A magnetic grain riding the spinning roll stays stuck to the surface as long as the roll's centrifugal pull is smaller than gravity plus the magnetic holding force; it lets go the moment centrifugal force wins. Per unit mass, at surface angle θ measured clockwise from the top of the roll:
centrifugal accel = ω²R
holding accel = g·cosθ + B·k (magnetic grain)
holding accel = g·cosθ (non-magnetic grain)
detachment: cosθ_d = (ω²R − B·k) / g
Because a magnetic grain's holding term is larger, it needs a bigger θ (further round, closer to the bottom of the roll) before it lets go — so it detaches moving mostly straight down and drops close to the roll. A non-magnetic grain lets go almost immediately at the top, still carrying most of its tangential speed horizontally, and is flung out to land much further away. After release each grain is a free projectile under gravity (x = x₀+v·cosθ·t, y = y₀+v·sinθ·t+½gt²); wherever it lands relative to the splitter blade decides which bin it falls into.
- Recovery — the share of all magnetic grains fed in that end up in the concentrate bin.
- Grade — how much of what's in the concentrate bin is actually magnetic material, vs. gangue that landed short.
- Mass pull — the fraction of total feed mass reporting to the concentrate bin.