I am teaching myself basic mechanics from a standing start. I am trying to understand Angular Acceleration and have set myself a problem to solve. My answer 'feels' wrong, so I'd like some help to understand if I've misunderstood, or miscalculated anything. I've taken many liberties with rounding, please ignore, this is more about the basic process/theory than accuracy. Thanks in advance!!
Problem
An object is travelling around a circle with a radius of 40m. It's speed at (A) is calculated as 50mph. 5 seconds later, it's speed at (B) is calculated as 40mph. Determine the Angular Acceleration.
Basic conversions
Circumference = $2\pi r = 251\text{ m}$
Velocity (A) = $22\text{ m/s}$
Velocity (B) = $18\text{ m/s}$
Angular Velocity at (A)
251 / 22 = 11.4. Therefore one full revolution would take 11.4 seconds.
$$\omega = \theta/t$$
$$\omega = 2\pi /t$$
$$\omega = 2\pi/11.4$$
$$\omega = 0.55 \text{ rad/s}$$
Angular Velocity at (B)
$251/18 = 13.9$. Therefore one full revolution would take $13.9$ seconds.
$$\omega = \theta/t$$
$$\omega = 2\pi /t$$
$$\omega = 2\pi/13.9$$
$$\omega = 0.45\text{ rad/s}$$
Angular Acceleration
$$\alpha = \frac{d\omega}{dt} $$
$$\alpha = \frac{0.45 - 0.55}{5 - 0}$$
$$\alpha = -0.1 / 5$$
Answer to Problem
$\alpha = -0.02\text{ }\mathrm{rad/s^2}$