Statement
difficulty
A body moves describing a circular trajectory with constant linear and angular velocity equal to 3 m/s and 6π rad/s respectively. Determine its position vector when it has traveled exactly one meter.
Solution
Data
ω = 6 π rad/s
v = 3 m/s
Resolution
If we apply the definitions of the angular magnitudes, we know that:
Now applying the definition of distance traveled based on the angular position and the radius:
Now that we know the radius and the angular position when the distance traveled is 1 m, we can determine the position vector using the following expression: