Please explain each response to each prompt using physics terms/ideas/formulas/proofs. I would like to check my own work. Please NO REPOSTS of other work.

Note: reference is below.

Reference: Polar coordinates for pendulums Let's practice using polar coordinates in a simple scenario. A pendulum could be made of anything that hangs and swings back and forth, but let's consider a ball with mass m hanging by a string of length E. It's important that ball is small compared to the length of the string and that the mass of the string is much less than the mass of the ball. The pendulum traces out a circular arc of length 5 as the string makes an angle 19 to the vertical. Our equations for position, velocity, and acceleration change slightly. Cartesian Polar :17 s = {'9 d3: d3 d9 1; : a we : a : HE de (123: deg (123 0326 azz aezzz Notice the similarities between linear motion and angular motion along an arc of length 3. We will get to angular motion in more detail later in the course, but for now we can use What Wo know about Newton's laws to see how a pendulum works. frictionless pivot amplitude massless rod bob's' ~ - q- _\\_' trajectory ' massive bob eqUIIIbrIum position 5 n f Practice Problems (3.) The pendulum moves in two dimensions, but polar coordinates (r, 6) are better than Cartesian coordinates (.r, 3;). Where should we put the origin in our polar coordinate system? (1)} Does r, the radial coordinate of the mass on the pendulum, change as it swings? c W'rite out the force balance e