Computing the normal scalar component of acceleration

[Han_Cholo]

Hi, I have this math problem where I need to find the scalar component of acceleration at a given time under certain conditions. Usually these problems aren't bad for me, but this one has left me scratching my head.

Its giving me ||a|| = 4 and (a_T)(T) = 5i +5j -k

I have the formula a_N = (||a||²-a_T²)^1/2

that I think I can use, and I also have a=a_TT + a_NN that I also think I can use, but whichever one I try I have failed.

I'm liking the first equation more, but I don't know how to get a_T from a_TT

Any hints to push me in the right direction?

 

[Simon Bridge]

Well, "the scalar component of acceleration" would be it's magnitude - though it would not normally be considered a component.
A component is usually the amount the vector points in a particular direction.

You seem to want to know the magnitude of the component of the acceleration that is normal to something.
What is it normal to? You can be normal to a curve, to a surface... It looks like you have a tangential acceleration (tangent to what?) ... in general you cannot get components in other directions without more information than supplied here.

You have a bunch of formulas you do not know how to use - I cannot tell you because I don't know the context of the problem.
Please provide the problem statement as you received it.

 

[Han_Cholo]

Well, "the scalar component of acceleration" would be it's magnitude - though it would not normally be considered a component.
A component is usually the amount the vector points in a particular direction.

You seem to want to know the magnitude of the component of the acceleration that is normal to something.
What is it normal to? You can be normal to a curve, to a surface... It looks like you have a tangential acceleration (tangent to what?) ... in general you cannot get components in other directions without more information than supplied here.

You have a bunch of formulas you do not know how to use - I cannot tell you because I don't know the context of the problem.
Please provide the problem statement as you received it.

I figured it out! I had to normalize a_TT and realized T=1, so then I just had to plug that value into the a_N equation along with the other given value. Thanks for responding anyways!

 

[Simon Bridge]

OK Well done.

In future, you will get better assistance if you supply the context too.
This is why the standard template asks for the problem statement ... I know typing it out can be a pain but it saves trouble overall.