Angular acceleration question with spring and damper

1. Oct 6, 2004

ddd61

Hello everyone!!

I need to solve the angular acceleration on a sunglass bin on an over head console of a car.
The sunglass bin rotates open.
It has a torsional spring and gravity that forces it to open and a small rotary damper that slows it down. There is a gear on the sunglass bin and on the over head bin there is rotary damper which is a gear (with a Torque of .18 N*cm at 25 RPM) and reduces the speed of the sunglass bin as it opens.

I would greatly appreciate if anyone could assist me in solving this problem.
Thank you!

2. Oct 6, 2004

NateTG

This seems like a rather straightforward problem. You should just be able to add up the torques, and divide by the moment of inertia.

3. Oct 6, 2004

ddd61

Torque for torsional spring = k*(change in angular position)
Torque for torsional damper = b*(change in angular velocity)
Does this look right?
How would you solve for the angular velocity?
Also, doesn't the angular acceleration change with time? So wouldn't the net torque / moment of inertia equation not work?
Correct me if I'm wrong.

4. Oct 6, 2004

NateTG

Well, now you're changing your mind about what you want to know. I don't think you have all of the equations just right, but I don't have the same problem in front of me.

The instantaneous net torque should still follow the described equation.

5. Oct 6, 2004

ddd61

Which equations do not look right to you?

6. Oct 6, 2004

NateTG

Torque for torsional damper = b*(change in angular velocity)

The torque for the damper should probably be constant.

7. Oct 7, 2004

ddd61

Once again, thank you for your continuous help!

8. Oct 11, 2004

ddd61

One more thing, what if you want to solve for time.
Would you use Conservation of energy? And add in the damper and spring forces?

Thanks again!

9. Oct 11, 2004

NateTG

Conservation of energy gets tricky if friction is involved. Unless you want to account for heat, conservation of energy isn't going to work well for you. If you really want to use conservation of energy, you could account for the work done by the damper seperately.

10. Oct 11, 2004

ddd61

What do you suggest to use to solve for time?

11. Oct 11, 2004

NateTG

Generating equations of motion for things like this can be quite tricky. You could certainly try using energy, but you'll end up with the same position dependance -> time dependance problem that involves differential equations.

Perhaps there is some larger context for this?

12. Oct 11, 2004

ddd61

Not really.

I was given a project in physics to model a sunglass bin opening.
I took Differential equations so I should be able to do this...I think.
How would you suggest to model this with ODE?

Thanks!

13. Oct 11, 2004

NateTG

Well, it should be easy to calculate the net torque as a function of position, and go from there.

i.e.
$$\frac{dp}{dt}=\frac{\tau_{net}(p)}{I}$$

14. Oct 11, 2004

ddd61

Shouldn't that be the second derivative?

15. Oct 11, 2004

NateTG

Yeah. My bad. I need to get more sleep, or more cafeine.

16. Oct 11, 2004

ddd61

Well, thank you for your contiuous help!