Problem: An object moves around a circle of radius 10 meters, making a revolution every 5 seconds. Assume that its angular velocity is constant. Starting at t = 0, when its angular position is 0 radians, what are the x and y coordinates of its position after t seconds?
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Solution: Moving through a revolution, which is 2 `pi radians, in 5 seconds, the object will have an angular velocity of
`omega = 2 `pi radians/( 5 seconds) = 1.256 radians/second.
After t seconds, starting at 0 radians when t = 0, the angular position will be
theta = 1.256 radians/second (t seconds) = 1.256 t radians.
Its x and y coordinates are therefore
x1 = 10 meters * COS( 1.256 t)
and
y = 10 meters * SIN( 1.256 t).