An annular disk of mass M, inner radius a and outer radius b is placed on a horizontal surface with coefficient of friction μ, as shown in the figure. At some time, an impulse $J_0$ x̂ is applied at a height h above the center of the disk. If h = hm then the disk rolls without slipping along the x-axis. Which of the following statement(s) is(are) correct ?

Question

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 A: For μ ≠ 0 and a → 0, hm = b/2; B: For μ ≠ 0 and a → b, hm = b; C: For h = hm, the initial angular velocity does not depend on the inner radius a.; D: For μ = 0 and h = 0, the wheel always slides without rolling..