Finding tangential and normal components of acceleration

[burt]

I am working on a problem involving finding the tangential and normal components of acceleration. This particular problem asks to find the tangential and normal components of acceleration for the function \(r(t)=<\cos(2t),\sin(2t)>\) at \(t=0\) and \(t=1\).
The attached picture is my work. My problem is that my twon components don't change based on the value of t - they are both fixed.

Is this correct? Where am I messing up?
Thank you!

 

[Cubist]

I can't (personally) verify the individual steps of your work but your final result looks good to me. This is circular motion at a constant angular speed therefore I'd expect no tangential acceleration, and there should be a constant "inward" acceleration of v^2/r where v is the angular velocity in radians per second and r is the radius. (Search for "circular motion acceleration").

 

[burt]

I can't (personally) verify the individual steps of your work but your final result looks good to me. This is circular motion at a constant angular speed therefore I'd expect no tangential acceleration, and there should be a constant "inward" acceleration of v^2/r where v is the angular velocity in radians per second and r is the radius. (Search for "circular motion acceleration").

Thanks, that answers my question! I see now why the numbers are constant!