Newton’s Laws of Motion

Newton’s First Law of Motion

If the net force acting on an object is zero, the object will have a constant velocity (or zero velocity) and the acceleration of the object will be zero.

This means that if an object is at rest it will remain at rest until it is acted on by a net force.

It also means that if an object is moving, but the resultant force is zero (no net force), it will continue to move at constant velocity.

Net (Resultant) Force – the vector sum of all the forces acting on a body.

Let’s look at the two objects below:

Both objects have a starting velocity of 5ms^-1. However, the net force on the first object is 0N:

Net force on object A = 5N – 5N = 0N 

Whereas the net force on the second object is 5N to the right:

Net force on object B = 10N – 5N = 5N 

Therefore, from Newton’s first law of motion we know that object A has a constant velocity of 5ms^-1. It does not accelerate as the net force is zero.

Object B, on the other hand, does not have constant velocity. The net force on the object is not zero and so the object will accelerate.

Newton’s Second Law of Motion

If the net force on an object is greater than zero, the object will accelerate in the direction of the net force. The net force is equal to the product of the acceleration and mass of the object.

Newton’s second law of motion can be defined with the following equation:

Where F is the net force acting on an object, m is the mass of the object and a is the acceleration of the object.

We can see from this equation that the acceleration is directly proportional to the net force, but inversely proportional to the mass of the object.

From the example above we know that the net force acting on object B is 5N. The mass of object B is 10kg. We can now use this information, with Newton’s second law, to calculate the acceleration of the object. Inputting the values into the equation we get:

Newton’s Third Law of Motion

If object A exerts a force on object B, then object B exerts a force on object A that is equal in magnitude but opposite in direction. The forces act on different objects.

This law can also be defined with an equation:

Let’s look at the two objects below:

Object A exerts a force on object B and so object B exerts a force that is equal in magnitude and opposite in direction on object A. 

These forces are acting on different objects. One force is acting on object A (F_{B on A}) and the other is acting on object B (F_{A on B}). 

The motion of an object is affected by the net force on that object, as we can see from the first and second laws. As these forces are acting on different objects, they do not cancel each other out when we look specifically at one of the objects.

Think about what happens when you push open a door. You are exerting a force on the door F­­_you ­_{on door­}, and so by Newton’s third law the door also exerts an equal force on you F­_{door on you}.

Despite these forces being equal in magnitude, but opposite in direction the door still opens. This is because when we consider the motion of the door, we only look at the forces acting on the door itself: F_{you on door} along with friction and air resistance. As long as F_{you on door} is greater than the air resistance and friction the door will open. F_{door on you} is only acting on you, and not the door:

Worked Examples

Example 1

A 10kg ball is falling towards Earth. What force must act upwards on the ball to keep its velocity constant? Assume g is equal to 9.81ms^-2.

This question requires knowledge of weight.

Example 2

Is the ball below accelerating? If yes calculate the acceleration of the ball.

Please leave any questions you have in the comments below and follow me on Pinterest and Instagram to stay up to date with the latest posts. For general information on forces click here.