When the speed of the object is doubled, the net force needed for that object's circular motion is doubled. By the above equation, this change in the net force is predicted to be the square of the change in the speed. Thus, doubling the speed of an object moving in uniform circular motion doubles the net force required for that motion. However, as has been discussed previously, Fnet and v are not constants in the equation. They are related to each other by the following equations:
The concepts presented in the preceding problems can be extended to solve circular motion problems in which the radius of the circle (r) is unknown. This can be achieved by combining the circular motion equations presented above with the known equation for the radius of a circle. In this case, an unknown quantity, r, is substituted into the equation for the radius of a circle. Then, the equation for circular motion is used to solve for the acceleration of the object and the radius of the circle. The solution for this problem is found as follows:
The first problem can be solved using a = Fnet / m 2. The answer to problem 2 can be obtained by reversing the process, or by using a different but equivalent manner of solving the problem.
A solution to problem 3 can be created by using problem 2 to solve for the acceleration of the object. The radius of the circle can then be estimated by using a different but equivalent approach. For example, if the radius of the circle is greater than 10 meters, it is most likely that the object in circular motion is located on the ground. For this case, the radius of the circle will be calculated as follows:
In the case of real-world motion, the object's speed is the quantity that is altered. The equation that governs the effect of an alteration of the object's speed on its acceleration has the following form: