Saint Mary's Academy

Archive for October, 2010

This article is a continuation of “Teaching Rolling Motion”. A description of the notation I use can be found in still another article “Teaching Rotational Dynamics”. In the rolling motion article, I analyzed the motion of a sphere rolling down an incline. I assumed no slipping and then determined what condition that assumption imposed on the coefficient of static friction. This article describes a situation for which that condition is not satisfied – so slipping occurs.

Problem. A sphere rolls down an incline steep enough that slipping occurs. What is the linear acceleration of the sphere’s center of mass? What is the sphere’s angular acceleration around the axis through its center of mass? The mass of the sphere is M, its radius is R, its moment of inertia around the center of mass is Icm = 2(MR**2)/5, the incline angle is th, and the coefficient of kinetic friction between the sphere and incline is Uk.