The formula to calculate Angular Displacement (θ) is:
\[ θ = \frac{ω1^2 - ωo^2}{2 \cdot α} \]
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.
Final Angular Velocity is the velocity after covering the required angular displacement in time \(t\).
Initial Angular Velocity is the velocity at which motion starts.
Angular acceleration refers to the time rate of change of angular velocity.
Let's assume the following values:
Using the formula:
\[ θ = \frac{ω1^2 - ωo^2}{2 \cdot α} \]
Evaluating:
\[ θ = \frac{11^2 - 14^2}{2 \cdot 1.6} \]
The Angular Displacement is -23.4375.
| Final Angular Velocity (ω1) | Initial Angular Velocity (ωo) | Angular Acceleration (α) | Angular Displacement (θ) |
|---|---|---|---|
| 10 | 13 | 1.5 | -23.000000000000000 |
| 10 | 13 | 1.6 | -21.562500000000000 |
| 10 | 13 | 1.7 | -20.294117647058822 |
| 10 | 13 | 1.8 | -19.166666666666664 |
| 10 | 13 | 1.9 | -18.157894736842103 |
| 10 | 13.5 | 1.5 | -27.416666666666668 |
| 10 | 13.5 | 1.6 | -25.703125000000000 |
| 10 | 13.5 | 1.7 | -24.191176470588232 |
| 10 | 13.5 | 1.8 | -22.847222222222218 |
| 10 | 13.5 | 1.9 | -21.644736842105260 |
| 10 | 14 | 1.5 | -32.000000000000000 |
| 10 | 14 | 1.6 | -30.000000000000000 |
| 10 | 14 | 1.7 | -28.235294117647054 |
| 10 | 14 | 1.8 | -26.666666666666664 |
| 10 | 14 | 1.9 | -25.263157894736839 |
| 10 | 14.5 | 1.5 | -36.750000000000000 |
| 10 | 14.5 | 1.6 | -34.453125000000000 |
| 10 | 14.5 | 1.7 | -32.426470588235290 |
| 10 | 14.5 | 1.8 | -30.624999999999996 |
| 10 | 14.5 | 1.9 | -29.013157894736835 |
| 10 | 15 | 1.5 | -41.666666666666664 |
| 10 | 15 | 1.6 | -39.062500000000000 |
| 10 | 15 | 1.7 | -36.764705882352935 |
| 10 | 15 | 1.8 | -34.722222222222214 |
| 10 | 15 | 1.9 | -32.894736842105260 |
| 10.5 | 13 | 1.5 | -19.583333333333332 |
| 10.5 | 13 | 1.6 | -18.359375000000000 |
| 10.5 | 13 | 1.7 | -17.279411764705880 |
| 10.5 | 13 | 1.8 | -16.319444444444443 |
| 10.5 | 13 | 1.9 | -15.460526315789471 |
| 10.5 | 13.5 | 1.5 | -24.000000000000000 |
| 10.5 | 13.5 | 1.6 | -22.500000000000000 |
| 10.5 | 13.5 | 1.7 | -21.176470588235293 |
| 10.5 | 13.5 | 1.8 | -19.999999999999996 |
| 10.5 | 13.5 | 1.9 | -18.947368421052627 |
| 10.5 | 14 | 1.5 | -28.583333333333332 |
| 10.5 | 14 | 1.6 | -26.796875000000000 |
| 10.5 | 14 | 1.7 | -25.220588235294116 |
| 10.5 | 14 | 1.8 | -23.819444444444439 |
| 10.5 | 14 | 1.9 | -22.565789473684205 |
| 10.5 | 14.5 | 1.5 | -33.333333333333336 |
| 10.5 | 14.5 | 1.6 | -31.250000000000000 |
| 10.5 | 14.5 | 1.7 | -29.411764705882351 |
| 10.5 | 14.5 | 1.8 | -27.777777777777775 |
| 10.5 | 14.5 | 1.9 | -26.315789473684205 |
| 10.5 | 15 | 1.5 | -38.250000000000000 |
| 10.5 | 15 | 1.6 | -35.859375000000000 |
| 10.5 | 15 | 1.7 | -33.750000000000000 |
| 10.5 | 15 | 1.8 | -31.874999999999996 |
| 10.5 | 15 | 1.9 | -30.197368421052627 |
| 11 | 13 | 1.5 | -16.000000000000000 |
| 11 | 13 | 1.6 | -15.000000000000000 |
| 11 | 13 | 1.7 | -14.117647058823527 |
| 11 | 13 | 1.8 | -13.333333333333332 |
| 11 | 13 | 1.9 | -12.631578947368419 |
| 11 | 13.5 | 1.5 | -20.416666666666668 |
| 11 | 13.5 | 1.6 | -19.140625000000000 |
| 11 | 13.5 | 1.7 | -18.014705882352938 |
| 11 | 13.5 | 1.8 | -17.013888888888886 |
| 11 | 13.5 | 1.9 | -16.118421052631575 |
| 11 | 14 | 1.5 | -25.000000000000000 |
| 11 | 14 | 1.6 | -23.437500000000000 |
| 11 | 14 | 1.7 | -22.058823529411761 |
| 11 | 14 | 1.8 | -20.833333333333329 |
| 11 | 14 | 1.9 | -19.736842105263154 |
| 11 | 14.5 | 1.5 | -29.750000000000000 |
| 11 | 14.5 | 1.6 | -27.890625000000000 |
| 11 | 14.5 | 1.7 | -26.249999999999996 |
| 11 | 14.5 | 1.8 | -24.791666666666664 |
| 11 | 14.5 | 1.9 | -23.486842105263154 |
| 11 | 15 | 1.5 | -34.666666666666664 |
| 11 | 15 | 1.6 | -32.500000000000000 |
| 11 | 15 | 1.7 | -30.588235294117645 |
| 11 | 15 | 1.8 | -28.888888888888886 |
| 11 | 15 | 1.9 | -27.368421052631575 |
| 11.5 | 13 | 1.5 | -12.250000000000000 |
| 11.5 | 13 | 1.6 | -11.484375000000000 |
| 11.5 | 13 | 1.7 | -10.808823529411763 |
| 11.5 | 13 | 1.8 | -10.208333333333332 |
| 11.5 | 13 | 1.9 | -9.671052631578945 |
| 11.5 | 13.5 | 1.5 | -16.666666666666668 |
| 11.5 | 13.5 | 1.6 | -15.625000000000000 |
| 11.5 | 13.5 | 1.7 | -14.705882352941176 |
| 11.5 | 13.5 | 1.8 | -13.888888888888888 |
| 11.5 | 13.5 | 1.9 | -13.157894736842103 |
| 11.5 | 14 | 1.5 | -21.250000000000000 |
| 11.5 | 14 | 1.6 | -19.921875000000000 |
| 11.5 | 14 | 1.7 | -18.749999999999996 |
| 11.5 | 14 | 1.8 | -17.708333333333332 |
| 11.5 | 14 | 1.9 | -16.776315789473681 |
| 11.5 | 14.5 | 1.5 | -26.000000000000000 |
| 11.5 | 14.5 | 1.6 | -24.375000000000000 |
| 11.5 | 14.5 | 1.7 | -22.941176470588232 |
| 11.5 | 14.5 | 1.8 | -21.666666666666664 |
| 11.5 | 14.5 | 1.9 | -20.526315789473681 |
| 11.5 | 15 | 1.5 | -30.916666666666668 |
| 11.5 | 15 | 1.6 | -28.984375000000000 |
| 11.5 | 15 | 1.7 | -27.279411764705880 |
| 11.5 | 15 | 1.8 | -25.763888888888886 |
| 11.5 | 15 | 1.9 | -24.407894736842099 |
| 12 | 13 | 1.5 | -8.333333333333334 |
| 12 | 13 | 1.6 | -7.812500000000000 |
| 12 | 13 | 1.7 | -7.352941176470588 |
| 12 | 13 | 1.8 | -6.944444444444444 |
| 12 | 13 | 1.9 | -6.578947368421051 |
| 12 | 13.5 | 1.5 | -12.750000000000000 |
| 12 | 13.5 | 1.6 | -11.953125000000000 |
| 12 | 13.5 | 1.7 | -11.249999999999998 |
| 12 | 13.5 | 1.8 | -10.624999999999998 |
| 12 | 13.5 | 1.9 | -10.065789473684209 |
| 12 | 14 | 1.5 | -17.333333333333332 |
| 12 | 14 | 1.6 | -16.250000000000000 |
| 12 | 14 | 1.7 | -15.294117647058822 |
| 12 | 14 | 1.8 | -14.444444444444443 |
| 12 | 14 | 1.9 | -13.684210526315788 |
| 12 | 14.5 | 1.5 | -22.083333333333332 |
| 12 | 14.5 | 1.6 | -20.703125000000000 |
| 12 | 14.5 | 1.7 | -19.485294117647058 |
| 12 | 14.5 | 1.8 | -18.402777777777775 |
| 12 | 14.5 | 1.9 | -17.434210526315788 |
| 12 | 15 | 1.5 | -27.000000000000000 |
| 12 | 15 | 1.6 | -25.312500000000000 |
| 12 | 15 | 1.7 | -23.823529411764703 |
| 12 | 15 | 1.8 | -22.499999999999996 |
| 12 | 15 | 1.9 | -21.315789473684205 |