Angular acceleration question with spring and damper

[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!

 

[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.

 

[ddd61]

Thanks for the quick reply.

Torque for torsional spring = k*(change in angular position)
Torque for torsional damper = b*(change in angular velocity)
Torque for mass = Weight*radius
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.

Thank you for your assistance!

 

[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.

 

[ddd61]

Which equations do not look right to you?

Thanks for your continuous help!

 

[NateTG]

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

The torque for the damper should probably be constant.

 

[ddd61]

Once again, thank you for your continuous help!

 

[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!

 

[NateTG]

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?

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 separately.

 

[ddd61]

What do you suggest to use to solve for time?

Thanks for your contiuous help.

 

[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 dependence -> time dependence problem that involves differential equations.

Perhaps there is some larger context for this?

 

[ddd61]

Perhaps there is some larger context for this?

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!

 

[NateTG]

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?

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

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

 

[ddd61]

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

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

Shouldn't that be the second derivative?

 

[NateTG]

Shouldn't that be the second derivative?

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

 

[ddd61]

Well, thank you for your contiuous help!