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## Kinematics

The way in which matter and energy behave is a set of explanations that help explain physics.

When we talk about matter and energy and the way they behave, we must consider the following:

• Displacement
• Velocity
• Acceleration

### Displacement

The basic concept of displacement looks at an object and determines where and how far it has gone.

The calculation involved to determine displacement takes the final position of the object and then minuses the original position.

Along a straight line, because it has both magnitude and direction, displacement is a vector quantity, and a very simple example thereof.

It’s important to realize that when compared to magnitude, direction is just as important in many measurements.

That’s because, if both the position the object started in as well as the final position thereof can be determined, then we can use the simple displacement equation:

• Displacement = final position – original position

### Velocity

The basic concept of velocity looks at an object and determines the rate it moves from one position to another.

The calculation involved to determine velocity takes the change in position and divides it by the change in time.

How quickly an object is moving is the question that working out its velocity will answer.

Two objects can have the same displacement but travel at different velocities.

For example, if a car and an aircraft travel between two cities, they have the same displacement (the distance traveled).

The time they take to complete the journey, however, is very different.

The aircraft has a faster velocity than the car and therefore will complete the journey quicker.

On the exam, you may be asked to determine the average velocity of an object.

To do this, you will need to know two variables.

These are:

• Displacement
• How long it took to cover the distance traveled

So the calculation to work out average velocity is:

• Average velocity = displacement/change in time.

It can also be expressed in another way:

• Average velocity = final position – original position / final time – original time

So in our example between the car and the aircraft, let’s say that the two cities were 100 miles apart.

If the aircraft covers the distance in 1 hour, then the calculation of average velocity is 100 miles / 1 hour.

That gives us an average velocity of the aircraft of 100 miles per hour.

For the car, however, the distance is covered in 2 hours, so then the calculation of average velocity is 100 miles / 2 hours.

That gives us an average velocity of the car of 50 miles per hour.

Don’t confuse velocity with speed, however, as this is something that often occurs.

When we talk about velocity, we’ve seen that it focuses on a vector in the average displacement.

The distance covered or the path length, however, is the basis for average speed with the equation for that as follows:

• Average speed = total distance traveled/change in time

Note that because speed is path dependent, change in position is not used, the total distance is.

### Acceleration

The basic concept of acceleration looks at an object and determines how quickly it moves from one velocity to the next.

The calculation involved to determine acceleration takes the change in velocity and divides it by the change in time.

To further understand acceleration, let’s take the example of two cars.

One can accelerate 0 to 60 mph in just two seconds, and at that point, is traveling 88 feet per second).

The other, however, isn’t as fast and takes 8 seconds to accelerate from 0 to 60 mph.

So to work out the acceleration of these cars, we would use the following equation:

• Average acceleration = change in velocity/change in time

So let’s plug in the information we know for car 1 into that equation.

Here, the average acceleration would be 88 feet per second / 2 seconds which equals 44 feet / second².

For car 2, the equation is as follows.

Average acceleration would be 88 feet per second / 8 seconds which equals 11 feet / second².

Whenever we talk about acceleration, we will divide distance divided by time squared.

## Projectile motion

Projectile motion is a specific application of motion theory.

When an object is in the air and the force of gravity is working on it, well that’s a case of simple projectile motion.

While drag will come into play, it’s not something that you will have to worry about as it’s not covered in the exam.

In some cases, however, an object won’t be falling straight down to the ground.

An excellent example of this is a ball that has been thrown.

Two characteristics of projectile motion are the following:

• There is no change in the horizontal component of velocity
• The vertical component of velocity is affected by vertical acceleration due to gravity

Gravity only acts in a downward direction and because of this, objects that have projectile motion are only subject to acceleration in the vertical (y-direction).

This means that while it is in flight, there is no change to the horizontal component of the object’s velocity.

So the velocity of an object in a vertical direction will have gravity affecting it.

The acceleration as a result of gravity is as follows:

• g=9.8 m/a² or 32 ft/a² downwards

At any point, the vertical component of velocity will equal:

• Vertical velocity = original vertical velocity – g x time

Because of this, during the flight of a projectile, there are three points of interest.

To start off, the object will be given a large speed due to having both a vertical and horizontal component.

When it reaches the top of its flight path, the vertical velocity will be zero, and at this point, it is at the slowest part of its travel.

Its speed will be equal to its initial speed when the object moves through the same height as the launch.

This is because the current vertical velocity is the opposite of the initial vertical velocity.

Velocity can increase further if the object continues to fall past the height that it was initially launched at, for example, if it was thrown off the edge of a cliff.

## Newton’s Laws of Motion

On the exam, you may come across questions regarding Newton’s Laws of Motion, which revolve around the concept of force.

There are three Laws of Motion that you will need to understand.

• Newton’s 1st law: When a body is at rest, it will usually remain at rest. When a body is in motion, unless an external force acts upon it, it will tend to stay in motion.
• Newton’s 2nd law: An object’s acceleration is directly proportional to the force it is exerted to but inversely proportional to its mass.
• Newton’s 3rd law: There is an equal and opposite force for every force.

Let’s look at these in a little more detail.

### Newton’s 1st law

The basic concept of this law deals with the fact that an object won’t stop or start moving unless something interferes with it.

We can all agree that an object won’t start moving until a force acts on it, but also, if something is moving, it won’t do so forever.

It can, in perfect condition, where there is no resistance or friction acting on it, for example, but if a car is moving, it will come to an eventual stop because of the forces acting on it.

### Newton’s 2nd law

The basic concept of this law deals with the fact that due to force, acceleration will increase linearly.

This is best expressed in the following equation:

• Force = mass x acceleration, or
• Acceleration = force/mass, or
• Mass = force/acceleration

These three equations allow us to look at the same relationship differently.

### Newton’s 3rd law

The basic concept of this law deals with the fact that an object cannot be pushed or pulled without it being pushed or pulled at the same time.

If an object is exerting a force on another, the second object will exert the opposite force back on it.

### Force

Newton’s Laws of Motion mention the concept of force often, so we do need to touch on that.

The basic concept here is that force is the push or pull that an object can experience.

The calculation for force is as follows:

• Force = mass x acceleration

An acceleration of a body is caused by a force that has both direction and magnitude.

An object can be acted upon by multiple forces.

Consider an object that is placed at the origin of a coordinate plane.

It will move in the direction of the x-axis when pushed along its positive direction.

It will move in the direction of the y-axis, when pushed along its positive direction.

Should the object have both forces applied to it at exactly the same moment, then the movement of the object is at an angle to both the x and y-axis.

The amount of force applied in each direction will determine what that angle is.

### Friction

The basic concept of friction is a resistance to motion and results from contacting surfaces.

Let’s examine that a little by using the concept of a book that’s placed on a tabletop.

While it sits there, when compared to the normal force, the force of the weight of the book is equal and opposite.

If a force is exerted on the book, however, by pushing it to the side, for example, a force will act against it that is equal and opposite to the force being applied.

This is known as static frictional force.

When force is increased on the book, at some point, the static friction force is overcome and the book will start to move.

There is still a frictional force being applied to it, but this is known as kinetic frictional force.

Compared to the amount of force needed to initiate the movement of the book, this will now be far less to maintain that movement.

## Rotation

While the exam will not include any angular calculations when it comes to rotation, you will need to understand torque which is the angular version of force.

The basic concept of torque deals with the fact that it is a twisting force that an object experiences.

The calculation for this is expressed as follows:

• Torque = radius x force

Just like force, torque is a vector.

This means that it also has direction and magnitude.

Therefore, the angular acceleration of an object will be affected by the sum of torques that act upon it.

Understanding how a lever arm works is key to solving problems that involve torque.

This is the equation that helps in that regard:

• Torque = force x distance perpendicular to the force from the center of the rotation

Note that it’s to the radius that torque is directly proportional to and because of this, the size of the lever arm plays a part.

The bigger it is, the more torque is applied with the same amount of force.

### Rotational kinematics

The basic concept of rotational kinematics deals with the fact that increasing the radius will see linear speed increase as well.

The calculation for this is expressed as follows:

• Linear speed = radius x rotational speed

Motion rotation is another interesting application of the study of rotational kinematics.

So let’s just confirm what rotation is.

Well, simply put, it’s when an object rotates at a constant speed around a point.

When these questions appear on the exam, they will provide you with the radius (the distance from the center of the rotation to the rotating object).

What you will have to then work out is the object’s linear speed.

A point further from the center of rotation will have a greater linear speed than one closer to it.

So let’s take a potter’s wheel for example.

Clay that is six inches away from the center is spinning faster than some that are three inches away from the center.

There is no linear velocity for clay that is placed in the exact center of the spinning wheel.

The following equation is used to work out the linear speed of rotating objects:

## Potential and Kinetic energy

The basic concept of energy deals with something’s ability to work on another object.

Energy can be a confusing word, because, in the English language, it can have several different meanings.

We are only focusing on what it means in physics, however.

Here, it deals with the way in which a body’s ability to do work can be measured.

It’s also critical to note that there are many forms that energy can take up in physics.

For this guide, the focus is on mechanical energy which is the sum of the potential and kinetic energy of an object.

The basic forms of mechanical energy which we will cover are:

• Kinetic energy: By virtue of its motion, this is the energy an object possesses
• Gravitational energy: By virtue of its height, this is the energy an object possesses
• Elastic potential energy: By virtue of compression or tension, this is energy stored

Mechanical energy is conserved if we neglect frictional forces.

Let’s take a bouncing ball for example, with its weight being the only force that will act on it.

When it bounces and begins to rise, that weight will work on the ball. This means that as it moves to its highest point, the speed will decrease, along with the kinetic energy while its potential energy increases.

When it reaches its highest point, the potential energy dissipates as kinetic energy again builds up, reaching its highest point when the ball makes an impact with the ground.

We must also consider when friction and air resistance are in play, however.

If we slide a block along the floor, friction will cause it to come to a stop.

This is very different to a bouncing ball, for example, as there is no way for a block to regain any kinetic energy, there isn’t any way it can return to its original position.

Because of this fact, there is no kinetic energy stored as potential energy.

Let’s look at the various energy forms in more detail.

### Kinetic energy

An object’s kinetic energy – which can never be negative – is the energy it has because of it being in motion.

When other forces work on the object, then changes in kinetic energy will result.

Kinetic energy changes are then related to the amount of work carried out on the object and the relationship between these factors is called the work-energy theorem.

Let’s consider this for objects that are in free fall.

To start, let’s imagine that the weight of the object is the force acting on it.

This force will be equal to the force of gravity (g) times its mass.

Because the force is exerted in the direction the object moves, the work done by it is positive.

Therefore, according to the work-energy theorem, the kinetic energy will grow.

An object will reach terminal velocity when it is dropped for a sufficient height.

When this occurs, the weight of the object is equal to the force of drag it experiences.

The kinetic energy will then remain constant because the object is no longer accelerating.

### Gravitational potential energy

The potential of a particular amount of work being done by one object on another object is described as gravitational potential energy.

When we talk about objects in everyday life, this energy is equal to the amount of energy our planet can have on a chosen object.

Gravity acts on an object that moves either partially or entirely in the vertical and this is equal to the earth’s exerted force on that object (weight) times the distance traveled in the force’s direction (for example, the height the object started above the ground).

Here’s the equation for this:

• Gravitational potential energy = weight x height

### Elastic potential energy

Using tension or compression, elastic potential energy is the potential for work to be done by one object on another.

When we talk of this type of energy, one simply has to think of a spring.

It will resist any tension from its natural position, which is also known as its equilibrium position.

#### Power

The basic concept of power is rate of work.

The calculation for this is work/time.

Much like energy and work, power is a quantity that can scale.

More power is expended if more work is carried out in a shorter amount of time.

Power can be expressed in numerous ways.

For example, horsepower is used when describing the power from the engine of a car while watts or joules per second is the preferred metric expression.

### Impulse and linear momentum

#### Linear momentum

The basic concept of linear momentum is how much a body will resist coming to rest.

The calculation for this is:

• Momentum = mass x velocity

As per the equation above, multiplying an object’s mass and velocity gives its linear momentum and these two factors always occur in the same direction.

This is backed up by Newton’s 2nd law which we covered earlier and in which momentum is detailed.

Momentum will never increase or decrease in a closed/isolated system where no objects can either enter or leave and because of this, we can describe momentum as a constant.

Even in situations with subatomic particles or in high-velocity situations, the law of conservation of linear momentum applies in physics in a universal manner.

#### Collisions

When taking collisions into account, the idea of momentum takes on some importance.

An isolated event, a collision sees two bodies collide with a strong force acting between them when this occurs, and only for a small time period.

Simply put, when two objects hit each other, a collision has taken place.

In this case, each will exert an opposite force on the other and due to this, the linear momentum of the objects will change.

However, the net momentum in a collision is conserved when both bodies are considered.

Collisions can be broken down into two types:

• Elastic
• Inelastic

The way in which kinetic energy is conserved during the collision highlights the difference between them.

In an elastic collision, the total kinetic energy of the system is conserved and this is visually seen when objects bounce off each other in a perfect manner.

If the bodies have the same mass, the body that was moving stops.

The body that was at rest initially will move at the same velocity as the original moving body before they collided together.

A collision is inelastic when some of the kinetic energy is transformed.

This can occur when it becomes another form of energy, for example, heat.

From a visual perspective, the objects won’t return to their original positions but will bounce off each other (but not perfectly) or stick together.

## Electricity

Electricity is around us every day and not only when we use it as a source of power.

In this section we look at an electric charge, current, resistance, and voltage, as well as how basic circuits work.

### Electric charge

An electric charge is considered a force and it occurs between objects.

Let’s break this down into the building blocks of the universe, protons, and electrons.

Protons have a positive charge while electrons have a negative one.

A net charge will result in an object when there is an imbalance of protons and electrons.

It’s also critical to note that there is both a push and pull factor to electrical forces, unlike gravity which only pulls.

Also, opposite charges will attract each other while the same charge will repel.

### Current

By switching from one atom to a different one, electrons move through conductive materials.

Energy like mechanical systems can be manipulated by this electrical flow.

Current is the term given to the rate at which charge moves through a conductive material.

Current can be seen as the number of electrons moving through a certain point over a certain time frame.

This is because each electron carries a specific charge.

We use Amperes (A) to measure current.

### Voltage

The potential for electric work is called voltage (measured in volts) and you can imagine it as the push that drives any electrical work.

In a way, gravitational potential energy and voltage are very similar.

A voltage source is something that is able to generate voltage and the perfect example of this would be a battery.

### Resistance

The flow of any electrical current can be restricted by resistance and you can think of it as something similar to friction.

A specific electrical component, known as a resistor is manufactured to have a specific resistance output.

This is measured in Ohms.

### Circuits

A close loop through which current flows is known as a circuit.

A voltage source, as well as a resistor, are found in simple circuits.

It’s from the positive side of the voltage source that current flows, through the resistor and then back to the negative side of the voltage source.

There are similarities here to gravitational potential energy.

Think of the circuit as a track and the electrons that flow through the circuit as balls.

The voltage source will provide the electrons with their highest voltage, and therefore, their highest potential energy.

This drops when they reach the resistor.

## Electricity and magnetism

When opposite poles of magnetic materials are attracted to each other, or when there is repulsion between similar poles, magnetism is occurring.

While magnetism can occur naturally, we can also use electric currents to induce it.

When you have two polar sides, north and south, a field of magnetism will always exist between them.

A magnetic field also exists in objects between two poles with like poles repelling each other and different poles attracting each other. 