Question

Around object of mass M and radius R rolls with out slipping down an inclined plane set on angle θ to horizontal. Find –

(a) Linear acceleration of centre of mass.

(b) Minimum coefficient of friction required for perfect rolling. assuming M.I. w.r.t. an axis passing through centre of mass is MK ² .

Answer 1

For translatory motion

mg sin α – f_r = ma ...(1)

For rotatory motion

f_r R = MK ² (α) ...(2)

and a – Rα = 0 ...(3)

solve equation (1), (2) and (3)

∴ f_r ≤ µ mg cos θ (for perfect rolling)