# Motion

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

## Motion

Motion is the acceleration, displacement, or velocity of an object relative to a given frame of reference.  There are four basic types of motion with each one moving different than the other.  There is a fifth called irregular motion which does not actually count as one.

### Types of Motion

• Linear motion is anything that moves in a straight line.
• Oscillating motion (simple harmonic motion) moves repeatedly back and forth.
• Rotary motion is anything that moves in a circle.
• Reciprocating motion moves backwards and forwards in a straight line.
• Irregular motion is any motion that has no fixed pattern.

## Linear Motion

### Linear Motion Formula

$$\large{ x = \bar {v} t \;\;\;\;\; \bar {v} = \frac{v_i + v }{2} }$$

$$\large{ v = v_i + at }$$

$$\large{ x = v_i t + \frac {1}{2} at^2 }$$

$$\large{ v^2 = v_{i}{^2} + 2ax }$$

Where:

$$\large{ x }$$ = position (linear motion)

$$\large{ a }$$ = acceleration

$$\large{ v }$$ = velocity

$$\large{ v_i }$$ = initial velocity

$$\large{ \bar {v} }$$ = averave velocity

$$\large{ t }$$ = time

## Rotational Motion

### Rotational Motion Formula

$$\large{ \theta = \bar {\omega} t }$$

Where:

$$\large{ \theta }$$  (Greek symbol theta) = angular position (rotational motion)

$$\large{ \bar {\omega} }$$  (Greek symbol omega) = averave angular velocity

$$\large{ t }$$ = time

Tags: Equations for Motion