Question

An airplane propeller rotates with an angular speed of 260 rad/s though what angul does the propeller rotate in 5.0s? Give your answer in both radians and degrees

Answer 1

Answer:

1300 rad ($74522^{\circ}$)

Explanation:

The angular speed of an object is the rate of change of angular position.

It is given by:

$\omega=\frac{\theta}{t}$

where

$\omega$ is the angular speed

$\theta$ is the angular displacement of the object

t is the time elapsed

For the propeller rotating in this problem, we have

$\omega=260 rad/s$ is the angular speed

t = 5.0 s is the time elapsed

Therefore, the angular displacement is:

$\theta=\omega t=(260)(5.0)=1300 rad$

And since $2\pi rad = 360^{\circ}$, the angle in degrees is

$\theta=\frac{1300}{2\pi}(360)=74522^{\circ}$