A uniformly accelerated wheel reaches the angular velocity ω = 20 rad/s in 10 revolutions after rotation begins. Determine the angular acceleration of the wheel.

Solution

Here, we have
Initial angular velocity, $straight omega subscript straight o space equals space 0 space rad divided by straight s$
Velocity attained after some time, $space straight omega equals 20 space rad divided by straight s$
$No. space of space revolutions space taken comma space straight theta space equals space 10 space rev space equals space 20 straight pi space rad$
Now, using the formula,
$straight omega squared minus straight omega subscript straight o superscript 2 equals 2 αθ$
$rightwards double arrow$ $straight alpha equals fraction numerator straight omega squared minus straight omega subscript straight o superscript 2 over denominator 2 straight theta end fraction$
∴ $space space space space space straight alpha equals fraction numerator left parenthesis 20 right parenthesis squared minus left parenthesis 0 right parenthesis squared over denominator 2 cross times 20 straight pi end fraction$
$equals 10 over straight pi equals 3.18 space rad divided by straight s squared$ , is the angular acceleration of the wheel.