The formula to calculate Angular Displacement (θ) is:
\[ θ = \left(\frac{ωo + ω1}{2}\right) \cdot t \]
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.
Final Angular Velocity is the velocity after covering the required angular displacement in time \(t\).
Time Taken to Travel the Path is the total time taken by an object to reach its destination.
Let's assume the following values:
Using the formula:
\[ θ = \left(\frac{ωo + ω1}{2}\right) \cdot t \]
Evaluating:
\[ θ = \left(\frac{14 + 11}{2}\right) \cdot 6 \]
The Angular Displacement is 75.
| Initial Angular Velocity (ωo) | Final Angular Velocity (ω1) | Time Taken to Travel the Path (t) | Angular Displacement (θ) |
|---|---|---|---|
| 10 | 10 | 5 | 50.000000000000000 |
| 10 | 10 | 5.5 | 55.000000000000000 |
| 10 | 10 | 6 | 60.000000000000000 |
| 10 | 10 | 6.5 | 65.000000000000000 |
| 10 | 10 | 7 | 70.000000000000000 |
| 10 | 11 | 5 | 52.500000000000000 |
| 10 | 11 | 5.5 | 57.750000000000000 |
| 10 | 11 | 6 | 63.000000000000000 |
| 10 | 11 | 6.5 | 68.250000000000000 |
| 10 | 11 | 7 | 73.500000000000000 |
| 10 | 12 | 5 | 55.000000000000000 |
| 10 | 12 | 5.5 | 60.500000000000000 |
| 10 | 12 | 6 | 66.000000000000000 |
| 10 | 12 | 6.5 | 71.500000000000000 |
| 10 | 12 | 7 | 77.000000000000000 |
| 10 | 13 | 5 | 57.500000000000000 |
| 10 | 13 | 5.5 | 63.250000000000000 |
| 10 | 13 | 6 | 69.000000000000000 |
| 10 | 13 | 6.5 | 74.750000000000000 |
| 10 | 13 | 7 | 80.500000000000000 |
| 10 | 14 | 5 | 60.000000000000000 |
| 10 | 14 | 5.5 | 66.000000000000000 |
| 10 | 14 | 6 | 72.000000000000000 |
| 10 | 14 | 6.5 | 78.000000000000000 |
| 10 | 14 | 7 | 84.000000000000000 |
| 10 | 15 | 5 | 62.500000000000000 |
| 10 | 15 | 5.5 | 68.750000000000000 |
| 10 | 15 | 6 | 75.000000000000000 |
| 10 | 15 | 6.5 | 81.250000000000000 |
| 10 | 15 | 7 | 87.500000000000000 |
| 11 | 10 | 5 | 52.500000000000000 |
| 11 | 10 | 5.5 | 57.750000000000000 |
| 11 | 10 | 6 | 63.000000000000000 |
| 11 | 10 | 6.5 | 68.250000000000000 |
| 11 | 10 | 7 | 73.500000000000000 |
| 11 | 11 | 5 | 55.000000000000000 |
| 11 | 11 | 5.5 | 60.500000000000000 |
| 11 | 11 | 6 | 66.000000000000000 |
| 11 | 11 | 6.5 | 71.500000000000000 |
| 11 | 11 | 7 | 77.000000000000000 |
| 11 | 12 | 5 | 57.500000000000000 |
| 11 | 12 | 5.5 | 63.250000000000000 |
| 11 | 12 | 6 | 69.000000000000000 |
| 11 | 12 | 6.5 | 74.750000000000000 |
| 11 | 12 | 7 | 80.500000000000000 |
| 11 | 13 | 5 | 60.000000000000000 |
| 11 | 13 | 5.5 | 66.000000000000000 |
| 11 | 13 | 6 | 72.000000000000000 |
| 11 | 13 | 6.5 | 78.000000000000000 |
| 11 | 13 | 7 | 84.000000000000000 |
| 11 | 14 | 5 | 62.500000000000000 |
| 11 | 14 | 5.5 | 68.750000000000000 |
| 11 | 14 | 6 | 75.000000000000000 |
| 11 | 14 | 6.5 | 81.250000000000000 |
| 11 | 14 | 7 | 87.500000000000000 |
| 11 | 15 | 5 | 65.000000000000000 |
| 11 | 15 | 5.5 | 71.500000000000000 |
| 11 | 15 | 6 | 78.000000000000000 |
| 11 | 15 | 6.5 | 84.500000000000000 |
| 11 | 15 | 7 | 91.000000000000000 |
| 12 | 10 | 5 | 55.000000000000000 |
| 12 | 10 | 5.5 | 60.500000000000000 |
| 12 | 10 | 6 | 66.000000000000000 |
| 12 | 10 | 6.5 | 71.500000000000000 |
| 12 | 10 | 7 | 77.000000000000000 |
| 12 | 11 | 5 | 57.500000000000000 |
| 12 | 11 | 5.5 | 63.250000000000000 |
| 12 | 11 | 6 | 69.000000000000000 |
| 12 | 11 | 6.5 | 74.750000000000000 |
| 12 | 11 | 7 | 80.500000000000000 |
| 12 | 12 | 5 | 60.000000000000000 |
| 12 | 12 | 5.5 | 66.000000000000000 |
| 12 | 12 | 6 | 72.000000000000000 |
| 12 | 12 | 6.5 | 78.000000000000000 |
| 12 | 12 | 7 | 84.000000000000000 |
| 12 | 13 | 5 | 62.500000000000000 |
| 12 | 13 | 5.5 | 68.750000000000000 |
| 12 | 13 | 6 | 75.000000000000000 |
| 12 | 13 | 6.5 | 81.250000000000000 |
| 12 | 13 | 7 | 87.500000000000000 |
| 12 | 14 | 5 | 65.000000000000000 |
| 12 | 14 | 5.5 | 71.500000000000000 |
| 12 | 14 | 6 | 78.000000000000000 |
| 12 | 14 | 6.5 | 84.500000000000000 |
| 12 | 14 | 7 | 91.000000000000000 |
| 12 | 15 | 5 | 67.500000000000000 |
| 12 | 15 | 5.5 | 74.250000000000000 |
| 12 | 15 | 6 | 81.000000000000000 |
| 12 | 15 | 6.5 | 87.750000000000000 |
| 12 | 15 | 7 | 94.500000000000000 |
| 13 | 10 | 5 | 57.500000000000000 |
| 13 | 10 | 5.5 | 63.250000000000000 |
| 13 | 10 | 6 | 69.000000000000000 |
| 13 | 10 | 6.5 | 74.750000000000000 |
| 13 | 10 | 7 | 80.500000000000000 |
| 13 | 11 | 5 | 60.000000000000000 |
| 13 | 11 | 5.5 | 66.000000000000000 |
| 13 | 11 | 6 | 72.000000000000000 |
| 13 | 11 | 6.5 | 78.000000000000000 |
| 13 | 11 | 7 | 84.000000000000000 |
| 13 | 12 | 5 | 62.500000000000000 |
| 13 | 12 | 5.5 | 68.750000000000000 |
| 13 | 12 | 6 | 75.000000000000000 |
| 13 | 12 | 6.5 | 81.250000000000000 |
| 13 | 12 | 7 | 87.500000000000000 |
| 13 | 13 | 5 | 65.000000000000000 |
| 13 | 13 | 5.5 | 71.500000000000000 |
| 13 | 13 | 6 | 78.000000000000000 |
| 13 | 13 | 6.5 | 84.500000000000000 |
| 13 | 13 | 7 | 91.000000000000000 |
| 13 | 14 | 5 | 67.500000000000000 |
| 13 | 14 | 5.5 | 74.250000000000000 |
| 13 | 14 | 6 | 81.000000000000000 |
| 13 | 14 | 6.5 | 87.750000000000000 |
| 13 | 14 | 7 | 94.500000000000000 |
| 13 | 15 | 5 | 70.000000000000000 |
| 13 | 15 | 5.5 | 77.000000000000000 |
| 13 | 15 | 6 | 84.000000000000000 |
| 13 | 15 | 6.5 | 91.000000000000000 |
| 13 | 15 | 7 | 98.000000000000000 |
| 14 | 10 | 5 | 60.000000000000000 |
| 14 | 10 | 5.5 | 66.000000000000000 |
| 14 | 10 | 6 | 72.000000000000000 |
| 14 | 10 | 6.5 | 78.000000000000000 |
| 14 | 10 | 7 | 84.000000000000000 |
| 14 | 11 | 5 | 62.500000000000000 |
| 14 | 11 | 5.5 | 68.750000000000000 |
| 14 | 11 | 6 | 75.000000000000000 |
| 14 | 11 | 6.5 | 81.250000000000000 |
| 14 | 11 | 7 | 87.500000000000000 |
| 14 | 12 | 5 | 65.000000000000000 |
| 14 | 12 | 5.5 | 71.500000000000000 |
| 14 | 12 | 6 | 78.000000000000000 |
| 14 | 12 | 6.5 | 84.500000000000000 |
| 14 | 12 | 7 | 91.000000000000000 |
| 14 | 13 | 5 | 67.500000000000000 |
| 14 | 13 | 5.5 | 74.250000000000000 |
| 14 | 13 | 6 | 81.000000000000000 |
| 14 | 13 | 6.5 | 87.750000000000000 |
| 14 | 13 | 7 | 94.500000000000000 |
| 14 | 14 | 5 | 70.000000000000000 |
| 14 | 14 | 5.5 | 77.000000000000000 |
| 14 | 14 | 6 | 84.000000000000000 |
| 14 | 14 | 6.5 | 91.000000000000000 |
| 14 | 14 | 7 | 98.000000000000000 |
| 14 | 15 | 5 | 72.500000000000000 |
| 14 | 15 | 5.5 | 79.750000000000000 |
| 14 | 15 | 6 | 87.000000000000000 |
| 14 | 15 | 6.5 | 94.250000000000000 |
| 14 | 15 | 7 | 101.500000000000000 |
| 15 | 10 | 5 | 62.500000000000000 |
| 15 | 10 | 5.5 | 68.750000000000000 |
| 15 | 10 | 6 | 75.000000000000000 |
| 15 | 10 | 6.5 | 81.250000000000000 |
| 15 | 10 | 7 | 87.500000000000000 |
| 15 | 11 | 5 | 65.000000000000000 |
| 15 | 11 | 5.5 | 71.500000000000000 |
| 15 | 11 | 6 | 78.000000000000000 |
| 15 | 11 | 6.5 | 84.500000000000000 |
| 15 | 11 | 7 | 91.000000000000000 |
| 15 | 12 | 5 | 67.500000000000000 |
| 15 | 12 | 5.5 | 74.250000000000000 |
| 15 | 12 | 6 | 81.000000000000000 |
| 15 | 12 | 6.5 | 87.750000000000000 |
| 15 | 12 | 7 | 94.500000000000000 |
| 15 | 13 | 5 | 70.000000000000000 |
| 15 | 13 | 5.5 | 77.000000000000000 |
| 15 | 13 | 6 | 84.000000000000000 |
| 15 | 13 | 6.5 | 91.000000000000000 |
| 15 | 13 | 7 | 98.000000000000000 |
| 15 | 14 | 5 | 72.500000000000000 |
| 15 | 14 | 5.5 | 79.750000000000000 |
| 15 | 14 | 6 | 87.000000000000000 |
| 15 | 14 | 6.5 | 94.250000000000000 |
| 15 | 14 | 7 | 101.500000000000000 |
| 15 | 15 | 5 | 75.000000000000000 |
| 15 | 15 | 5.5 | 82.500000000000000 |
| 15 | 15 | 6 | 90.000000000000000 |
| 15 | 15 | 6.5 | 97.500000000000000 |
| 15 | 15 | 7 | 105.000000000000000 |