Chapter 8, Problem 1RCQ

What are the units of measurement for tangential speed? For rotational speed?

To determine

Units to measure tangential speed and rotational speed.

Answer to Problem 1RCQ

Solution:

Tangential speed is measure in meter per second, rotational speed is measured in radian per second.

Explanation of Solution

Tangential speed: Tangential speed is defined as the linear distance travelled by an object moving in a circular path per unit time.

Consider the object moving in a circular object.

Figure.1

The linear distance travel by an object in time $\text{Δ}t$ is; therefore, the tangential speed is given as:

$v_{\text{tangential}}=\frac{\text{Δ}s\left(\text{m}\right)}{\text{Δ}t\left(\text{sec}\right)}$

Unit to measure tangential speed is $\text{m/sec}$ .

Rotational speed: Rotational speed is defined as the angle turned by an object in a particular time.

In the given figure, angle turned by the object in time $\text{Δ}t$ is $\text{Δ}\theta$${\omega }_{\text{rotaional}}=\frac{\text{Δ}\theta \left(\text{rad}\right)}{\text{Δ}t\left(\text{sec}\right)}$

; therefore, the rotational speed is given as

Therefore, unit to measure rotational speed is $\text{rad/sec}$ .

Conclusion:

Tangential speed is measure in meter per second, and rotational speed is measured in radian per second.