A 1 kg bead slides in a smooth radial groove of a horizontal disc rotating with constant angular speed 2 rad/s. At an instant the bead has radial speed dr/dt=3 m/s. If the magnitude of the groove reaction is N newton, find N.
Physics · Circular Motion · centripital force and centrifugal force
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Question

A 1 kg bead slides in a smooth radial groove of a horizontal disc rotating with constant angular speed 2 rad/s. At an instant the bead has radial speed dr/dt=3 m/s. If the magnitude of the groove reaction is N newton, find N.

Physics · Circular Motion · centripital force and centrifugal force

G1 Physics · Accepted Answer

Because the groove rotates with constant angular speed, θ̇=ω and θ̈=0. The transverse acceleration in polar coordinates is a_θ = rθ̈ + 2ṙθ̇ = 2ω(dr/dt). The groove reaction supplies this transverse acceleration. Therefore N = m·2ω|dr/dt| = 1×2×2×3 = 12 N.