Rotating wheel initial angular velocity given final and time

[vinnyzwrx]

Homework Statement

A rotation wheel required 3.0 s to complete 37 revolutions. its angular speed at the end of the 3.0 s interval is 98 rad/s. what was the original angular speed of the wheel?

Homework Equations

average omega = change in angle/change in time

The Attempt at a Solution

heres my thought on the answer, i wanted to make sure its right since i don't have the correct answer to compare my thoughts

i find the average angular velocity by 37*2pi over 3
since the acceleration is constant the average angular velocity is at 1.5 s
so then i find the difference between final angular velocity which is at 3 seconds and the velocity at 1.5 seconds which is 20.51 and subtract that from the average angular velocity to get the angular velocity at 0 seconds.

the final answer is 56.89 since the velocity at 1.5 seconds is 77.49

is this thought process correct, it seems to be from my point of view.

 

[fyzikapan]

That works (though you should check your final answer, it looks like you have a couple digits flipped around.

You can also do this with

$$\omega_f^2 = \omega_i^2 + 2 \alpha \Delta \theta$$
and
$$\alpha = \frac{\omega_f - \omega_i}{\Delta t}$$

I think your way is probably simpler, but requires breaking the problem into two steps. However, you do avoid having to solve a quadratic equation.

 

[vinnyzwrx]

right, 56.98 rad/s

Thanks!