Question

The blades of an airplane are rotating at the rate of $600$ revolutions per minute, the angular velocity of the blades is

• A. $\mathrm{\pi }{\mathrm{rads}}^{-1}$
• B. $2\pi {\mathrm{rads}}^{-1}$
• C. $10\pi {\mathrm{rads}}^{-1}$
• D. $20\pi {\mathrm{rads}}^{-1}$

Answer 1

The correct option is D

$20\pi {\mathrm{rads}}^{-1}$

Step 1: Given data

The blades of an airplane are rotating at the rate of $600rpm$

Step 2: Formula Used

Angular velocity,

$\omega =\frac{∆\theta }{∆t}$

where $∆\theta$ is the change in angular rotation and $∆t$ is the change in time

Step 3: Solution

The angle covered in $1$ revolution $=2\mathrm{\pi }$
Angle covered in $600$ revolutions, $∆\theta =600\times 2\mathrm{\pi }=1200\mathrm{\pi }$
Time taken, $∆t=1min=60s$

Angular velocity,

$$\begin{gathered} \omega =\frac{∆\theta }{∆t} \\ \Rightarrow \omega =\frac{1200\mathrm{\pi }}{60} \\ \Rightarrow \omega =20\mathrm{\pi }{\mathrm{rads}}^{-1} \end{gathered}$$
Therefore, the angular velocity of the blades is $20\pi {\mathrm{rads}}^{-1}$

Hence, option D is correct.