dx/dt = -rsinθ(dθ/dt)
second derivative of x with respect to time t:
d2x/dt2 = -rcosθ(dθ/dt)2−rsinθ(d2θ/dt2)
use calculus chain rule. θ can be differentiated with respect to time.
evaluate the second derivative at θ = 0
d2x/dt2 = -r(dθ/dt)2
dθ/dt is usually called the angular velocity, which is the rate of change of the angle θ. units used is radians/second.
w ≡ dθ/dt.
d2x/dt2 = -rw2
time is "it defines of what the clock reads"
it is also a component quantity of various measurements used to sequence events.