Question

The unit of angular velocity is: ____.

• A. m min
• B. rad s
• C. revolutions min
• D. all of these

Hint:

To convert from RPM ($N$) to rad/s ($\omega$), use the formula: $\omega = \frac{2\pi N}{60}$. This is a very common calculation in mechanical and electrical engineering.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Angular velocity ($\omega$) measures the rate of change of angular displacement of an object as it rotates around a center or axis. It describes "how fast" something is spinning. The unit of angular velocity depends on the unit of angular displacement and time.

Step 2: Key Formula or Approach:
Angular velocity is given by: \[ \omega = \frac{\Delta \theta}{\Delta t} \] where $\Delta \theta$ is the angular displacement and $\Delta t$ is the time interval.

Step 3: Detailed Explanation:
Angular displacement $\theta$ is measured in radians (rad), which is a dimensionless quantity. Time $t$ is measured in seconds (s) in the SI system. Therefore, the unit of angular velocity is: \[ \text{Unit of } \omega = \frac{\text{rad}}{\text{s}} = \text{rad/s} \] Alternatively, angular displacement can also be measured in revolutions (rev), where $1 \text{ rev} = 2\pi \text{ rad}$. If time is measured in minutes (min), then the unit becomes revolutions per minute (RPM or rev/min). Thus: \[ 1 \text{ RPM} = \frac{2\pi \text{ rad}}{60 \text{ s}} = \frac{\pi}{30} \text{ rad/s} \] Since both rad/s and RPM are valid units for angular velocity, and given that an option includes "all of these," it implies that all listed units are correct representations of angular velocity in different contexts.

Step 4: Final Answer:
The units of angular velocity include rad/s, RPM, and others.