Angular acceleration from angular velocity

[robothito]

Hello everybody. I would really appreciate some help

Homework Statement

I have some problem where I have measured angular velocity data. This measurements are not equally spaced, meaning there were taken after some (variable) delay passed.

I need to find what is the angular acceleration at each point of measurement.

Homework Equations

ummmm I don't know... perhaps α= Δω/Δt??

The Attempt at a Solution

So I have some measures like

Time(μs)    Speed(rad/s)           Accel(rad/s^2)
------------------------------------------------------------
15115        2.078458          
24184       3.464097                  91.67310552 ??
31238       4.453629
37207        5.263176
42474        5.964667

My question is how to fill the Acceleration values...

I have tried accel=(speed2-speed1)/(time2-time1) (see the 91.67310552)

Is this flawed??

The graphic of the speed show a almost linear increase of speed (until it becomes constant), so by theory this should give a constant acceleration and then 0 right? But my calculations become kind of crazy after a whileand give a zigzag curve after a promising start...

so can anyone check if my ideas are ok?

thanks

 

[andrewkirk]

I have tried accel=(speed2-speed1)/(time2-time1) (see the 91.67310552)

That's a fine way to do it. But you seem to have done the calc wrong. I get 153, not 91.7.
You can calculate four angular acceleration values from your data, and they make a nice smooth progression, with a slight, gradual decline from the original value, which seems realistic.

 

[robothito]

Thank you very much for your reply.
Yeah I realized my calculation mistake. Thanks.
I did the calculations for all the data and I got the following graphs

Well although the speed graphs seems quite nice, the acceleration graphs have some ups and downs. I suppose physical systems are not the same as theory so instead of the square curve I was expecting I got that. Seems close enough I guess..

Thanks again for the help. It is very appreciated. It has been years since I took physics and frankly I remember very few...

 

[haruspex]

Thank you very much for your reply.
Yeah I realized my calculation mistake. Thanks.
I did the calculations for all the data and I got the following graphs
View attachment 97468

Well although the speed graphs seems quite nice, the acceleration graphs have some ups and downs. I suppose physical systems are not the same as theory so instead of the square curve I was expecting I got that. Seems close enough I guess..

Thanks again for the help. It is very appreciated. It has been years since I took physics and frankly I remember very few...

The zigzags suggest rounding error. Can you post the data for that part?