In Module 5 you saw that uniform circular motion is a special case of two-dimensional motion. An examination of uniform motion revealed the relationships among speed, frequency, period, and radius for circular motion; and it became evident that acceleration is directed toward the centre of a circle. You applied Newton’s laws of motion to help explain uniform circular motion, and then you used circular motion to approximate elliptical orbits and explain planetary, natural, and artificial satellite motion. You were able to predict the mass of a celestial body from the orbital data of a satellite in uniform circular motion around that body. Finally, you examined the relationship between Kepler’s laws and the development of Newton’s universal law of gravitation.
At the beginning of this module you were asked, “What conditions are necessary to maintain circular motion?” Throughout the module, you gained understanding to help you answer this question. When an object travels in a circular path, there must be an inward force causing the direction of the motion to change—so, if there is circular motion, there is also a centripetal force. Free-body analysis can be used to visualize the forces acting on an object, and the equation for centripetal force helps you understand the conditions that are necessary to maintain circular motion.
Module 6 examined the relationships among kinetic, gravitational potential, and total mechanical energies of a mass at any point between maximum potential energy and maximum kinetic energy. You analyzed kinematics and dynamics problems that related to the conservation of mechanical energy in an isolated system, and you looked at the change in mechanical energy in a system that is not isolated. This helped you to understand the difference between conservative and non-conservative forces. You came to see that while work is a measure of the mechanical energy transferred, power is the rate of doing work. You then applied your knowledge of work and power to solve related problems.
In an isolated system, no energy is lost but, rather, is transferred from gravitational potential to kinetic and back. You saw this with the examples of skiers using a chairlift. However, in a system that is not isolated, energy can be lost to friction, heat, and sound. Energy can be gained from motors and other outside sources. Even if energy is lost from the system, it is not destroyed—it is merely transformed. Energy that has been gained has not been created but, rather, transferred from an outside source into the system. This knowledge is used to design more efficient energy transfer systems in society.