Question

The angle through which a rotating wheel has turned in time t is given by \(\theta = 8.5t-15.0t^2+1.6 t^4\) where \(\theta is in radians and t in seconds. . What is the average angular velocity , and the average angular acceleration between t =2.0s and t =3.0s?
Please, help

Answer 1

I have to find out \(\theta_3~~and~~\theta2\) then apply formula \(\bar\omega=\dfrac{\theta_3-\theta_2}{dt}\) to find out the average angular velocity.
My question is why cannot I use \(\bar\omega = \dfrac{\omega_3-\omega2}{2}\).

Answer 2

Usually, when you find an average of two numbers you add them and divide by 2, is that what you meant @Loser66 ?

Like this?
$$
\overline \omega=\cfrac{\omega_3+\omega_2}{2}
$$

Answer 3

yes

Answer 4

They should be equal.

Answer 5

If it is a continuous function with no discontinuities that go to infinity like this:
Using the calculus technique, you would find that in my sketch, the average would be positive infinity.
So it appears that you can use (a+b)/2 for averages if there are no vertical asymptotes.