The question
Name: ______________________ Date: ____________ Clay on two turntables (8 points)
Experimental setup
Clay on two turntables
Two turntables have the same mass M and the same radius R, and each turns freely on a frictionless vertical axle. Turntable A is a uniform solid disk (IA = ½MR², given). Turntable B is a ring with nearly all its mass at the rim (IB = MR², given). Both spin at the same angular velocity ω₀. A small lump of clay of mass m is dropped straight down onto each turntable and sticks at its rim. Model the clay as a point object.
(a) After the clay sticks, which turntable spins faster, or do they spin at the same rate? Justify your answer without using equations. [2 points]
(b) A turntable has rotational inertia I = βMR², where β is a number that depends on its shape. Derive an expression for its angular velocity ω after the clay sticks, in terms of β, M, m and ω₀. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. [3 points]
(c) Explain how your expression from part (b) supports or contradicts your answer to part (a). [3 points]