A uniform solid sphere rolls down an incline. (a) What must be the incline angle (deg) if the linear acceleration of the center of the sphere is to have a magnitude of 0.23g? (b) If a frictionless block were to slide down the incline at that angle, would its acceleration magnitude be more than, less than, or equal to 0.23g?

Answer 1

The slope pushed up slope to cause the roll velocity to increase.
F R = I alpha
so
total downslope force = m g sin theta - I alpha/R

force = m a =m g sin theta - (2/5) m R^2 alpha/R
but alpha = a/R
so
force = m a = m g sin theta - (2/5) m a
a(7/5) = g sin theta
g sin theta = .23 (7/5)
check algebra, solve for theta

if friction less, no friction force upward, accelerates faster down slope.