Question

Part complete the angular acceleration of a wheel is given in rad/s2 by 46 t 3 - 11t 4, where t is in seconds. if the wheel starts from rest at t = 0.00 s, when is the next time the wheel is at rest?

Answer 1

Angular acceleration is given by

$\alpha = 46 t^3 - 11t^4[\tex]we can write it as[tex]\frac{dw}{dt} = 46 t^3 - 11 t^4$

integrating both sides we will have

$w - 0 = 11.5 t^4 - 2.2 t^5$

now if final angular speed is again ZERO

$0 = 11.5 t^4 - 2.2 t^5$

$t = 5.23 s$

So it will be at rest after 5.23 s