(III) A wheel with rotational inertia I = 1/2 MR² about its horizontal central axle is set spinning with initial angular speed ω₀ . It is then lowered, and at the instant its edge touches the ground the speed of the axle (and cm) is zero. Initially the wheel slips when it touches the ground, but then begins to move forward and eventually rolls without slipping.
(b) How long does the wheel slip before it begins to roll without slipping? [Hint: Use ∑ F (→ above F) = m a (→ above a), ∑ ₜ꜀ₘα꜀ₘ , and recall that only when there is rolling without slipping is v꜀ₘ = ωR .]