A washing machine drum spin-drying a load of wet clothes ends up dynamically…
PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Rotation, rigid bodies and accelerated frames · Rotation, rigid bodies and accelerated frames
Action and Symmetry, Ch The inertia tensor, principal axes and Euler angles
Problem
A washing machine drum spin-drying a load of wet clothes ends up dynamically unbalanced: two clumps of clothing, each of mass 150g, cling to the drum wall at radius r=0.20m, on opposite sides of the drum. One clump lies d=0.10m to one side of the drum's mid-plane and the other 0.10m to the other side, so the combined centre of mass of the load lies on the spin axis (the load passes a static balance test at rest). The drum spins at 1200rpm about a fixed horizontal axis held in two bearings 0.30m apart. Treat each clump as a point mass and ignore any imbalance in the drum itself.
((a)) Find the product of inertia Ixz the two clumps produce, taking z along the spin axis and the instant at which they lie in the plane containing the spin axis and the horizontal.
((b)) Find the torque the bearings must supply, and check it by computing directly the couple of the clumps' centripetal forces.
((c)) Estimate the extra force each bearing must exert, and compare it with the total weight of the load (2×0.150kg, with g=9.8ms−2).