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Classical mechanics (view source)
Revision as of 04:57, December 17, 2009
, 04:57, December 17, 2009Added Newton's three laws, angular motion
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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. <math>\Sigma \vec F = m \times \vec a</math>''' where
* <math>\Sigma \vec F</math> = net external force acting on an object or system of objects
* m = mass of the object, or total mass of the system of objects
* <math>\vec a</math> = acceleration of the object or system
Newton originally wrote this as <math>\Sigma \vec F = \frac{d \vec p}{dt}</math> where <math>\vec p</math> 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==
==Distance, Velocity, Acceleration==
In addition, <tt>Δx=vt</tt> is true for any average velocity. It therefore follows:
In addition, <tt>Δx=vt</tt> is true for any average velocity. It therefore follows:
:<math>\frac{(v_f+v_0)}{2} t = \delta x</math>
:<math>\frac{(v_f+v_0)}{2} t = \Delta x</math>
:<math>(v_f+v_0)*a*t = 2*a*\delta x</math>
:<math>(v_f+v_0)*a*t = 2*a*\Delta x</math>
:<math>(v_f+v_0)*\delta v = 2*a*\delta x</math>
:<math>(v_f+v_0)*\Delta v = 2*a*\Delta x</math>
:<math>v_f^2-v_0^2 = 2*a*\delta x</math>
:<math>v_f^2-v_0^2 = 2*a*\Delta x</math>
These, then, are the four basic kinematics equations:
These, then, are the four basic kinematics equations:
:<tt>Δv=at</tt>
:<tt>Δv=at</tt>
:<tt>Δx=v<sub>av</sub>t</tt>
:<tt>Δx=v<sub>av</sub>t</tt>
:<math>v_f^2-v_0^2 = 2*a*\delta x</math>
:<math>v_f^2-v_0^2 = 2*a*\Delta x</math>
===Angular Mechanics===
These same basic laws are true with respect to angular motion and acceleration, with position being measured in [[radian]]s. 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:
:<tt>Δθ=ωt</tt>
:<tt>Δω=αt</tt>
:<tt>Δθ=ω<sub>av</sub>t</tt>
:<math>\omega_f^2-\omega_0^2 = 2* \alpha *\Delta \theta</math>
[[Category:Physics]]
[[Category:Physics]]