Constant angular acceleration situations
In a situation in which the angular acceleration is constant we can apply a method very similar to the method we applied to handle one-dimensional motion situations with constant acceleration.
- Draw a diagram.
- Choose an origin.
- Choose a positive direction (generally clockwise or counter-clockwise).
- Make a table summarizing everything you know.
- Only then, assuming the angular acceleration is constant, should you turn to the equations.
These equations relate displacement, velocity, acceleration, and time, and apply under the following conditions:
- the acceleration (or angular acceleration) is constant
- the motion is measured from t = 0
- the fact that several variables are vectors is accounted for with appropriate plus and minus signs
| Straight-line motion | Rotational motion |
|---|
| v = vo + at
| w = wo + a t
|
| x - xo = vo t + ½ a t2
| q - qo = wo t + ½ a t2
|
| v2 = vo2 + 2 a (x - xo)
| w 2 = wo2 + 2 a (q - qo)
|