Question

A uniform solid sphere rolls down an incline without slipping. if the linear acceleration of the center of mass of the sphere is 0.24g, then what is the angle the incline makes with the horizontal?

Answer 1

Get the linear acceleration of center of sphere denoting it as y

then the vertical gravitation would be x

To look for the angle of inclination which is b we do the following steps:

90 - b = a
so cosine(a)= x/y

cosine(a)= (.24g)/g

a = 76 degrees (by using calculator or trig table)

then b would be = 14 degrees