An object in circular motion about a center point feels an outward tug. In fact, this is due to the object's tendency to travel in a straight line -- it must be acted on by a force in the direction of the center of rotation in order to keep its circular path. The magnitude of this "centripetal acceleration" is given by a = v^2 / r, where v is the speed at which the object would fly away if allowed to do so, and r is the radius of the circle.
Let r be the distance from Buster's hip to his ankle. Let F be the force required to pull off his sock. Let m be the mass of the sock. Then, the sock will fly off when (v^2 / r) > (F / m), that is, when v > sqrt(r * F / m). It is clear from this inequality that shortening Buster's legs (decreasing r), using slicker socks (decreasing F), or using heavier socks (increasing m) result in a reduction in the minimum value of v.
Suppose, for instance, that r = 1 meter, F = 20 Newtons, and m = 100 grams. Then sqrt(r * F / m) = sqrt(200 m^2/s^2) = 14.1 m/s. The tangential velocity of Buster's foot must exceed 14.1 m/s in order to knock his socks off by the whipping action alone. This is equivalent to 14.1 / 3.14 = 4.49 revolution per second, or 269 rpm, about the hip joint....
Let r be the distance from Buster's hip to his ankle. Let F be the force required to pull off his sock. Let m be the mass of the sock. Then, the sock will fly off when (v^2 / r) > (F / m), that is, when v > sqrt(r * F / m). It is clear from this inequality that shortening Buster's legs (decreasing r), using slicker socks (decreasing F), or using heavier socks (increasing m) result in a reduction in the minimum value of v.
Suppose, for instance, that r = 1 meter, F = 20 Newtons, and m = 100 grams. Then sqrt(r * F / m) = sqrt(200 m^2/s^2) = 14.1 m/s. The tangential velocity of Buster's foot must exceed 14.1 m/s in order to knock his socks off by the whipping action alone. This is equivalent to 14.1 / 3.14 = 4.49 revolution per second, or 269 rpm, about the hip joint....