A dancer completes 3.4 revolutions in a pirouette. What is her angular displacement?
The first three pirouettes leave her where she started. Then she turns an additional 0.4 * (2 pi) = 2.51 radians
To find the angular displacement, we need to know the number of revolutions completed by the dancer and convert it into radians.
First, let's convert the number of revolutions to radians. Remember that one revolution is equal to 2π radians. So, for every revolution, we have 2π radians.
Angular displacement = (Number of revolutions) x (2π radians/revolution)
In this case, the dancer completes 3.4 revolutions, so the angular displacement is:
Angular displacement = (3.4 revolutions) x (2π radians/revolution)
Now, let's calculate it:
Angular displacement = (3.4)(2π) radians
Angular displacement ≈ 21.36 radians
Therefore, the angular displacement of the dancer in the pirouette is approximately 21.36 radians.