A dancer completes 2.6 revolutions in a pirouette. What is her angular displacement?
2.6 * 2 pi radians or 2.6 * 360 degrees
She is only 0.6 revolutions from the starting point:
2.6-2 = 0.6 rev.
Disp. = 0.6 * 360 = 210 degrees.
To find the angular displacement of a dancer completing 2.6 revolutions in a pirouette, we need to know the relationship between revolutions and angular displacement.
Angular displacement is a measure of how much an object has rotated or moved with respect to a reference position, usually measured in degrees or radians. One revolution is equal to 360 degrees or 2π radians, which means that a complete circle has an angular displacement of 360 degrees or 2π radians.
In this case, the dancer completes 2.6 revolutions, which is equivalent to 2.6 × 360 degrees or 2.6 × 2π radians.
Calculating the angular displacement:
Angular displacement (in degrees) = Number of revolutions × 360 degrees
= 2.6 × 360 degrees
= 936 degrees
Angular displacement (in radians) = Number of revolutions × 2π radians
= 2.6 × 2π radians
= 5.2π radians
Therefore, the angular displacement of the dancer in this pirouette is 936 degrees or 5.2π radians.