Question

The Simpson method for angular speed is not radians per second.
It is degrees per second: ωD=r⋅D (ωD is known as Doh-mega).
In order to communicate effectively with his coworkers, Homer needs to
convert from Doh-mega to ω and from ω to Doh-mega.
(a) Write a formula to convert measurements in degrees per second (ωD) to
radians per second (ω).
(b) Write a formula to convert measurements in radians per second (ω) to
degrees per second (ωD).

Answer 1

Task:

The Simpson method for angular speed is not radians per second.

It is degrees per second: $\omega D = r \cdot D$ ($\omega D$ is known as Doh-mega).

In order to communicate effectively with his coworkers, Homer needs to convert from Doh-mega to $\omega$ and from $\omega$ to Doh-mega.

(a) Write a formula to convert measurements in degrees per second ($\omega D$) to radians per second ($\omega$).

(b) Write a formula to convert measurements in radians per second ($\omega$) to degrees per second ($\omega D$).

Solution:

We know that a straight angle is 180 degrees and it has a measure of $\pi$ radians. Therefore $180{}^{\circ} = \pi$ radians. Hence we get $1 rad = \left(\frac{180}{\pi}\right){}^{\circ}$, and $1{}^{\circ} = \left(\frac{\pi}{180}\right) rad$.

Based on the above relations, we get:

(a)

$$\omega = \omega D \cdot \left(\frac{\pi}{180}\right) rad = \left(\frac{\pi \cdot \omega D}{180}\right) rad \approx (0.0174 \cdot \omega D) rad$$

(b)

$$\omega D = \omega \cdot \left(\frac{180}{\pi}\right){}^{\circ} = \left(\frac{180 \cdot \omega}{\pi}\right){}^{\circ} \approx (57.325 \cdot \omega){}^{\circ}$$

Answer: (a) $(0.0174 \cdot \omega D)$ and (b) $(57.325 \cdot \omega)$.