Uniform circular motion

UCM.R

# x direction
x_t <- function(R, omega, t) {  R * cos(omega * t) }
v_x <- function(R, omega, t) { -R * omega * sin(omega * t) }
a_x <- function(R, omega, t) { -R * omega^2 * cos(omega * t) }

# y direction
y_t <- function(R, omega, t) {  R * sin(omega * t) }
v_y <- function(R, omega, t) {  R * omega * cos(omega * t) }
a_y <- function(R, omega, t) { -R * omega^2 * sin(omega * t) }

# Radius of orbit
R <- 1
# Angular speed
w <- 2 # radians per second

# full cycle when T = 2*pi/omega
T <- 2*pi/w
L <- 100
t <- seq(0, T, len = L)

library(tidyverse)
d <- tibble(t = t,
            x = x_t(R, w, t),
            vx = v_x(R, w, t),
            ax = a_x(R, w, t),
            y = y_t(R, w, t),
            vy = v_y(R, w, t),
            ay = a_y(R, w, t))

theme_set(theme_minimal())
ggplot(data = d, aes(t, x)) + geom_line() +
  geom_line(aes(t, y), color = 'red')
  
ggplot(d, aes(x, y)) + geom_path(linewidth = 0.2) 

library(grid)
d_sub <- d |> filter(row_number() %% 2 != 1)

ggplot(d_sub, aes(x = x, y = y)) +
  geom_segment(aes(xend = x + vx/4, yend = y + vy/4),
               arrow = arrow(length = unit(0.1, "cm")),
               color = 'green') +
  geom_segment(aes(xend = x + ax/16, yend = y + ay/16),
               arrow = arrow(length = unit(0.1, "cm")), 
               color = 'red', linewidth = 0.2) +
  geom_point(x = 0, y = 0)