how to prove points towards center

Physics 121 Fall 2025 Document #13: Homework AM Reading Assignment page 6 of 7 Problem 4: A Special Kind of Motion Suppose a particle has a position which is defined by a position vector expression as follows: r{l) = Reoa(wl)i + Rsin(wl)j Prove that this represents Uniform Circular Motion. In other words, prove that the following three things are true: * Prove that this particle travels on a path that is a circle by demonstrating that the particle is always found at a distance /? from the origin. Hint: Trig identity: sin?(@) + cos*(@) 1 for any angle * Prove that this particle has a constant speed v, where wv wii. * Prove that the acceleration vector always has fixed magnitude 1*/ J? and points toward the center of the circular path