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## Main Question or Discussion Point

Hi guys

Have lurked the forums for a while but this is my first contribution. I am in first year physics at uni and I was having a discussion with my tutor regarding the relative error for an experiment (circular motion / moment of inertia). (I tried searching for an answer to this with no luck)

The relative error for the radius of a wheel needs to be calculated as part of the experiment.

The radius was calculated by measuring the diameter of the wheel with verniers and dividing by 2. The smallest division on the verniers is 0.05 mm and for arguments sake the diameter of one of the wheel is 20 mm (there are actually several wheels that need measuring).

I understand relative error to be half the smallest division on the measuring instrument divided by the measured total, units irrelevant provided they are both the same. In the above instance this equates to an error rate of 0.025/20 = 0.125% for the diameter.

Now for the radius my tutor is telling me that you keep the 0.025 (half smallest division on verniers) and divide by the radius which doubles your error to 0.025/10 = 0.25%.

I believe this to be incorrect and that relative error should be the same as for the diameter. My argument for this is that the radius is defined as exactly half of the diameter, and as such exactly half of any absolute error in the diameter should be attributed to the radius. I don't know whether this relative error is best explained by halving the smallest division when you halve the measurement or by leaving the error for the diameter untouched. The other possibility is that I am indeed wrong.

Looking forward to your comments, thanks.

Have lurked the forums for a while but this is my first contribution. I am in first year physics at uni and I was having a discussion with my tutor regarding the relative error for an experiment (circular motion / moment of inertia). (I tried searching for an answer to this with no luck)

The relative error for the radius of a wheel needs to be calculated as part of the experiment.

The radius was calculated by measuring the diameter of the wheel with verniers and dividing by 2. The smallest division on the verniers is 0.05 mm and for arguments sake the diameter of one of the wheel is 20 mm (there are actually several wheels that need measuring).

I understand relative error to be half the smallest division on the measuring instrument divided by the measured total, units irrelevant provided they are both the same. In the above instance this equates to an error rate of 0.025/20 = 0.125% for the diameter.

Now for the radius my tutor is telling me that you keep the 0.025 (half smallest division on verniers) and divide by the radius which doubles your error to 0.025/10 = 0.25%.

I believe this to be incorrect and that relative error should be the same as for the diameter. My argument for this is that the radius is defined as exactly half of the diameter, and as such exactly half of any absolute error in the diameter should be attributed to the radius. I don't know whether this relative error is best explained by halving the smallest division when you halve the measurement or by leaving the error for the diameter untouched. The other possibility is that I am indeed wrong.

Looking forward to your comments, thanks.