Question

If the angular displacement made by a rotating wheel in 10 s is $150\pi$ radian, then the number of revolutions made by it is:

• A. 75
• B. 100
• C. 300
• D. 150
• E. 50

Hint:

To convert radians to revolutions, divide by $2\pi$. Time is irrelevant unless you are calculating frequency or angular velocity.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem requires converting an angular displacement given in radians to the number of revolutions. A revolution is a full circle.
Step 2: Key Formula or Approach:
The conversion factor between revolutions and radians is based on the fact that one full revolution corresponds to an angle of \( 2\pi \) radians. \[ 1 \text{ revolution} = 2\pi \text{ radians} \] Therefore, to convert from radians to revolutions, we divide the total angle in radians by \( 2\pi \). \[ \text{Number of revolutions} = \frac{\text{Total angular displacement in radians}}{2\pi} \] Step 3: Detailed Explanation:
We are given: - Total angular displacement, \( \Delta\theta = 150\pi \text{ radians} \) - The time taken (10 s) is not needed to find the number of revolutions. Using the conversion formula: \[ \text{Number of revolutions} = \frac{150\pi}{2\pi} \] Cancel the \( \pi \) from the numerator and denominator: \[ \text{Number of revolutions} = \frac{150}{2} = 75 \] Step 4: Final Answer:
The number of revolutions made by the wheel is 75.