Solving Angular Kinematics: Swing Bridge Turned in 120 secs

[MMCS]

A swing bridge has to be turned through a right angle in 120 seconds. The first 50.4 seconds is a period of uniform angular acceleration ; the subsequent 34.8 seconds is a period of uniform angular velocity and the third period of 34.8 seconds is a period of uniform angular retardation. Input your answers to five decimal places when appropriate, and find

the angular displacement that occurred during time period two, (0%) rads
the angular displacement in time period three
the angular acceleration of the bridge , (0%) rads/sec2
the maximum angular velocity (0%) rads/sec
the retardation

Answers:0.706±0.05 rads, 0.353±0.05 rads, 4E-4±1E-4 rads/sec2,0.0202±0.01 rads/sec
-6E-4±1E-4 rads/sec2

Doing some revision and can't work out how to get answers, Tried to write angular displacement in terms of period 2 but can't figure out how to do that

Thanks

 

[haruspex]

If you create unknowns for the two accelerations, what equations can you write down?

 

[MMCS]

I don't know? acceleration1 = angular velocity1 / 50.4
acceleration2 = angular velocity2 / 34.8

??

 

[haruspex]

I don't know? acceleration1 = angular velocity1 / 50.4
acceleration2 = angular velocity2 / 34.8

??

OK, but what do you mean by the unknowns angular velocity1 and angular velocity 2? (Aren't they the same value?) And acceleration2 should be negative, agreed?
How about some equation relating acceleration, time and angular distance? You are probably familiar with such for uniform linear acceleration. Well, it's just the same for uniform angular acceleration, but now 'distance' means an angle.

 

[MMCS]

i can't work this out, if the angular velocitys are the same should i be using then acceleration1 - acceleration2 / 15.6 s? because that would give me two unknowns when used in the acceleration, time and angular distance formula. as you can tell I am new to this type of problem,

Thanks for your help

 

[HallsofIvy]

Was there a reason you chose NOT to use the standard format? In particular the "relevant equations" section would have told us if you know the basic equations.

You should know that for a constant acceleration, velocity equals acceleration times time so it should be easy to determine the velocity of the bridge at the end of that first period. A little bit more complicated, but you are certainly expected know it by the person who gave you this problem is that, with constant acceleration, a, with initial speed v0, the distance traveled is (1/2)at^2+ v0t. Those are the equations you need to solve this problem.

 

[MMCS]

Coping the formulas from a textbook and inputting values is no problem, neither is understanding their use. I am having trouble rearranging any formula algebraically to give me anything with less than 2 unknowns. with the formula (1/2)at^2+ v0t the angular displacement and accelerration are both uknowns.

 

[haruspex]

You have a known duration of unknown acceleration to reach an unknown angular velocity: one equation, 2 unknowns.
You can also write down the angle travelled: 1 more equation, one more unknown.
You then have a second known duration. One more equation, one more unknown (the angle traveled in this phase)
Finally, a known period of unknown deceleration to get back to rest. As with the acceleration phase, two equations, but only two more unknowns.
Adding up the angular distances, one more equation, no more unknowns.
You now have an equal number of equations and unknowns, so a solution should be possible.
Please write out all the equations and show your attempt at solving them.

 

[MMCS]

period 1

angular velocity 2 = 0 + ang acceleration * 50.4
angular displacement = 0.5*acceleration*50.4^2

period 2

angular velocity = angular displacemnt/34.8

period 3

angular displacement = angular velocity1 * 34.8 + 0.5*acceleration*34.8^2

ang displacement 1+2+3 = 1.5708 rads

 

[haruspex]

period 1

angular velocity 2 = 0 + ang acceleration * 50.4
angular displacement = 0.5*acceleration*50.4^2

period 2

angular velocity = angular displacemnt/34.8

period 3

angular displacement = angular velocity1 * 34.8 + 0.5*acceleration*34.8^2

ang displacement 1+2+3 = 1.5708 rads

OK, now turn that into equations using normal style variable notation. That will help remove ambiguities I see above. And you're missing one equation (from the fact that it finishes at rest). The see what you can do in terms of solving the equations.

 

[MMCS]

come on your speaking in cryptic clues to me here. Its common sense getting up to this point, i need help getting an equation with one unknown in and ill be sorted then. From the point I am at now i don't know how to do that. even an example on how to use one of these equations to solve another would be a help.

Thanks

 

[haruspex]

come on your speaking in cryptic clues to me here. Its common sense getting up to this point, i need help getting an equation with one unknown in and ill be sorted then. From the point I am at now i don't know how to do that. even an example on how to use one of these equations to solve another would be a help.

Thanks

My job is to lead you through it, one step at a time if necessary.
Please do as I ask wrt writing out the equations. I need to make sure you have the right number of unknowns.
The missing equation is the one that says the system finishes at rest. I'm sure you can figure out what I mean from that.
Once we've got to there, I'll show you how to start eliminating variables.