A ring of mass m is thrown in horizontal direction on a rough horizontal surface with a speed v₀. The speed of the ring, when it start pure rolling, is -

Question

G1 Physics · Accepted Answer

For a ring initially sliding without rotation, friction gives dv/dt=-µg and α=µg/R. Pure rolling begins when v=ωR, giving v=v₀/2. Hence A. 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 v₀/2..