Forces and vector diagrams

​​In a nutshell

The forces between objects touching are contact forces. The forces between objects that don't touch are non-contact forces. A quantity can be a scalar or a vector. Force is a vector quantity. It can be represented using an arrow with a size and direction.

Contact and non-contact forces

Forces push or pull on an object. They can act by direct contact or at a distance from the object.

Contact forces

​​Definition

A contact force is a force that requires two objects to be touching for it to act.

Contact force	Explanation	Example
Friction	Acts in opposition to the motion of one object against another.	When sliding a box (1.) across a carpet (4.), there is friction (3.) opposing the movement of the box (2.).
Normal contact force	A reaction force from an object in contact with a surface. Acts perpendicular to the contact surface.	A book resting on a table (3.) will feel a normal contact force (1.) acting upwards. It also experiences the force of weight (2.).
Air Resistance	Acts in opposition to the motion of an object moving through air.	A skydiver (3.) falling towards the ground has the force of their own weight (2.) pushing them down and they will also experience the force of air resistance (1.) pushing them upwards. This slows their descent.

Non-contact forces

Definition

A non-contact force is a force exerted on an object by an object that is at a distance from it.

Non-contact force	Explanation	Example
Gravity	An attractive force that acts between two objects with mass that are not in contact.	The Earth exerts a gravitational force on the Moon. The Moon (2.) exerts a force of gravitational force on the Earth (1.).
Magnetic force	A force between two magnetic poles that either repels or attracts them.	If two north poles (1.) are brought together, the magnetic force will repel the poles away from each other.
Electrostatic force	A force between two charges that either repels or attracts them.	The electrostatic force between a positive charge (1.) and a negative charge (2.) is attractive and pulls them together.

Curiosity: These three non-contact forces are the only non-contact forces! Every other force is a contact force.

Scalars and vectors

Definition

A scalar only has a magnitude (size). A vector has both a magnitude and a direction.

Example

• A scalar would be energy, mass, temperature, speed (not velocity), etc.
  
• A vector would be force, momentum, velocity, etc.

Note: Some scalars are just the magnitude of a vector! This includes distance (scalar) and displacement (vector), and speed (scalar) and velocity (vector). You can change a scalar into a vector by giving it a direction, and vice-versa.

Force vector diagrams

A scalar is just a number. Whereas a vector is a number and a direction. This means it can easily be represented using an arrow. The arrow's length depends on the magnitude of the force, and the angle of the arrow depends on the direction to the vector.

Force is a vector. This is because it has a magnitude and a direction.

As force is a vector, it can be represented by an arrow.

Tip: Often questions will give the force's directions using the directions of a compass. The mnemonic 'Never-Eat-Shredded-Wheat (North-East-South-West) will help in remembering directions. (Start at North and work clockwise)

Example

A force with a magnitude of $$12\,N$$​ acts towards the east. Another force with a magnitude of $$6\,N$$​ acts at an angle of $$270\degree$$​ with respect to north.

Tip: When finding an angle with respect to the North, move in a clockwise direction from the direction of north.