Problem: An object moves around a circle of radius 5 meters, moving at constant angular velocity 9.400 radians/second. Starting at t = 0, when its angular position is 0 radians, what are the x and y coordinates of its position after 10 seconds, and after 5 seconds?
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Solution: The object has angular velocity `omega = 9.400 radians/second. Therefore, after 10 seconds, starting at 0 radians when t = 0, the angular position will be
`theta1 = ( 9.400 radians/second)( 10 seconds) = 94 radians.
On a circle of radius 5 meters, the x and y coordinates will therefore be
x1 = 5 meters * COS( 94 radians) = 4.847 meters
and
y1 = 5 meters * SIN( 94 radians) = .6175 meters.
After 5 seconds, the angular position will be
`theta2 = 9.4 radians/second( 5 seconds) = 47 radians.
On a circle of radius 5 meters, the x and y coordinates will therefore be
x2 = 5 meters * COS( 47 radians) = -.9615 meters
and
y2 = 5 meters * SIN( 47 radians) = -.2260 meters.