A dancer completes 3.2 revolutions in a pirouette. What is her angular displacement?
3.2 * 2pi
When a dancer completes 3 revolutions he is at the same place where it started.
3.2 - 3 = 0.2 revolutions
1 revolution = 2 π radians
( 3.2 - 3 ) ∙ 2 π = 0.2 ∙ 2 π = 0.4 π radians
OR
1 revolution = 360°
( 3.2 - 3 ) ∙ 360° = 0.2 ∙ 360° = 72°
To find the angular displacement, you need to know the number of revolutions and convert it to radians.
One revolution is equal to 2π radians.
So, if the dancer completes 3.2 revolutions, her angular displacement can be calculated as follows:
Angular Displacement = Number of revolutions × 2π
Angular Displacement = 3.2 × 2π
Angular Displacement ≈ 6.4π radians
Therefore, the dancer's angular displacement is approximately 6.4π radians.