The formula to calculate Angular Displacement (θ) is:
\[ θ = \frac{scir}{Rcurvature} \]
Where:
Angular Displacement is defined as the shortest angle between the initial and the final points for a given object undergoing circular motion about a fixed point.
Distance Covered on the Circular Path is the distance covered by the object on the circular path.
Radius of Curvature refers to the radius of the circle that best approximates the curvature of a curve at a particular point.
Let's assume the following values:
Using the formula:
\[ θ = \frac{scir}{Rcurvature} \]
Evaluating:
\[ θ = \frac{10}{15.235} \]
The Angular Displacement is 0.656383327863472 Radians.
| Distance Covered on the Circular Path (Meters) | Radius of Curvature (Meters) | Angular Displacement (Radians) |
|---|---|---|
| 8 | 14 | 0.571428571428571 |
| 8 | 14.5 | 0.551724137931035 |
| 8 | 15 | 0.533333333333333 |
| 8 | 15.5 | 0.516129032258065 |
| 8 | 16 | 0.500000000000000 |
| 9 | 14 | 0.642857142857143 |
| 9 | 14.5 | 0.620689655172414 |
| 9 | 15 | 0.600000000000000 |
| 9 | 15.5 | 0.580645161290323 |
| 9 | 16 | 0.562500000000000 |
| 10 | 14 | 0.714285714285714 |
| 10 | 14.5 | 0.689655172413793 |
| 10 | 15 | 0.666666666666667 |
| 10 | 15.5 | 0.645161290322581 |
| 10 | 16 | 0.625000000000000 |
| 11 | 14 | 0.785714285714286 |
| 11 | 14.5 | 0.758620689655172 |
| 11 | 15 | 0.733333333333333 |
| 11 | 15.5 | 0.709677419354839 |
| 11 | 16 | 0.687500000000000 |
| 12 | 14 | 0.857142857142857 |
| 12 | 14.5 | 0.827586206896552 |
| 12 | 15 | 0.800000000000000 |
| 12 | 15.5 | 0.774193548387097 |
| 12 | 16 | 0.750000000000000 |