I have a problem concerning the weight of a cylinder. I have a cylinder with a "hub" in the middle that is difficult to measure. As such, I want to take the hub out of the equation so the diameter or radius of the hub doesn't have to be factored in. Here is what I have done so far.
((R1+R3)^2*P)-((R2+R3)^2*P)=W where R1 is the radius from the hub to the outside of the cylinder, R2 is the radius from the hub to the inside of the cylinder, R3 is the radius of the hub, P is equal to pi*density*length of the cylinder, and W is the weight. I have derived as follows so far:
((R1^2+R1*R3+R3^2)*P)-((R2^2+R2*R3+R3^2)*P)=W
P(R1^2+R1R3-R2^2-R2R3)=W
P(R1^2-R2^2+R1R3-R2R3)=W
P(R1^2-R2^2+R3(R1-R2)=W
I am at a loss as to how to remove R3 from the equation so that no longer has to be measured. Am I missing something? Is this possible? Thank you for your time and help.
((R1+R3)^2*P)-((R2+R3)^2*P)=W where R1 is the radius from the hub to the outside of the cylinder, R2 is the radius from the hub to the inside of the cylinder, R3 is the radius of the hub, P is equal to pi*density*length of the cylinder, and W is the weight. I have derived as follows so far:
((R1^2+R1*R3+R3^2)*P)-((R2^2+R2*R3+R3^2)*P)=W
P(R1^2+R1R3-R2^2-R2R3)=W
P(R1^2-R2^2+R1R3-R2R3)=W
P(R1^2-R2^2+R3(R1-R2)=W
I am at a loss as to how to remove R3 from the equation so that no longer has to be measured. Am I missing something? Is this possible? Thank you for your time and help.