Question

The angular speed of a flywheel is increased from 600 rpm to 1200 rpm in 10 s. The number of revolutions completed by the flywheel during this time is: ____.

• A. 300
• B. 150
• C. 900
• D. 600

Hint:

Alternatively, use the formula $N = \frac{\theta}{2\pi}$. Calculate $\alpha = (\omega_2 - \omega_1)/t$ and then $\theta = \omega_1 t + \frac{1}{2}\alpha t^2$. However, the "average frequency" method used above is much faster for simple acceleration.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The number of revolutions in a given time can be found by calculating the average angular velocity (in revolutions per unit time) and multiplying by the total time.

Step 2: Key Formula or Approach:
\[ \text{Total Revolutions} = \text{Average frequency} \times \text{time} \] \[ \text{Revolutions} = \left( \frac{n_1 + n_2}{2} \right) \times t \]

Step 3: Detailed Explanation:
Given: $n_1 = 600$ rpm, $n_2 = 1200$ rpm, $t = 10$ s. 1. Convert the frequencies to revolutions per second (rps): - $n_1 = 600/60 = 10$ rps - $n_2 = 1200/60 = 20$ rps 2. Calculate the average frequency: - $n_{avg} = \frac{10 + 20}{2} = 15$ rps 3. Calculate total revolutions in 10 seconds: - $\text{Revolutions} = 15 \text{ rps} \times 10 \text{ s} = 150$

Step 4: Final Answer:
The flywheel completes 150 revolutions.