Final answer:
The circle defined by the equation (x² + y²) = 196 has a center at the coordinates (0, 0) and a radius of 14 units. Other problems related to circular motion will require applications of trigonometry and physics.
Step-by-step explanation:
The equation (x² + y²) = 196 represents a circle in a two-dimensional coordinate system. To find the coordinates of the centre and the radius of the circle, we need to compare this equation with the general equation for a circle centered at (h, k) with radius r: (x - h)² + (y - k)² = r².
For the given equation, the circle is centered at the origin because there are no terms h or k to shift the circle along the x or y-axis. Therefore, the coordinates of the center are (0, 0). To find the radius, we take the square root of 196, which gives us a radius of 14 units.
When we move on to other related problems, such as calculating velocity or centripetal force for particles in circular motion or analyzing rotational systems, we apply concepts of trigonometry and physics that involve angular velocities and acceleration vectors.