Question

What is the angular displacement of a wheel that accelerates from rest to 6 rad/s with an angular acceleration of 2 rad/s²?

Answer 1

We have given here,

Initial angular velocity W0 = 0

Final angular velocity W1 = 6 rad/s

Angular acceleration   = 2 rad/ s2

Now from the formula we have ,

W1 = W0 + t

On putting values we will have,

t = W1/ = 6/ 2 = 3sec

Now also we have one more relation as

= W1t + (1/2) (alpha) t^2 = 0+ (1/2)×2×9 =9m

Also we have one more way as,

W1^2 = W0^2 + 2

Where is the required angular displacement

So ,   = 36/ 2×2 = 9 m

Hence required angular displacement is 9 m