The formula to calculate the Angular Displacement is:
\[ \theta = \omega_o \cdot t + \frac{\alpha \cdot t^2}{2} \]
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.
Initial angular velocity is the velocity at which motion starts.
Time Taken to Travel the Path is the total time taken by an object to reach its destination.
Angular acceleration refers to the time rate of change of angular velocity.
Let's assume the following values:
Using the formula:
\[ \theta = 14 \cdot 6 + \frac{1.6 \cdot 6^2}{2} \]
Evaluating:
\[ \theta = 14 \cdot 6 + \frac{1.6 \cdot 6^2}{2} \]
The Angular Displacement is approximately 112.8 Radian.
| Initial Angular Velocity (Radian per Second) | Angular Acceleration (Radian per Square Second) | Time Taken to Travel the Path (Second) | Angular Displacement (Radian) |
|---|---|---|---|
| 12 | 1.4 | 5 | 77.500000000000000 |
| 12 | 1.4 | 6 | 97.200000000000003 |
| 12 | 1.4 | 7 | 118.299999999999997 |
| 12 | 1.5 | 5 | 78.750000000000000 |
| 12 | 1.5 | 6 | 99.000000000000000 |
| 12 | 1.5 | 7 | 120.750000000000000 |
| 12 | 1.6 | 5 | 80.000000000000000 |
| 12 | 1.6 | 6 | 100.799999999999997 |
| 12 | 1.6 | 7 | 123.200000000000003 |
| 12 | 1.7 | 5 | 81.250000000000000 |
| 12 | 1.7 | 6 | 102.599999999999994 |
| 12 | 1.7 | 7 | 125.650000000000006 |
| 13 | 1.4 | 5 | 82.500000000000000 |
| 13 | 1.4 | 6 | 103.200000000000003 |
| 13 | 1.4 | 7 | 125.299999999999997 |
| 13 | 1.5 | 5 | 83.750000000000000 |
| 13 | 1.5 | 6 | 105.000000000000000 |
| 13 | 1.5 | 7 | 127.750000000000000 |
| 13 | 1.6 | 5 | 85.000000000000000 |
| 13 | 1.6 | 6 | 106.799999999999997 |
| 13 | 1.6 | 7 | 130.199999999999989 |
| 13 | 1.7 | 5 | 86.250000000000000 |
| 13 | 1.7 | 6 | 108.599999999999994 |
| 13 | 1.7 | 7 | 132.650000000000006 |
| 14 | 1.4 | 5 | 87.500000000000000 |
| 14 | 1.4 | 6 | 109.200000000000003 |
| 14 | 1.4 | 7 | 132.300000000000011 |
| 14 | 1.5 | 5 | 88.750000000000000 |
| 14 | 1.5 | 6 | 111.000000000000000 |
| 14 | 1.5 | 7 | 134.750000000000000 |
| 14 | 1.6 | 5 | 90.000000000000000 |
| 14 | 1.6 | 6 | 112.799999999999997 |
| 14 | 1.6 | 7 | 137.199999999999989 |
| 14 | 1.7 | 5 | 91.250000000000000 |
| 14 | 1.7 | 6 | 114.599999999999994 |
| 14 | 1.7 | 7 | 139.650000000000006 |
| 15 | 1.4 | 5 | 92.500000000000000 |
| 15 | 1.4 | 6 | 115.200000000000003 |
| 15 | 1.4 | 7 | 139.300000000000011 |
| 15 | 1.5 | 5 | 93.750000000000000 |
| 15 | 1.5 | 6 | 117.000000000000000 |
| 15 | 1.5 | 7 | 141.750000000000000 |
| 15 | 1.6 | 5 | 95.000000000000000 |
| 15 | 1.6 | 6 | 118.799999999999997 |
| 15 | 1.6 | 7 | 144.199999999999989 |
| 15 | 1.7 | 5 | 96.250000000000000 |
| 15 | 1.7 | 6 | 120.599999999999994 |
| 15 | 1.7 | 7 | 146.650000000000006 |
| 16 | 1.4 | 5 | 97.500000000000000 |
| 16 | 1.4 | 6 | 121.200000000000003 |
| 16 | 1.4 | 7 | 146.300000000000011 |
| 16 | 1.5 | 5 | 98.750000000000000 |
| 16 | 1.5 | 6 | 123.000000000000000 |
| 16 | 1.5 | 7 | 148.750000000000000 |
| 16 | 1.6 | 5 | 100.000000000000000 |
| 16 | 1.6 | 6 | 124.799999999999997 |
| 16 | 1.6 | 7 | 151.199999999999989 |
| 16 | 1.7 | 5 | 101.250000000000000 |
| 16 | 1.7 | 6 | 126.599999999999994 |
| 16 | 1.7 | 7 | 153.650000000000006 |