Question

What is the relation between $\mathrm{rad}/{\mathrm{s}}^2$ and ${\mathrm{rps}}^2$?

Answer 1

Step 1: Definition

1. The angular acceleration of a circularly moving object has been defined as the amount at which its angular velocity varies with time.
2. The S.I unit of angular acceleration is $\mathrm{radians}\mathrm{per}\mathrm{second}\mathrm{square}(\mathrm{rad}/{\mathrm{s}}^2)$.

Step 2: Finding the relation between $\mathrm{rad}/{\mathrm{s}}^2$ and ${\mathrm{rps}}^2$

As we know, both $\mathrm{rad}/{\mathrm{s}}^2$ and ${\mathrm{rps}}^2$ are the units of angular acceleration.

then,

$1{\mathrm{rps}}^2=2\mathrm{\pi }\mathrm{rad}/{\mathrm{s}}^2$

Therefore, the relation between $\mathrm{rad}/{\mathrm{s}}^2$ and ${\mathrm{rps}}^2$ is $1{\mathrm{rps}}^2=2\mathrm{\pi }\mathrm{rad}/{\mathrm{s}}^2$.