Final answer:
To find the unknowns a, b, and r, use at least three points on the circle to create a system of equations. Kinematic or trigonometric equations help when certain motion parameters are given.
Step-by-step explanation:
To solve for the three unknowns a, b, and r from the equation (x-a)² + (y-b)² = r², which represents a circle with center (a, b) and radius r, you need at least three different points (x, y) on the circumference of the circle. With these points, you can set up a system of equations by plugging in their x and y coordinates into the equation and solving for a, b, and r. If only certain aspects like the angular velocity or the angle are known, relevant kinematic or trigonometric relationships can be utilized to find the required distances or velocities. For instance, the kinematic equation w² = wo² + 2aθ can help solve for angular velocity w when initial angular velocity wo, angular acceleration a, and angle θ are known.