Rather than rotate completely horizontally, a carousel rotates at an angle of 10° from horizontal, with a constant angular velocity of 1.571 RAD/s. A box is placed 1.5 m from the axis of rotation. What’s the minimum coefficient of static friction so the box will not slip?

Answer 1

acceleration down slope = w^2 R cos 10
so m a = m w^2 R cos 10

Force down slope = m g sin 10 + mu m g cos 10

so
g sin 10 + mu g cos 10 = w^2 R cos 10

g tan 10 + mu g = w^2 R

mu = ( w^2 r/g -tan 10)

= 0.201