During an acceleration, the angular speed of an engine increases from 900 rpm to 2800 rpm in 4.5 s. What is the average angular acceleration of the engine?
average a = (final velocity-initial v)/time elaspsed
= (2800rpm/900rpm)/4.5s
To find the average angular acceleration of the engine, we can use the formula:
Angular acceleration (α) = (final angular speed - initial angular speed) / time
Given:
Initial angular speed (ω1) = 900 rpm
Final angular speed (ω2) = 2800 rpm
Time (t) = 4.5 s
Let's plug in the values into the formula:
Angular acceleration (α) = (2800 rpm - 900 rpm) / 4.5 s
Now, let's calculate the angular acceleration:
Angular acceleration (α) = 1900 rpm / 4.5 s
To simplify the units, we need to convert rpm (revolutions per minute) to radians per second (radian/s) since the unit of angular acceleration is radian/s^2:
1 revolution = 2π radians
1 minute = 60 seconds
So, to convert rpm to radian/s, we can use the conversion factor:
1 rpm = (2π radians / 1 revolution) * (1 revolution / 60 seconds)
Now, let's substitute the conversion factor:
Angular acceleration (α) = (1900 rpm / 4.5 s) * [(2π radians / 1 revolution) * (1 revolution / 60 seconds)]
Angular acceleration (α) = (1900 / 4.5) * (2π / 60) radians/s^2
Angular acceleration (α) ≈ 167.55 radians/s^2
Therefore, the average angular acceleration of the engine is approximately 167.55 radians/s^2.