Cycloid?. A particle moves in the ?xy?-plane. Its coordinates are given as functions of time by x?? ?) =?? t? ? sin ??? ?? t) = ?R?(1 ? cos? t?) Where ?R? and ??? are constants. (a) Sketch the trajectory of the particle. (This is the trajectory of a point on the rim of a wheel that is rolling at a constant speed on a horizontal surface. The curve traced out by such a point as it moves through space is called a cycloid.) (b) Determine the velocity components and the acceleration components of the particle at any time ?t?. (c) At what times is the particle momentarily at rest? What are the coordinates of the particle at these times? What are the magnitude and direction of the (d) Does the magnitude of the acceleration depend on time? Compare to uniform circular motion.

Chapter 1 Introduction Physics o The study of nature The Domains of Physics o Microscopic Domain The domain of atoms, molecules, electrons, protons, pion and mesons, etc. Extreme small in mass Uncertainty of physical properties Unpredictable behavior o Macroscopic Domain The domain of man, house, car, ball, even a planet Daily life experiences Physics experienced on earth Governed by gravity, Newton's Laws (orbit) Predictable behavior o Galactic Domain The domain of galaxies and their clusters characterized by huge masse