A flywheel starting from rest acquires the speed of 300 rpm in 20s. What is the angular acceleration of the flywheel? Also find the angular displacement of the flywheel in first 10s.

Solution

Here,
Angular speed, $straight omega space equals space 300 space rpm space equals space 10 space rad divided by straight s$
Initial speed, $straight omega subscript straight o space equals space 0$
Time of travel, t = 20s
By using the relation $space space straight omega equals straight omega subscript straight o plus at comma$ we have
$straight alpha equals fraction numerator straight omega minus straight omega subscript straight o over denominator straight t end fraction$
$rightwards double arrow$ $straight alpha equals fraction numerator 10 straight pi minus 0 over denominator 20 end fraction equals straight pi over 2 space rad divided by straight s$
The angular displacement of flywheel is,
$straight theta equals straight omega subscript straight o straight t plus 1 half αt squared$
Here, we have
$straight omega subscript straight o space equals space 0 comma space space space space straight alpha equals straight pi divided by 2$ and t = 10s
∴ $straight theta equals 1 half straight pi over 2 left parenthesis 10 right parenthesis squared equals 25 straight pi space rad$
$rightwards double arrow$ $space space straight theta space equals space 12.5 space rev$