At t = 0 seconds the angular position of an object is 0 radians, and it moves at constant angular velocity of .9378 rad/sec around a circle of radius 3.6 meters. What are the x and y coordinates of its position at t = `t1 seconds and at t = `t2 seconds?
The object has angular velocity `omega = .9378 radians/second. Therefore, after 6.3 seconds, starting at 0 radians when t = 0, the angular position will be
`theta1 = ( .9378 radians/second)( 6.3 seconds) = 5.90814 radians.
On a circle of radius 3.6 meters, the x and y coordinates will therefore be
x1 = 3.6 meters * cos( 5.90814 radians) = 3.349 meters
and
y1 = 3.6 meters * sin( 5.90814 radians) = -1.319 meters.
After 12.67 seconds, the angular position will be
`theta2 = .9378 radians/second( 12.67 seconds) = 11.88193 radians.
On a circle of radius 3.6 meters, the x and y coordinates will therefore be
x2 = 3.6 meters * cos( 11.88193 radians) = 2.789 meters
and
"y2 = 3.6 meters * sin( 11.88193 radians) = -2.277 meters.