The valve can be placed in the same angular position, ʌ/2 rad, by rotating the wheel in
the other direction, by rotating it clockwise three quarters of a turn. By convention,
angular position decreases with clockwise motion, so this rotation would be described
as an angular position of í 3 ʌ/2 rad.
An angular position can be greater than 2 ʌrad. An angular position of 3 ʌ rad
represents one and a half counterclockwise revolutions. The valve would be at 9 o’clock
in that position.Radian measure
ș = angle in radians
s = arc length
r = radius
What is the arc length?
s = rș = (0.35 m)(ʌ/3 rad)
s = 0.37 m
9.2 - Angular displacement
Angular displacement: Change in angular
position.
In Concept 1 you see a pizza topped with a single mushroom (we are not going back to
that pizzeria!). We use a mushroom to make the rotational motion of the pizza easier to
see. As the pizza rotates, its angular position changes. This change in angular position
is called angular displacement.To calculate angular displacement, you subtract the initial angular position from the final
position. For instance, the mushroom in the Equation illustration moves from ʌ/2 rad to
ʌ rad, a displacement of ʌ/2 rad. As you can see in this example, angular displacement
in the counterclockwise direction is positive.
Revolution is a common term in the study of rotational motion. It means one complete
rotational cycle, with the object starting and returning to the same position. One
counterclockwise revolution equals 2 ʌ radians of angular displacement.
The angular displacement is the total angle “swept out” during rotational motion from an initial to a final position. If the pizza turns
counterclockwise three complete revolutions, its angular displacement is 6 ʌradians.
The definition of angular displacement resembles that of linear displacement. However, the discussion above points out a difference. A
mushroom that makes a complete revolution has an angular displacement of 2 ʌ rad. On the other hand, its linear displacement equals zero,Angular displacement
Change in angular position
Counterclockwise rotation is positive(^176) Copyright 2007 Kinetic Books Co. Chapter 09