Question

The propeller of an airplane is at rest when the pilot starts the engine; and its angular acceleration is a constant value. Two seconds later, the propeller is rotating at 10rad/s. Through how many revolutions has the propeller rotated through during the first two seconds?

Answer 1

Answer: The propeller has rotated 5 revolutions

Explanation:

Number of revolutions = angular velocity/ time

Given:

Angular velocity=10rad/s

Time=2seconds

Number of revolutions = 10/2= 5 revolutions.

Answer 2

Answer:0.318 revolutions

Explanation:

Given

Initially Propeller is at rest i.e. $\omega _0=0 rad/s$

after $t=10 s$

$\omega =10 rad/s$

using $\omega =\omega _0+\alpha t$

$10=0+\alpha \cdot 10$

$\alpha =1 rad/s^2$

Revolutions turned in 2 s

$\theta =\omega _0t+\frac{\alpha t^2}{2}$

$\theta =0+\frac{1\times 2^2}{2}$

$\theta =2 rad$

To get revolution $\frac{\theta }{2\pi }$

=$\frac{2}{2\pi}=0.318\ revolutions$