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 μ. If dumbbell stops in time $t=\frac{K\omega_0l}{2\mu g}$ where K is a constant, then find the value of K.
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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 μ. If dumbbell stops in time $t=\frac{K\omega_0l}{2\mu g}$ where K is a constant, then find the value of K.

Your answer

G1 Physics · Accepted Answer

Write translation ΣF=Ma and rotation Στ about CM=I about CMα, together with the no-slip relation v of CM=ωR and a of CM=αR whenever pure rolling applies. Solving the equations for the shown geometry gives 2.