Important concepts and equations in classical physics

[Sriman Dutta]

Lets start a thread that includes all important as well as useful concepts and equations commonly found in kinematics, mechanics, Newtonian physics and the whole classical physics in general.

Lets see how far the list goes.......

 

Newton's Laws of Motion

1. Every body continues its state of rest or uniform motion in a straight line until and unless it is acted upon by an external force.

2. The force impacted by a body is directly proportional to the rate of change of linear momentum.

[math]F = \frac{dp}{dt} [/math]

Or, [math] F=ma[/math]

3. Every action has an equal and opposite reaction.

[math] F_1 = -F_2[/math]

Edited May 30, 2017 by Sriman Dutta

[OldChemE]

The Laws of motion-- definite yes (and for engineers especially the three forms v = v(0) + at, x = x(0) +vt + 1/2 at^2, and v^2 = v(0)^2 + 2a(x -x(0)))

 

Also the various formulas for Kinetic energy, Potential energy, and Work

[Sriman Dutta]

Equations of Motion

1. [math] v=u+at[/math]

2. [math] S=ut+\frac{1}{2}at^2[/math]

3. [math] v^2 = u^2 +2aS[/math]

Displacement during the nth second: [math] S_n = u+\frac{a}{2}(2n+1)[/math]

 

For free fall in one-dimension;

[math] h_{max} = \frac{u^2}{2g}[/math]

time taken to reach highest point: [math] t_o = \frac{u}{g}[/math]

When [math]t<t_o[/math]

[math] distance = displacement = ut-\frac{1}{2}gt^2[/math]

When [math]t=t_o[/math]

[math]distance = displacement = h_{max}[/math]

When [math]t>t_o[/math]

[math]displacement = ut -\frac{1}{2}gt^2[/math]

[math] distance = h_{max} + \frac{1}{2}g(t-t_o)^2[/math]

 

 

Projectile Motion

When [math]u[/math] is the initial velocity and [math]\theta[/math] is the launch angle given;

[math]v_x = ucos\theta[/math] and [math] v_y=usin\theta -gt[/math]

[math]a_x=0[/math] and [math]a_y =-g[/math]

[math]x=utcos\theta[/math] and [math] y=ut sin \theta -\frac{1}{2}gt^2[/math]

Time of flight: [math]T=\frac{2usin\theta}{g}[/math]

Range : [math]R=\frac{u^2 sin 2\theta}{g} [/math]

Maximum height : [math]h_{max} = \frac{u^2 sin^2 \theta}{2g} [/math]

Equation of the path of projectile: [math] y = xtan \theta - \frac{gx^2}{2u^2cos^2 \theta } [/math]

Relation between [math]R[/math] and [math]h_{max}[/math] is : [math]R=\frac{4h_{max}}{tan \theta}[/math]

Edited June 5, 2017 by Sriman Dutta