Question

During a dynamic test a got this question and I just couldn't solve it.
a wheel starts from rest. the alpha =10 theta^1/3. the radius of the wheel is 0,4m.
What is the omega at 4s.

My approach was:
because I haven't got a time dependant variable I thought to use the (alpha) d(theta) = omega d(omega). But I'm not quit sure how to apply it.

I know how to apply the normal dynamic equivalent a ds = v dv -> a = v*(d/ds(v)). But when I try to apply it with (alpha) d(theta) = omega d(omega). I get omega = (10theta^1/3)*(d(theta)/d(omega)). And that can't work.

Anybody any ideas to tackle

Answer 1

What are the initial values of θ and ω?

Answer 2

What is alpha? Am I right in assuming theta is the angle rotated through since t=0?

Answer 3

@vincent -> it starts at rest so \[\theta=0; \omega=0\]
@cheese3 -> theta is indeed the angle rotated. and alpha is the equivalent of acceleration. Omega is the equivalent of speed.

Answer 4

You wrote : θo = 0 and ωo = 0

Then the answer is pretty simple: your disc never starts to move, because according to you formula, angular acceleration is also zero at the beginning.
So answer for ω at t=4s is zero !

The only point is that it should be an unstable position, because as soon as θ is only slightly off zero then the body will start to move.

Answer 5

I think I finally got it. Could somebody please check. The answer is 12.84 rad/s see attached file for complete solution.