Circular motion. Uniform and accelerating. (Bridge)

[EVriderDK]

Homework Statement

A bridge takes 2 minutes to open up fully from 0 to 80 degrees. The first 20 degrees it is accelerating, and the last 60 degrees it is traveling with even velocity.

I will have to find acceleration for the first 20 degrees and angular velocity for the last 60 degrees.

http://peecee.dk/upload/view/357409 Illustration.

The Attempt at a Solution

I have tried setting up three equations with three unknowns:

http://peecee.dk/upload/view/357410

I have tried isolating a in the first two equations, and then put 1=2. Then isolating ω in this new equation, and replacing this with the ω in the third equation. Then i isolate t, and get 48 second. This gives the correct answer to the acelleration, but i don't know why. Can you help?

Is there other way to do it maybe?

Thank you in advance.

 

[tiny-tim]

Hi EVriderDK!

That looks ok … you eliminated α, then you solved for t, that is the way to do it.

…This gives the correct answer to the acelleration, but i don't know why.

I don't understand. If it solves the equations, isn't that enough justification?

 

[EVriderDK]

Why is it correct to use these three equations. I didn't come up with them my self.
I was just told that this i s the correct way to do it, but i lack the understanding.

 

[tiny-tim]

… I didn't come up with them my self.

ah!

ok, first, are you familiar with the standard constant acceleration equations for ordinary (linear) motion?

 

[EVriderDK]

Yes I'm familiar with all the formulas, i just cannot see, how the person who put them together, knew, that this was the way to do it.

 

[tiny-tim]

if a is constant …​

then dv/dt = a, so ∆v = at

d²x/dt² = a, so ∆x = v_ot + 1/2 at²

a = dv/dt = dv/dx dx/dt = vdv/dx = 1/2 d(v²)/dx, so ∆(v²) = 2as

 

[EVriderDK]

But how did he know, that I had to use these three equations, in that order etc. ?

 

[tiny-tim]

because they're the only three equations …

see the pf library on constant acceleration ​

 

[EVriderDK]

Argh! :D

Let me rephrase.

How to find out how many equations you are going to work with, and what these equations have to contain?

 

[tiny-tim]

it's always obvious which one to use …

it's the one that has the variables you're given, and the variable you want

one has s u a and t

one has u v a and s

one has u v a and t​

 

[EVriderDK]

So because i don't have ω in the first equation, i have to have an equation with ω in it? Because the third equation needs this ω ?