What is the Magnitude of Total Acceleration at Point A?

[smashbrohamme]

Ok you have a disk that is originally rotating at a Wo=6rad/s. The Angular acceleration=4rad/s². Determine the magnitude of the total acceleration (combinaton of An and At) at point A just after 2 revolutions.

The Circle is a 2ft Diameter circle with point A being 1.5ft distance from the center.

Ok first in order to use the total acceleration equations which is An=W²r and At=*angularacceleration*r

you have to find the final angular velocity of this disk.

so you would use the equation W²=Wo²+2(4)(2pie*2) I converted to revolutions using 2pie.

that would give me a W=11.68.

Now that I have a W of the whole wheel, I can simple use the An,At formulas to find the true acceleration at POINT A.

An=(11.68)²*1.5= 204.6 r=1.5 is simply the distance from the center of POINT A right?
At=(4)(1.5)=6 same deal, R is simply 1.5 since it is the distance from the center, or distance of contact with POINT A.

Now you just simply do 204.6²+6²= and square root the answer...

I am making sure I am doing this correctly. Please verify if this is the correct way.

 

[gneill]

Looks like you're doing fine. And yes, you add the two accelerations in quadrature, because they are right-angle components of the total acceleration.