Classical mechanics and its counterparts, relativistic & quantum mechanics, define the motion and the conditions of equilibrium of natural entities. Classical mechanics can be further subdivided into three primary branches, namely:
Again, there are three primary approaches to solving problems in classical mechanics: Newtonian, Lagrangian, and Hamiltonian. Newton's Laws formed the basis of Newtonian mechanics. Among the three laws, it is the second law, the equation the particle of mass m subject to the influence of a particular force F. Lagrangian mechanics is a bit more sophisticated and has its basis in the least action principle. It is highly effective when we are dealing with mechanical systems with constraints. Hamiltonian mechanics is much more advanced than even Lagrangian mechanics and acts as a bridge between classical & quantum mechanics.
Among them all, Newtonian mechanics is the most straightforward. In this article, we take a deep look into the laws, postulates, and concepts powering Newtonian mechanics, the three laws conceived by the great Isaac Newton.
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To understand Newton’s Laws and Newtonian Mechanics, we first need to consider three fundamental quantities, mass, motion, & force.
The Three Different Types of Newton’s Laws
The First Law of Motion defines zero force and lays down the definition of an inertial frame.
When bodies move at constant velocities in a straight line, no forces act upon that body, or the net resultant of all the forces acting on the body is equal to zero. But, if the body changes its velocity, then there must be some acceleration and, thereby, a total non-zero force acting on the body. Motion or velocities on bodies can change when either the magnitude or direction of the velocity changes.
If the relative velocity between two particular reference frames (that is, systems concerning which we measure something) is constant, then the relative acceleration between those two reference frames is zero. Such reference frames are considered inertial reference frames. The inertial frame is just a frame of reference wherein the first law holds.
Note that the first law does not hold in any arbitrary frame. For example, it fails in a rotating frame of reference.
The Equation: F=ma signifies that a body will undergo acceleration if a force acts upon it. Conversely, if there's no force acting, the body will remain in its current state.
Newton’s Second Law of Motion If a particular force generates a change in motion, then if we increase the magnitude of the force, there will be a corresponding & proportional change in the displacement properties of the body.
Change of motion can be described by the difference in the momentum of a body. For point mass particles, momentum can be defined as the product of mass and velocity.
Suppose a force is applied to a body for a time interval. Then, considering that the particle's mass remains constant, the momentum change rate is equal to the impulsive force applied to the body. And the instantaneous action that the force has on the body at a time t is denoted by taking the mathematical limit as a time interval that becomes smaller and smaller.
The Equation: Again, the same equation relates the change in acceleration to the amount of force applied to a body.
Newton’s Third Law of Motion If we consider two bodies mutually interacting, then all real forces arise due to mutual interaction. And if the acceleration of a body is due to any outside of the force, then there must be an equal and opposite force somewhere in the Universe.
The Equation: The normal force exerted on a body with a weight of mg by a rigid surface is an example of Newton’s third law. N= mg= W, where the normal force acts as the reaction to the action of the weight upon it.
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These three entities together give rise to the famous three laws of motion called the Newton Laws of Motion.
Law 1: All bodies continue to be in a state of rest or uniform rectilinear motion unless compelled or influenced by any external force acting to change it from its state.
Law 2: The change in the motion of a particular body is directly proportional to the force applied and acts in the direction of the straight line in which the force is acting.
Law 3: Every action has an equal and opposite reaction. Mutual action and reaction both occur in the same straight line and are equal & opposite to one another.
The basis of Newtonian Mechanics is the above three laws, particularly the second law of motion that relates the mass of an object with force acting upon it.
Newtons’ three laws form the basis of the three equations of motion in Classical Mechanics à
where u= initial or starting velocity, v= final velocity, a= acceleration/deceleration experienced, s= body’s displacement, and t= time taken
And that wraps up this write-up. Hope this article helps readers understand the classical laws better.
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