Engineering
Physics
Instantaneous Centre and Instantaneous Axis of Rotation
Question

A dumbbell consists of two identical particles of mass m connected by a rigid light rod of length 2ℓ. The dumbbell is set spinning with angular speed ω0 on a surface with a small friction coefficient µk. At what time (in sec) dumbbell stop. (ω0 = 8 rad/sec, ℓ = 1m, µk = 0.4)

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Solution
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τ=2μmg×==mℓ2+mℓ2α

α=μg

ω=0=ω0αt

t=ω0μg=8×14=2sec

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