Question

A yo-yo is made from two uniform disks,eachwith mass M/2 and radius R, connected by a light axle of radiusr(R>r). Since the axle is nearly massless, the total mass oftheyo-yo is M. A light, thin string is wound several times aroundtheaxle.The yo-yo is placed on a rough horizontal surface;thecoefficient of static friction between the yo-yo and the surfaceismu_s. The string is held so that it exits the yo-yo horizontallyonthe lower side of the stem. The string is then pulledhorizontallywith a force of magnitude F.

(a) Assuming the yo-yo rolls without slipping, find the magnitudeofthe static frictional force on the yo-yo by the surface.

(b) Assuming the yo-yo rolls without slipping, find theaccelerationof the center of mass of the yo-yo. State magnitudeanddirection.

(c) What is the maximum value of F for which the yo-yo willrollwithout slipping?

Here are the answers, I amjusthaving trouble finding them :(

(a) F*(2r+R)/(3R)

(b) 2F*(R-r)/(3MR)

(c) 3*mu_s*MgR/(2r+R)

Thanks in Advanced :)