The moment of a force is a measure of the turning effect of the force on an object.
The moment of a force about a pivot = force x perpendicular distance from the line of action of the force to the pivot.
To increase the moment of a force, increase the force or distance to the pivot.
When using a lever to make the job easier, the force we are trying to move is called the load and the force applied to the lever is called the effort.
A lever acts as a force multiplier, so the effort we apply can be much less than the load.
Perpendicular distance: the shortest distance from the line that the force acts along
2.2 Centre of mass
The centre of mass of an object is that point where its mass may be though to be concentrated.
Any object that is freely suspended will come to rest with its centre of mass directly below the point of suspension.
The object is then in equilibrium.
The centre of mass of a symmetrical object is along the axis of symmetry.
2.3 Moments in balance
For an object in equilibrium:
the sum of the anticlockwise moments about any point = the sum of the clockwise moments about that point.
This is known as the principle of moments.
If an object at rest doesn't turn, the above statement must apply.
To calculate the force needed to stop an object turning we use the equation above.
We need to know all the forces that don't act through the pivot and their perpendicular distances from the line of action to the pivot.
The line of action of the weight of an object acts through its centre of mass.
If the line of action of the weight lie outside the base of an object, there will be a resultant moment and the object will tend to topple over.
An object topples over if the resultant moment about its point of turning is not zero.
The stability of an object is increased by making its base as wide as possible and its centre of mass as low as possible.
Pressure = force / the area which the force acts on.
The unit of pressure is the pascal (Pa) which is equal to 1 N/m squared.
The pressure in a fluid acts equally in all directions.
A hydraulic system uses the pressure in a fluid to exert a force.
The force exerted by a hydraulic system depends on the force exerted on the system, the area of the cylinder which this force acts on and the area of the cylinder that exerts the force.
A hydraulic pressure system is usually used as a force multiplier.
2.6 Circular motion
The velocity of an object moving in a circle at constant speed is continually changing as the object's direction is continually changing.
Centripetal acceleration is the acceleration towards the centre of the circle of an object that is moving round the circle.
If the centripetal force stops acting, the object will continue to move in a straight line at a tangent to the circle
The centripetal force needed to make an object perform circular motion increases as:
- the mass of the object increases
- the speed of the object increases
- the radius of the object decreases
Centripetal force is not a force in its own right. It is always provided by another force e.g. gravitational or electric force, or tension.
An object only accelerates when a resultant force acts on it - this is called the centripetal force and always acts towards the centre of mass.
2.7 The pendulum
A pendulum moves to and fro along the same line. This is an example of oscillating motion.
The time period of a simple pendulum depends only on its length
To measure the time period of a pendulum, we can measure the average time for 20 oscillations and divide the timing by 20.
Friction at the top of a playground swing and air resistance will stop it oscillating if it is not pushed repeatedly.
The amplitude of the oscillation is the distance of the equilibrium position to the highest position on either side.
Time period (s) = 1/frequency (Hz)
The frequency of the oscillations is the number of complete cycles of oscillation per second.
Finding the centre of mass
Finding the centre of mass of a thin, irregular sheet of material:
- Suspend the sheet from a pin held in a clamp stand
- Because it is freely suspended, it is able to turn
- When it comes to rest, hang a plumbline from the same pin
- Mark the position of the plumbline against the sheet
- Hang the sheet with the pin at another point and repeat the procedure
- The centre of mass is where the lines that marked the position of the plumbline cross