Length:

Use a ruler or measuring tape

Volume of regularly shaped objects:

Use the following formulas to find the volume of regular solids:

-cube -> l³

-cuboid -> l x b x h

-cylinder -> πr²h

-sphere -> 4/3πr³

-cone -> 1/3πr²h

Volume of irregularly shaped objects:

Using displacement method

By measuring the volume of displaced liquid an object. We can find the volume of these solids with the help of a measuring cylinder.

The measurement of a small distance (use of a micrometer screw gauge).

Micrometers are used to measure small distances accurately. The screw micrometer is usually used to measure tiny or small objects.

In digital time the numbers are shown.

In analogue time the time is told of a clock.

Measuring a pendulum swing

One complete swing = A - B - A - C - A

Measure the time for 25 swings and divide the result by 25

Speed is the rate at which somethings moves.

Total Distance ÷ Total Time = Average Speed

Velocity is the speed with a direction, while speed does not have a direction.

Speed is a solar quantity - it is magnitude of the velocity. Speed is measured in unites of distance divided by time.

Acceleration is a measure of how quickly the velocity of an object changes.

Acceleration = Change in Velocity ÷ Time Taken

With this graph you can tell three things: speed, distance and acceleration.

You can read the speed directly of the graph.

You can find out the distance by calculating the area under the graph.

The acceleration is found by calculating the gradient of the line.

With distance time graph, you can find out the distance by reading it off the graph, and speed can be found by calculating the gradient of the time.

When a speed time graph is at rest the line meets the x axis. It moves with a constant speed when the line is parallel to the x axis.

If the line slopes it moves with a changing speed.

When an object is moving with a constant velocity, the line on the graph is horizontal. When the horizontal line is at zero velocity, the object is at rest. When an object is undergoing constant acceleration, the line on the graph is straight but sloped.

Linear motion is motion across a straight line. On a speed time graph, you can calculate the acceleration by calculating the gradient of the line. Acceleration on a speed time graph is constant when the line is straight. The equation for acceleration is:

Change in speed ÷ Change in time or

(speed 2 - speed 1) ÷ (time 2 - time 1)

They are both the same equation but the second one is calculated using sold values, it is the same formula for the gradient.

The distance travelled by an object can be calculated from the area under a velocity - time graph. The area under the graph can be calculated by: using geometry (if the lines are straight) counting the squares beneath the line (particularly if the lines are curved).

If on the speed time graph the line is bent or curved it does not have a constant acceleration, because the gradient of the line changes.

Both formulas for acceleration contain speed as a variable, therefore, we can deduce that acceleration changes when speed changes. From this, we can further deduce the change in acceleration is directly proportional to the change in speed. After all, acceleration is the rate at which speed changes.

The acceleration due to gravity is effectively 9.8m/s² over the entire surface of the Earth.

The main difference between mass and weight is that mass is the measure of the amount of matter in an object and weight is a force, caused due to its acceleration and mass. The mass of an object is constant but the weight changes according to the strength of its acceleration.

Every object with a mass has a gravitational field that pulls other masses closer to it however unless it has an extraordinary large mass this is normally negligible, but the earth does have an extraordinarily large mass and its gravitational force is what keeps us on it. The earth is the source for the gravitational field around it.

Unlike most people think, weight is just a force. When gravity acts on a mass there is a weight. It is measured in newtons and is calculated using the formula w=mg, where w is weight, m is mass and g is the force acting on an object (most of the time we use gravity). For an object that's not in motion and is on Earth we use gravity, it is constantly 9.8m/s² (often use 10).

Gravitational field strength is measured in newtons per kilogram (N/kg). The Earth's gravitational field strength is 10 N/kg. This means that for each kg of mass, an object will experience 10N of force.

Weight = Mass x Gravitational Field Strength

We can use equipment to measure weight and compare it.

Density = Mass ÷ Volume

Simply find the mass by weighing the object on a scale and then use a measuring cylinder to find the volume. Then divide the mass by the volume to get the density in g/cm³.

If you want to find the density of an irregular solid, the volume can be found using a displacement can (Eureka). First the can is filled to the level of the spout, then the solid is lowered into the water. The water collected out of the spout is poured into a measuring cylinder and that is the volume of the solid. Then, you just have weighed the mass and then apply the density formula to get the answer.

When an external force acts on a body, it may change the direction it moves in, its speed, or cause it to start moving from rest (like when you kick a ball). Sometimes, the force might cause a rearrangement of the molecules making up the body, causing it to change in size or shape (e.g. crushing a can, stretching a spring).

When an object increases in length, it undergoes extension.

When it decreases in length, it undergoes competition.

One experiment we can use to measure the relationship between force and extension is the Hooke's Law Experiment.

Hooke's Law states that within the elastic limit, the extension (x) of an object is directly proportional to the force (f) that causes the extension.

When written mathematically, it is F = kx

That means, for any value of x, if you multiply it by a certain number, you'll get F. That certain number is called a constant because the number does not change no matter the value of x or F. For this equation, k is the spring constant.

Different materials have different constants of elasticity because they may have different extensions for the same force. Generally the greater the constant of elasticity of a material, the harder it is to stretch.

Limit of proportionality is another phrase for elastic limit. They mean the same thing.

The point at which the graph goes from being a straight line to a curved line is the limit of proportionality.

This point describes Newton's second law of motion: 'For a constant mass, force equals mass times acceleration.'

Note that this is only true for the overall force acting on a mass. For example, if there were two forces, of equal sizes, acting on the same mass but in opposite directions, the two forces cancel each other out, resulting in an overall force of ON. Therefore, the object will have an acceleration of 0m/s². You can test this using any object you like - pick up a ball and push on its opposite sides using both hands. Exert the same amount of force with both hands. You will notice that the ball doesn't move in either direction.

When friction acts between two surfaces that are moving over each other, some kinetic energy is transferred into heat energy.

Air resistance is air pushing against a moving object.

If two or more forces are acting along the same line, they are either acting in the same direction or in opposite directions.

The first law describes what happens when the forces acting on a body are balanced (no resultant force acts) - the body remains at rest or continues to move at constant velocity (constant speed in a straight line).

The longer the spanner, the greater the turning effect (force).

Spanners are used for tightening and loosening nuts. They help to produce a larger turning effect.

The turning effect of a force is called a moment.

To increase the force applied to undoing a wheel nut, extend the length of the spanner - you can do this by inserting a length of pipe over the end.

Moment of a force about a point = Force x Perpendicular distance from the point

Moments may be described as clockwise or anticlockwise, and the moment of a force is also called a torque.

The principle of moments states that: 'If an object is in equilibrium, the sum of the clockwise moments about any points is equal to the anticlockwise moments about that point.'

This beam is in a state of balance.

In order to be balanced, the clockwise forces must be equal to the anticlockwise forces. We say that the beam is in a state of equilibrium

Hang up the object. Suspend a plumb line from the same place. Mark the position of the thread. The centre of mass is along the line of thread. Repeat the above steps with object suspended from different places. The centre of mass is where these lines cross.

The lower the centre of gravity of an object is, the stabler it is. Objects with higher centre of gravity are easier to topple than objects with lower centre of gravity. An object with a big base area is less likely to fall or topple over, than an object with a small base area. Furthermore, these two factors combine to decide the stability of an object. An object would fall over, if it's centre of gravity does not pass through its base when it is tilted.

Pressure is the force on an object that is spread over a surface area. If you walk through snow, you usually sink into it. This is because your shoes have a small surface area. Your weight is only spread out over a small area, so the pressure on the snow is high. However, you will not sink so far into the snow if you are on skis. This is because your weight is spread out over a greater surface area, so the pressure on the snow is low.

Pressure = Force ÷ Area

The unit of pressure here is N/m². Sometimes you will see another unit being used. This is called the pascal and it has the symbol Pa.