Finding the center of instantanous rotation

[Amaelle]

Homework Statement:

Look at the image

Relevant Equations:

v=w.r

[Mentor Note -- Improved versions of the two pictures are posted in a reply a few posts down]

Good day

and here is the solution

I have a problem in finding the value of AC and BC, I couldn't figure it out?
many thanks in advance!

 

[BvU]

I have a problem in finding the value of AC and BC, I couldn't figure it out?

I don't think your relevant equation is going to help you there. Don't you have anything else in your toolbox ? Something geometrical or trigonometrical, perhaps ? Keep searching !

[edit]ah, from the poor picture I can see they resort to geometry !
Free tip: photograph from above, or better: rendere your own drawing and post !

 

[Amaelle]

thanks a lot for your reply!
it's certainly something geometric but I couldn't figure it out

 

[berkeman]

Here are improved versions of the OP's dark pictures:

 

[BvU]

thanks a lot for your reply!
it's certainly something geometric but I couldn't figure it out

I made a drawing and needed the coordinates of D. From the picture it isn't all that clear but I guess you can check in your book that (180,0) isn't all that bad...
And what about B ?

With that settled, things are obvious, right ?

 

[Amaelle]

not really can you please be more explicit?

 

[BvU]

My post was actually a question:

Can you confirm that O and D are at the same y-coordinate in your book ? And B and D at the same x ?

To become even more explicit:
Long ago, I learned about Pythagoras. The numbers 3,4,5 and 5,12,13 are still hanging around in my head ...

 

[Amaelle]

yes I can confirm that O and D are at the same y-coodinate And B and D at the same x

 

[BvU]

With that settled, things are obvious, right ?

So what is the perpendicular distance from A to BD ?

 

[Amaelle]

60+180=240

 

[BvU]

So do you now see the 3,4,5 and 5,12,13 rectangular triangles ?

 

[Amaelle]

thanks for your prompt reply
so let's consider A' as the projection of A on BD
you are talking about the triangles AA'B and AA'C
we know all the values of the triangle AA'B but we only know one value the length AA' for the triangle AA'C
but I still can't see how can we apply that phytagora theorem (except from finding BA')
thanks a lot!

 

[BvU]

AD is the hypothenuse of a 3,4,5 triangle. So AA'C is also a 3,4,5 triangle

 

[Amaelle]

so, if I understood well, you are talking about a rule of two rectangular triangles one inside the other , you called 3,4,5 and 5, 12 , 13 , I tried to google it and only find something regarding Fibonacci numbers in Pythagorean triples
I would be very grateful if you give me a link to see that rule

many thanks in advance!

 

[BvU]

$$3^2+4^2=5^2$$is known, right ?

Since the two red angles are the same, AA' is the 3 of 3,4,5 in AA'C

 

[Amaelle]

thank you but the attachement does not open!

 

[BvU]

thank you but the attachement does not open!

I re-did it. Should be a picture now. But you have your own picture too, right ?

 

[Amaelle]

thanks a million! it's clear now
best regards!

 

[BvU]

The exercise is very artificial, but I enjoyed helping