# 3: Review of Newtonian Mechanics

- Page ID
- 9571

- 3.1: Introduction to Newtonian Mechanics
- Newtonian mechanics is based on application of Newton’s Laws of motion which assume that the concepts of distance, time, and mass, are absolute, that is, motion is in an inertial frame. The Newtonian idea of the complete separation of space and time, and the concept of the absoluteness of time, are violated by the Theory of Relativity. However, for most practical applications, relativistic effects are negligible and Newtonian mechanics is an adequate description at low velocities.

- 3.2: Newton's Laws of motion
- Newton’s laws, expressed in terms of linear momentum, are: Law of inertia: (1) A body remains at rest or in uniform motion unless acted upon by a force. (1) Equation of motion: A body acted upon by a force moves in such a manner that the time rate of change of momentum equals the force. and (3) Action and reaction: If two bodies exert forces on each other these forces are equal in magnitude and opposite in direction.

- 3.3: Inertial Frames of reference
- An inertial frame of reference is one in which Newton’s Laws of motion are valid. It is a non-accelerated frame of reference. An inertial frame must be homogeneous and isotropic. Physical experiments can be carried out in different inertial reference frames. The Galilean transformation provides a means of converting between two inertial frames of reference moving at a constant relative velocity.

- 3.4: First-order Integrals in Newtonian mechanics
- A fundamental goal of mechanics is to determine the equations of motion for an n−body system, where individual forces acts on the individual mass of the n-body system. Newton’s second-order equation of motion must be solved to calculate the instantaneous spatial locations, velocities, and accelerations for each mass. The solution involves integrating second-order equations of motion subject to a set of initial conditions.

- 3.5: Conservation laws in classical mechanics
- The power of conservation laws in calculating classical dynamics makes it useful to combine the conservation laws with the first integrals for linear momentum, angular momentum, and work-energy, when solving problems involving Newtonian mechanics. These three conservation laws will be derived assuming Newton’s laws of motion, however, these conservation laws are fundamental laws of nature that apply well beyond the domain of applicability of Newtonian mechanics.

- 3.7: Center of Mass of a many-body system
- A finite sized body needs a reference point with respect to which the motion can be described.

- 3.9: Angular Momentum of a Many-Body System
- For a many-body system it is possible to separate the angular momentum into two components. One component is the angular momentum about the center of mass and the other component is the angular motion of the center of mass about the origin of the coordinate system. This separation is done by describing the angular momentum of a many-body system using a position vector with respect to the center of mass plus the vector location of the center of mass.

- 3.10: Work and Kinetic Energy for a Many-Body System
- Path and time-independence of forces may be used to demonstrate conservation of energy and momentum, and vice versa.

- 3.11: Virial Theorem
- The virial theorem is an important theorem for a system of moving particles both in classical physics and quantum physics. The Virial Theorem is useful when considering a collection of many particles and has a special importance to central-force motion.

- 3.13: 2.13 Solution of many-body equations of motion
- The following are general methods used to solve Newton’s many-body equations of motion for practical problems.

- 3.14: Newton's Law of Gravitation
- In 1666 Newton formulated the Theory of Gravitation which he eventually published in the Principia in 1687. Newton’s Law of Gravitation states that each mass particle attracts every other particle in the universe with a force that varies directly as the product of the mass and inversely as the square of the distance between them.