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Original Message
Vectors.
Posted by Mark Kelly on October 21, 2012 at 18:17:50:
Skate force equals stylus friction reaction force times the quotient of linear offset and arm length.
Stylus friction reaction force equals the force normal to plane of the contact dimple times the friction coefficient.
On a blank disc, the force normal to plane equals the downforce. On a grooved disc, the force normal to each plane (groove wall) equals 1/sqrt2 times downforce so the sum for the two grooves equals sqrt2 times downforce.
The blank disc method therefore underestimates the skate force by about 30%.
The argument doesn't apply to balancing a linear tracker because the force which creates a side motion in an unbalanced arm is produced by gravity, not stylus reaction force.