Question concerning rotation etc

[JamesL]

Heres the question:

As a result of friction, the angular speed of a wheel changes with time according to the following equation :

angular speed = (initial speed)*e^(-phi*time)

where phi is some unknown constant.

The angular speed changes from an initial speed of 4.86 rad/s to 3.76 rad/s in 7.17 seconds.

Hint: use this information to determine the initial speed and phi.

Determine the magnitude of the angular acceleration after 2.19 seconds.

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Heres how i tried to do it.

using the equation given, i said:
3.76 = 4.86*e^(-phi * 7.17)... and got phi = .035791

Then using the equation again, i got the angular speed after 2.19 s as 4.4936 rad/s.

So i tried to determine the magnitude of the acceleration by saying :
4.4936 = 4.86 + (angular accel)*(2.19)

and so getting .167306 as the angular acceleration...

However, my online homework submission site told me this was wrong. I am not sure where i went wrong. The only thing i can think of is that, possibly, 4.86 is not the right value for the initial velocity (only thought of this bc of the hint given in the problem.. It says to use the above info to find the initial speed, but it is given to you in plain english?)... but i don't really know..

Anybody want to try to help out?

 

[cookiemonster]

You'd have more luck by simply differentiating the angular speed.

$$\frac{d\omega}{dt} = \alpha$$

cookiemonster

 

[JamesL]

Originally posted by cookiemonster
You'd have more luck by simply differentiating the angular speed.

$$\frac{d\omega}{dt} = \alpha$$

cookiemonster

I appreciate the response... could you elaborate a bit on how to do that?

 

[JamesL]

nevermind. i got it. thanks for the help again.