Centre of mass
- The centre of mass of an object is that point where its mass is thought to be concentrated.
- When a suspended object is in equilibrium, its centre of mass is directly beneath the point of suspension.
- The centre of mass of a symmetrical object is along the axis of symmetry. If the object has more than one axis of symmetry, the centre of mass is where the axes of symmetry meet.
A simple pendulum consists of a mass, called a bob, suspended on the end of a string. When the bob is displaced to one side and let go, the pendulum oscillates back and forth, through the equilibruium position. This is an example of oscillating motion.
- The amplitude of the oscillation is the distance from the equilibrium position to the highest position on each side.
- The time period of the oscillation is the time taken for one complete cycle, (the time taken from the highest position on one side to the highest position on the other side and back to the start position).
To measure the time period of a pendulum, we can measure the average time for 20 oscillations and divide the timing by 20.
- The time period depends only on the length of the pendulum and increases as its length increases.
- The frequency of the oscillations is the number of complete cycles of oscillation per second.
- The time period and frequency are related by the equation
T = 1/f
where T is the time period in seconds, s
f is the frequency in hertz, Hz.
- Friction ar the top of a playground swing and air resistance will stop it oscillating if it is not pushed repeatedly.
Moments at work
- The turning effect of a force is called its moment.
- The moment of a force is given by the equation
M = F x d
where M is the moment of the force in newton metres, N m
F is the force in newtons, N
d is the perpendicular distance from the line of action of the force to the pivot in metres, m.
- To increase the moment:
- either the force must increase
- or the distance to the pivot must increase.
- It is easy to undo a wheel nut by pushing on the end of a long spanner than a short one. That is because the long spanner increases the distance between the line of action of the force and a pivot.
- We make use of a lever to make a job easier. When using a lever the force we are trying to move is called the load and the force applied to the lever is the effort. A lever acts as a force multiplier, so the effort we apply can be much less than the load.
Moments in balance
- The principle of moments states that for an object that is not turning, the sum of the anticlockwise moments about any point = the sum of the clockwise moments about that point.
- 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 that face
W1 x d1 = W2 x d2
- The line of action of the weight of an object acts through its centre of mass.
- An object will tend to topple over if the line of action of its weight is outside its base.
- An object topples over if the resultant moment about its point of turning is not zero.
- The wider the base of an object, and the lower its centre of mass, the further it has to tilt before the line of action of the weight moves outside the base. So the stability of an object is improved by making its base wider and its centre of mass lower.
- The velocity of an object moving in a circle at constant speed is continually changing as the object's direction is continually changing. Therefore the object is accelerating.
- Centripedal acceleration is the acceleration towards the centre of the circle of an object that is moving round the circle.
- Centripedal force is the resultant force that causes the centripedal acceleration of an object moving round a circle.
- If the centripedal force stops acting, the object will continue to move is a straight line at a tangent to the circle
- The centripedal force needed to make an object perform circular motions increases as:
- the mass of the object increases
- the speed of the object increases
- the radius of the circle decreases.
Pressure is give by the equation:
p = F/A
where p is the pressure in pascals, Pa (or N/m²)
F is the force in newtons, N
A is the cross-sectional area in square metres (m²) at right angles to the direction of the force.
- Liquids are virtually incompressible and the pressure in a liquid is transmitted equally in all directions. This means that a force exerted at one point on a liquid will be transmited to other points in the liquid. This is made use of in hydraulic pressure systems.
- The force exerted by a hydraulic pressure system depends on:
- the force exerted on the system
- the area of the cylinder which this force acts on
- the area of the cylinder which exerts the force.
- The use of different cross-sectional areas on the effort and load side of a hydraulics system means that the system can be used as a force multiplier. Therefore, a small effort can be used to move a heavy load