Question

What is the difference between $rad\,{{s}^{-2}}$ and $rp{{s}^{2}}$?

Answer 1

Hint: The given units are radians per second square and $rp{{s}^{2}}$. This means that they are units representing physical quantities in rotational motion which is analogous to translational motion. Comparing the analogous units, we can determine which physical quantities are represented by the given units.

Complete answer:
Every body possesses two major types of motion; translational motion in straight line and rotational motion in a circle.
Rotational motion is a type of periodic motion wherein every particle in a body moves in a circle with the centre being at the rotation of the axis.
The rotational and translational motions are analogous to each other.
Radian is the unit of angle covered in a circular motion. It is the SI unit of angular displacement while seconds is the SI unit of time. $rad\,{{s}^{-2}}$ in circular motion is analogous to $m{{s}^{-2}}$ in translational motion which is the SI unit of acceleration. Therefore, we can say that $rad\,{{s}^{-2}}$ is a unit of angular acceleration.
Angular acceleration is the rate of change of angular velocity.
Similarly, $rp{{s}^{2}}$ is also a unit of angular acceleration. The relation between $rad\,{{s}^{-2}}$ and $rp{{s}^{2}}$ is given by-
$rp{{s}^{2}}=2\pi \,rad\,{{s}^{-2}}$
Therefore, the relation between both units is that $rad\,{{s}^{-2}}$ and $rp{{s}^{2}}$ are the units of angular acceleration.

Note: A rotational axis is an imaginary axis which passes through the point around which a rigid body is rotating. Angular displacement and angular acceleration are vector quantities as their analogous quantities in translational motion. The SI system is a system of units and measurements with an official status in almost all countries of the world.