Question

the propeller of a world war ii fighter plane is 2.1 m in diameter. show answer no attempt 33% part (a) what is its angular velocity in radians per second if it spins at 1220 rev/min?

Answer 1

The angular velocity of the propeller is approximately
`\(127.34 \, \text{rad/s}\).`

To find the angular velocity
`(\(\omega\))`in radians per second, you can use the formula:

`\[ \omega = \frac{2\pi * \text{revolutions}}{\text{time}} \]`

Given that the propeller spins at 1220 revolutions per minute, you can plug in the values:

`\[ \omega = \frac{2\pi * 1220 \text{ rev/min}}{1 \text{ min}} \]`

Now, you need to convert minutes to seconds because there are 60 seconds in a minute:

`\[ \omega = \frac{2\pi * 1220 \text{ rev}}{1 \text{ min}} * \frac{1 \text{ min}}{60 \text{ s}} \]`

Simplify the expression:

`\[ \omega = (2\pi * 1220)/(60) \text{ rad/s} \]`

Now, calculate the value:

`\[ \omega = (2 * 3.1416 * 1220)/(60) \]`

`\[ \omega \approx (7640.48)/(60) \]`

`\[ \omega \approx 127.34 \, \text{rad/s} \]`

So, the angular velocity of the propeller is approximately
`\(127.34 \, \text{rad/s}\).`