# PHY C4: Dynamics

Things you need to know for this topic:

• Momentum
• Mass
• Inertia
• Linear Momentum
• Force
• Newton’s Laws of Motion

Let’s get started.

Before we dive in, here are Newton’s 3 Laws of Motion.
For now, just keep them in mind as we go through the different parts of this topic.

At the end of this post, I’ll tie all of them together by explaining how these 3 laws describe everything we’ve learnt here.

Newton’s Laws of Motion:

 Newton’s 1st Law of Motion A body will continue in its initial state of motion (whether at rest or at a constant velocity) unless it is acted on by an external force. Newton’s 2nd Law of Motion For a body of constant mass, its acceleration is directly proportional to the resultant force applied to it. Newton’s 3rd Law of Motion When a body exerts a force on another body, the 2nd body exerts an equal & opposite force on the 1st. OR: For every action, there is an equal & opposite reaction.

Now, let’s start from the basics.

What is Mass?
The physical quantity of a body that resists motion.

In chemistry, mass is defined as the amount of matter in a substance,
but we can also define mass physically in terms of its effects.

Mass should NOT be confused with WEIGHT.
An object weightless in space will still resist motion.

This property of mass (resisting motion) manifests itself in a phenomenon known as INERTIA.

What is Inertia?
Resistance towards change in motion due to mass.
It is the tendency of objects to maintain their state of motion
(whether stationary or constant velocity).

Inertia is defined under NEWTON’s FIRST LAW OF MOTION.

What is Momentum?
The product of mass & velocity.
Every object with a mass possesses momentum when in motion.
When stationary, its momentum = 0.

In equation form,
Momentum = mass x velocity
p = mv

In units,
kg ms-1
OR
N s

Momentum is a VECTOR, since velocity is a vector.
The direction of motion corresponds to the direction of momentum.

There are 2 types of momentum:

• Linear momentum (possessed by a moving object)
• Angular momentum (possessed by a rotating object)

For now, we will focus on Linear Momentum.

Momentum is important when the velocity of the object CHANGES.
When there is a change in velocity to an object, its MOMENTUM will change:
It will experience an IMPULSE.

What is Impulse?
A CHANGE in MOMENTUM.

This change is caused by an external force acting upon the object,
or a collision with another object.

A FORCE is exerted onto it, called an IMPULSIVE FORCE.

What is Force?
The RATE of CHANGE of MOMENTUM.

F = Δp/Δt
F = (Δmv)/(Δt)

Since mass is constant*,
F = m(Δv)/(Δt)

& since Δv/Δt = a,
F = ma

In units,
Kg ms-2
OR
N (Newtons)

*This is the case for a solid object in motion.
However, later we’ll see how forces work for FLUIDS in motion (which have a changing mass flowing at a constant velocity).
For now though, we’ll stick to solid objects.

As you can see, if the difference in time is SMALL, the force exerted will be LARGE.
Thus, if the change in momentum is FAST, the object experiences a larger force.

Applications of this include:

 Reducing the force by increasing the time of contact Ex: Bending knees when landing after a jump Crumple zones in cars

Let’s use this same equation to understand the relationship between mass & force.

What is the relationship between mass & force?
An object with a mass will resist a CHANGE in motion, UNLESS a FORCE is applied upon it.
Thus, a force acting upon an object will cause a change in motion: ACCELERATION.

As you’ve seen, the equation relating them is:
F = ma

The F (force) here is the NET force acting upon an object.

If there are multiple forces acting on the object, you will have to calculate the RESULTANT force in order to substitute it into the formula F = ma.

For this reason, it may be useful to differentiate the forces when performing calculations:

• Write F1 & F2 etc. for the forces acting upon the object,
• Then write Fnet for the resultant force.
• You can use vector addition to find Fnet.
• Since it is the resultant force that causes an acceleration,
Fnet = ma.

Remember, the NET FORCE & the ACCELERATION are always in the SAME direction.
If an object is unable to move in a certain direction due to restrictions (a train on rails, for example), you need to find the COMPONENT of the force in that direction.
This can be done using trigonometry!

Now that we’ve seen explanations of each aspect, here’s how Newton’s Laws of Motion tie all of them together.

Newton’s Laws of Motion

 Law Standard Definition In terms of Inertia In terms of Momentum In terms of Force Newton’s 1st Law of Motion A body will continue in its initial state of motion (whether at rest or at a constant velocity) unless it is acted on by an external force. An object has inertia: The tendency to resist change in motion. When no external force is applied, momentum of an object is constant. If F = 0, p = constant. When an external force is applied, momentum (& thus velocity) will change. The object will ACCELERATE. F = ma Newton’s 2nd Law of Motion For a body of constant mass, its acceleration is directly proportional to the resultant force applied to it. A larger force will be needed to change the motion of an object with larger mass. F = ma Resultant force is proportional to the change in momentum. F = Δp/Δt Force causes a proportional acceleration. F = ma Newton’s 3rd Law of Motion When a body exerts a force on another body, the 2nd body exerts an equal & opposite force on the 1st. When 1 object exerts a force on another object, the 2nd object will resist the change in motion by exerting an equal force back on the 1st object. When two objects collide, opposing forces act on both objects. This causes CHANGES in their individual momenta. However, their TOTAL momentum is always conserved. Two objects in contact will experience equal opposing forces. F1 = -F2