# Newton's Laws of Motion

on . Posted in Classical Mechanics

Newton's laws of motion is one of the Clasical branches in physics.  These three laws show the relations between the forces acting on a body and the motion of the body.

### Newton's Laws of Motion Index

Together, these laws provide a framework for understanding and predicting the motion of objects and the forces that govern their behavior.  They form the basis of classical mechanics and have extensive applications in physics, engineering, and everyday life.

### Newton's First Law

Newton's first law of motion, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will continue moving in a straight line at a constant velocity, unless acted upon by an external force.  In simpler terms, the first law states that objects tend to "keep doing what they're doing" unless something makes them do otherwise.  If an object is stationary, it will stay stationary unless a force is applied to it.  If an object is already in motion, it will keep moving in the same direction and at the same speed unless a force acts on it to change its motion.

This law describes the concept of inertia, which is the tendency of an object to resist changes in its state of motion.  The greater the mass of an object, the greater its inertia and the more force is required to change its motion.

Newton's first law has important implications in our daily lives and is the foundation of many principles in physics.  For example, it explains why we need seat belts in cars to prevent us from continuing in motion if the vehicle suddenly stops.  It also helps us understand why objects tend to stay in motion in the absence of friction or other external forces.  It is important to note that Newton's first law applies to objects in the absence of any net external forces.  If there is a net force acting on an object, it will experience acceleration according to Newton's second law of motion.

### Newton's Second Law

Newton's second law of motion, also known as the Law of Resultant Force, describes the relationship between the motion of an object, the net force acting on it, and its mass.  It states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.  In simpler terms, the second law states that the acceleration of an object is directly related to the force applied to it.  If a greater force is applied to an object, it will experience a greater acceleration.  Similarly, if the mass of the object is increased, it will experience a smaller acceleration for the same force.

Newton's second law is fundamental in understanding the relationship between force, mass, and acceleration and is widely used in physics and engineering to analyze the motion of objects and design systems that involve the application of forces.

### Newton's Second Law formula

If the object is free fall with on other force other than gravity.

$$F = m \; a$$     (Newton's Second Law)

$$m = F \;/\; a$$

$$a = F \;/\; m$$

Symbol English Metric
$$F$$ = force $$lbf$$  $$N$$
$$m$$ = mass $$lbm$$ $$kg$$
$$a$$ = acceleration $$ft\;/\;sec^2$$ $$m\;/\;s^2$$

### Newton's Second Law for Rotation Formula

$$\tau = I \; \alpha$$     (Newton's Second Law for Rotation)

$$I = \tau \;/\; \alpha$$

$$\alpha = \tau \;/\; I$$

Symbol English Metric
$$\tau$$  (Greek symbol tau) = rotational force $$lbf-ft$$    $$N-m$$
$$I$$ = moment of inertia $$in^4$$  $$mm^4$$
$$\alpha$$  (Greek symbol alpha) = angular acceleration $$deg\;/\;sec^2$$  $$rad\;/\;sec^2$$

### Newton's Third Law

Newton's third law of motion, also known as the law of actions and reaction, states that for every action, there is an equal and opposite reaction. It means that whenever one object exerts a force on a second object, the second object exerts an equal and opposite force back on the first object.  In simpler terms, if object A applies a force on object B, then object B simultaneously applies an equal and opposite force on object A.  These two forces always occur as a pair, acting on two different objects.

For example, consider a person pushing a heavy box.  According to Newton's third law, as the person pushes the box forward with a certain force, the box exerts an equal and opposite force backward on the person.  These two forces are known as an action reaction pair.  It is important to note that the action and reaction forces act on different objects and are equal in magnitude but opposite in direction.  The forces do not cancel each other out because they act on different objects.  They are simply two parts of the same interaction.

Newton's third law of motion applies to all interactions in the universe.  It is the underlying principle behind many phenomena, such as the propulsion of rockets, the motion of vehicles, and the recoil of firearms.  Understanding and applying this law is crucial in analyzing and predicting the motion of objects in various situations.

### Newton's Third Law Formula

$$F_1 = - F_2$$
Symbol English Metric
$$F$$ = force $$lbf$$  $$N$$