In 1687, Isaac Newton revolutionized scientific thinking by formulating the laws of motion and universal gravitation published in his book Principia. Today, more than 300 years later too, if we want to describe the effect of forces on any moving or non-moving things around us then we take the help of Newton’s Laws of Motion. So let’s discuss Newton’s Law of Motion in detail.
Sir Isaac Newton gave three laws of motion that explain the relationship between a physical object and the forces acting upon it.
Newton’s ‘Philosophiæ Naturalis Principia Mathematica’ published in 1687; cover (left) and a page from the 1726 edition (right). (Source images: Principia title and Principia Page 1726.)
Newton’s first law: the Law of Inertia
In his first law, he discussed Inertia and that’s why Newton’s first law is also known as the law of inertia. But what does inertia stands for? It’s the tendency of an object to keep doing what it’s doing. It can be stated as
An object in motion will remain in motion, and an object at rest will remain at rest unless acted upon by a force.
The inertia of rest
Do you ever think that why a mango falls after you shake the trunk of a mango tree? It’s due to the inertia of rest.
The inertia of rest is the tendency of an object to continue its state of rest unless it is acted upon by an external force.
Activity
When a person or a machine applied a force on the trunk of a mango tree, it starts shaking but the mango which is connected by a tiny branch tries to maintain its state of rest, and due to that it detaches from the tiny branch.
Dust particles on a carpet fall if we beat the carpet with a stick is another example of the inertia of rest.
The inertia of motion
The inertia of motion is the tendency of an object to continue its state of motion unless it is acted upon by an external force.
That is, if an object is in a state of motion, then it will continue to move at the same speed in the same direction unless an external force is applied to change its state.
The passenger in a running bus tends to lean forward when the bus stops suddenly, which is an example of the inertia of motion.
The inertia of an object
Activity
Can we compare the inertia of two different things? The answer is yes. If you have two different objects of the same size and different masses then the object which is heavier is going to be harder to move, and harder to stop once it’s moving.
It happened because the heavier ball has more mass and hence it has more inertia. That means if you apply an equal force on two different objects then the object having lesser mass is easier to move and hence it will move with more acceleration. And this idea connects nicely to Newton’s second law:
Newton’s second law
It states that
the net force is equal to the mass times acceleration.
In a more precise way, you can say that the net force along the direction of the acceleration is equal to the mass times the acceleration in that direction. That is,
\begin{aligned}\vec{F} &= m\vec{a}\\\end{aligned}
where \vec{F} is the resultant force, m is mass of the body and \vec{a} is acceleration of the body.
Activity
Suppose there is a block sitting at a frictionless surface and you are pushing it along with a stick then the block is experiencing acceleration because the force along the horizontal direction isn’t being canceled out by any other forces. But if the block is sitting at the surface or sliding across the surface with a constant velocity, then all the forces are balanced out. And we say that the block is in equilibrium.
In another example, suppose you throw a 2\rm \ kg block straight up then after some time it returns back to you because the force of gravity acts along down and due to which the block accelerates downward at a rate of g = 9.8\rm \ m/s^2.
The force of gravity on the block can be found using the equation \vec{F} = m\vec{a} and it comes F = 19.6\rm \ kg m/s^2. Now, the unit \rm kg m/s^2 can be a bit of a mouthful, so we just call them Newton in honor of Sir Isaac Newton.
Here in the above example, there is only one force which is the force of gravity. But in other cases, there may be other forces acting on the block. Suppose a book is just put down on a horizontal table then the book is static. It is not accelerating. What does that mean? It means that the net force is zero. So, there must be some forces that are acting on the block that can cancel out the force of gravity. And this can be nicely explained by Newton’s third law.
Newton’s third law
Newton’s third law often stated as
for every action, there’s an equal and opposite reaction
Activity
If a block is placed on a self, then there is a force acting on the block which is equal and opposite to the force of gravity. And this force is called the NORMAL force which is always acting along the normal to the surface on which the object is placed.
Now, if you press the book from above then the normal force increases accordingly. It’s not like gravity because its magnitude is not fixed. But does the normal force always cancel out other forces? The answer is no. Otherwise, you cannot pick up anything from a surface. When you pick an object of mass m from the ground then the normal force decreases from mg to Zero.
Limitations of Newton’s laws of motion
Although the equation \vec{F} = m\vec{a} is the best-known relationship in Physics but it is not a fundamental principle.
A more fundamental relationship is;
\begin{aligned}\vec{F} &= \dfrac{d(m\vec{v})}{dt}\\\end{aligned}
And it becomes \vec{F} = m\vec{a} only if the mass is constant. Since the mass changes as the speed approaches the speed of light, \vec{F} = m\vec{a} is not going to be valid for a relativistic object.
So, the relation \vec{F} = m\vec{a} is strictly a non-relativistic relationship which can only apply on constant mass objects. And so, this is the LIMITATION of Newton’s laws of motion.
Thus Newton’s laws of motion are valid only in an inertial reference frame. But we can also use Newton’s 2nd Law for a variable mass system and for that we have to do a little bit of modification.
The generalization of Newton’s 2nd Law which can be applied to variable mass systems is given by;
\begin{aligned}\vec{F} &= \dfrac{d(m\vec{v})}{dt}\\&= m\dfrac{d\vec{v}}{dt}+\vec{v}\dfrac{dm}{dt}\\\end{aligned}
[Attributions & References]
- Openstax College Physics. Download the original article free at http://cnx.org/contents/031da8d3-b525-429c-80cf-6c8ed997733a@9.1:8
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