classical mechanics introduction about system .pptx
- 2. SESSION - I
- 3. MECHANICS • Mechanics is a branch of physics which deals with the physical objects in motion and at rest under the influence of external and internal interactions • Mechanics was developed since ancient times on the basis of observations on the motion of material particles. But no theoretical explanations was given for an motion of object. And the no relationship was given between force and motion • Many efforts has been made to propose theoretical hypotheses regarding the relationship between force and motion but not until Newton announced his laws of motion in 1687 • Based on Newton’s laws of motion, many scientist Lagrange, Hamilton and others discovered classical mechanics
- 4. When this mechanics deals with the Newton’s laws and their consequences, it may be called as Newtonian or vectorial mechanics because here, the quantities such as force, acceleration, momentum etc which are essentially vectors. In classical mechanics, developed by D’Alembert, Lagrangian, Hamilton and others is known as Analytical mechanics. The basic quantities are scalars rather than vectors and the dynamical relations are obtained by systematic process of differentiation. Studying about an object in motion is Dynamics. Studying about an object at rest is Statics. Mechanics can be classified by two: Classical mechanics and Quantum mechanics Classical mechanics deals with the study of an object that is macroscopic Quantum mechanics deals with the study of an particles that is microscopic
- 5. • Classical mechanics are based on the Newton’s three laws. • First Law: Law of Inertia - A body continues in its state of rest or constant velocity, unless not disturbed by some external influence. The property of a body that it cannot change its state of rest or constant velocity is called inertia and the influence under which the velocity of a particle changes is called force. • The quantitative definitions of force and measure of inertia of a body, which we call mass are contained in second and third laws of motion.
- 6. • Second law – Law of Force : The time-rate of change of momentum is proportional to the impressed force • P = mv and thus • Newton considered that mass of a body remains constant in motion. Therefore, • Force = mass * acceleration
- 7. • This is the fundamental law of classical mechanics. Quantitatively, first law is the special case of second law, because if force is not acting on a body, F = 0, then dv/dt = 0 and therefore v = constant, including zero. • Third law: Law of action and reaction : To every action there is always equal and opposite reaction. This means that two bodies interacting with equal force.
- 8. Mechanics for a System of Particles • Theorem of conservation of Linear Momentum • Conservation of Angular Momentum • Conservation of Energy 1. Theorem of conservation of Linear Momentum: The linear momentum of a particle of mass m and velocity vector v is defined as p = mv Therefore the net linear momentum for a system of n-particles is From Newton’s second and third laws, we obtain
- 9. • That is, the rate of change of linear momentum of a system of particles is equal to the net external force acting on the system. • If F external = 0, then • And integrating we get P = constant. Thus, if the net external force acting on a system of particles is zero, the net linear momentum of the system remains constant. This is the principle of conservation of linear momentum of a system of particles.