Classical mechanics

Classical mechanics refers to a branch of physics dealing with every-day laws of mechanics (as opposed to quantum mechanics). The term is interchangeable with "Newtonian physics", as it was Sir Isaac Newton who first proposed the first laws of motion. Classical mechanics is sufficient for explaining most observable phenomena.

Limitations

Classical mechanics only breaks down in extreme conditions, such as traveling close to the speed of light, being near extremely high gravity, or dealing with subatomic particles. For example, special relativity gives the correction factor at high speeds as

γ=

where v is the velocity of an object and c is the speed of light. At 1000 miles per hour, the correction is .999999999999991.

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Newton's Three Laws

"Newton’s laws establish the mechanical world view that forms the basis for the scientific revolution of the 17th century." Newton's three laws of motion define classical mechanics:

1. An object subject to no net external force moves with constant velocity relative to an inertial reference frame.

An inertial reference frame is defined as one where Newton's laws are valid. Most non-accelerating reference frames are inertial.

2. where

• = net external force acting on an object or system of objects
• m = mass of the object, or total mass of the system of objects
• = acceleration of the object or system

Newton originally wrote this as where is the momentum of the object. This formulation is more general. Since p = m*v, it reduces to the first equation when the object has constant mass.

3. For every action, there is an equal and opposite reaction.

If object A exerts a force on object B, object B will exert a force equal in magnitude and opposite in direction on object A. If the earth pulls you down with a force of 1500 Newtons, you pull up on the earth with a force of 1500 Newtons. (Of course, since F=ma, and the earth's mass is much greater than yours, the earth accelerates much less than you do.)

Distance, Velocity, Acceleration

Velocity is defined as the derivative of position with respect to time, or . It therefore follows that, for motion at constant velocity, Δx=vt. Similarly, acceleration is defined as the derivative of velocity with respect to time, so Δv=at.

Putting these two equations together, we find that, for constant acceleration, Δx=v₀t+0.5at².

In addition, Δx=vt is true for any average velocity. It therefore follows:

These, then, are the four basic kinematics equations:

Δx=vt

Δv=at

Δx=v_avt

Angular Mechanics

These same basic laws are true with respect to angular motion and acceleration, with position being measured in radians. Its first derivative, ω (measured in radians/second), is called angular velocity; its second derivative α is called angular acceleration. By similar methods as above, we can derive:

Δθ=ωt

Δω=αt

Δθ=ω_avt