An object moves around a circle of radius 3.7 meters, moving at constant angular velocity .7392 radians/second. Starting at t = 0, when its angular position is 0 radians, what are the x and y coordinates of its position after 5.5 seconds, and after 15.65 seconds?
The object has angular velocity `omega = .7392 radians/second. Therefore, after 5.5 seconds, starting at 0 radians when t = 0, the angular position will be
`theta1 = ( .7392 radians/second)( 5.5 seconds) = 4.0656 radians.
On a circle of radius 3.7 meters, the x and y coordinates will therefore be
x1 = 3.7 meters * cos( 4.0656 radians) = -2.23 meters
and
y1 = 3.7 meters * sin( 4.0656 radians) = -2.953 meters.
After 15.65 seconds, the angular position will be
`theta2 = .7392 radians/second( 15.65 seconds) = 11.56848 radians.
On a circle of radius 3.7 meters, the x and y coordinates will therefore be
and
"y2 = 3.7 meters * sin( 11.56848 radians) = -3.11 meters.