A body is whirled in a horizontal circle at the rate of 800 revolutions per minute. Determine the angular velocity

Analysis

To solve this problem, we need to convert the frequency of rotation from "revolutions per minute" (rpm) to "radians per second" (rad/s), which is the standard unit for angular velocity ($\omega$).

Concept

Angular velocity ($\omega$) is defined as the rate of change of angular displacement. The relationship between angular velocity and frequency ($f$) is given by the formula:

Where:

• $f$ is the frequency in revolutions per second (Hz).
• $\omega$ is the angular velocity in radians per second (rad/s).

Step-by-Step Solution

Step 1: Convert revolutions per minute to revolutions per second. The body completes 800 revolutions in 60 seconds (1 minute).

Step 2: Calculate the angular velocity ($\omega$). Using the formula $\omega = 2\pi f$:

Step 3: Round to the appropriate decimal place. Rounding $26.66\pi$ to one decimal place gives $26.7\pi \text{ rad/s}$.

Conclusion

Comparing our result to the given options, we find that $26.7\pi \text{ rad/s}$ matches option D.

Exam Tip

When dealing with rotational motion questions in JAMB, always check your units first! If the question gives you revolutions per minute, divide by 60 to get revolutions per second before multiplying by $2\pi$. If you forget to divide by 60, you will end up with a much larger number that will lead you to the wrong answer.