamp stand to the bench.

Centre of Gravity

• The centre of gravity of an object is the point through which its weight acts.
• For symmetrical objects of uniform density, the centre of gravity lies at the point of symmetry (e.g. centre of a sphere).
• Is along the axis of symmetry for a symmetrical object.
• The position of the centre of gravity affects an object's stability.
• An object is stable when its centre of gravity lies above its base.
• If the line of action of the weight force lies outside the base of the object, there will be a resultant moment, and the body will topple.
• The most stable objects have a low centre of gravity and a wide base.
• Taller objects with a narrow base have a higher centre of gravity and are less stable.
• The car can be tilted to 60 degrees without toppling however the bus topples at 45 degrees.

Investigating Centre of Gravity

• Aims to determine the position of the centre of gravity of an irregularly shaped plane lamina.
• The independent variable is the position of the centre of gravity.
• The dependent variable is the shape of the plane lamina.
• Holes should be punched in the plane lamina before determining the line of action of the weight force.
• The plane lamina will need to be irregularly shaped, the hole punch will make a hole to tie string on the point of suspension and you'll need string to hang the plane lamina with a clamp.
• Punch holes near the outer edges of the plane lamina in different locations.
• Use a plumb line aligned with the hanging thread to mark a line of the weight force on the plane lamina.
• The plumb line should be viewed straight on to avoid parallax error.
• Dots should be made whilst in position and a ruled line should be made after the plane has been removed from the clamp.