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:0.318 revolutions

Step-by-step 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+(\alpha t^2)/(2)`

`\theta =0+(1* 2^2)/(2)`

`\theta =2 rad`

To get revolution
`(\theta )/(2\pi )`

=
`(2)/(2\pi)=0.318\ revolutions`

Answer 2

Answer: The propeller has rotated 5 revolutions

Step-by-step explanation:

Number of revolutions = angular velocity/ time

Given:

Angular velocity=10rad/s

Time=2seconds

Number of revolutions = 10/2= 5 revolutions.