# Point on Spinning Circle

See image.

## Homework Equations

ωx (ωx r) = anormal
αx r =atangent

x=rcos*theta
y=-rsin*theta

## The Attempt at a Solution

I also got the correct answer using the cross products. My problem is I am trying to do this problem in rectangular coordinates (I really like rectangular), but I am doing something wrong and I cannot see it.

So, I assume r is constant:

BUT, y'' is giving me a headache:
I keep getting rsin(45)[ω^2-α] and I get = 15.66 and NOT the right answer of 7.07 in/s. There is a lurking negative sign and I cannot find it. That - should be a + and then I get a correct answer. Am I just deriving incorrectly?

Thanks!!
And apologizes if this is pretty novice: its from my Junior-level engineering class...or a freshman Physics class. ;p

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jedishrfu
Mentor
from the problem you know that va = 8 in/sec and aa=6 in/sec/sec

and you know that va is tangent to the circle and that aa is along the radius

so the unit vector for aa=cos (theta) i + sin(theta) j

and the unit vector for va = - sin(theta) i + cos(theta) j

now figure out theta and factor in the vector magnitudes into the unit vector equations to get the vector equations of motion.

Lastly, if you do unit vector va dot aa = -sin(theta) cos(theta) + cos(theta) sin(theta) = 0 meaning they are perpendicular as a check

That make's sense. Shouldn't I be able to use y=-rsin*theta to kind of derive that? Everything you said makes perfect sense (I do like the dotting notion!), but I am still wondering why rectangular equation has issues.

jedishrfu
Mentor
you should be able to start with s(x,y) and then diferentiate to get va
and differentiate again to aa.

s(x,y) = R*cos(w*t + offset)) i + R*sin(w*t + offset) j

make sure you're using radian measure for all angle values that could be where your problem lies.