Chapter 8, Problem 1CQ

Which units would not be appropriate for describing a rotational velocity: rad/min², rev/s, rev/h, m/s? Explain.

To determine

The units which are not be appropriate for describing a rotational velocity.

Answer to Problem 1CQ

$\text{rad}/{\text{min}}^2$, $\text{rev}/\text{h}$ are the units which are not appropriate for describing a rotational velocity.

Explanation of Solution

Given info: The four units are $\text{rad}/{\text{min}}^2,\text{rev}/\text{s, }\text{rev}/\text{h, }\text{m}/\text{s}$.

Write the expression for the rotational displacement.

$\omega =\frac{\Delta \theta }{t}$

Here,

$\omega$ is the angular velocity

$\Delta \theta$ is the change in angular displacement

$t$ is the time

The Rotational velocity is the rotational displacement divided by time.

It is the rate of change of rotational displacement.

$\text{rad}/\text{min}$ is the commonly used unit of the rotational velocity.

The units $\text{rev}/\text{s}$ and $\text{rev}/\text{h}$ are the units that appropriate the rotational velocity.

$\text{rad}/{\text{min}}^2$ is the unit of rotational acceleration and $\text{m}/\text{s}$ is the unit of linear velocity.

Conclusion:

Therefore, $\text{rad}/{\text{min}}^2$ and $\text{m}/\text{s}$ are units which are not appropriate for describing a rotational velocity.