The physics
A hammer on a wire moves on a circle. Its spin rate ω is in radians each second. One turn is 2π radians, so ω = 2πf.
ω = 2π f v = ω r
At a steady speed, the velocity keeps turning. So the hammer accelerates toward the centre. The wire gives the pull for it.
ac = v² / r = ω² r F = m ω² r
The velocity is along the tangent, at right angles to the radius. Let go, and the hammer flies off along the tangent.
When the thrower speeds up, a second acceleration at points along the path. The total leans ahead of the radius.
a = √(ac² + at²) tan φ = at / ac
A spin that slows evenly turns at its average rate, half the start. As a vector, the acceleration at θ is a = −(v²/r)(cos θ, sin θ).