Final answer:
The linear acceleration of a rolling sphere on an inclined plane can be found using Newton's second law. The force of friction on the sphere can be determined using a free-body diagram. The minimum coefficient of static friction to support pure rolling can be found by comparing the linear acceleration with the acceleration due to gravity.
Step-by-step explanation:
When a sphere of mass m rolls without slipping on an inclined plane, it experiences both linear and angular motion. The linear acceleration of the sphere can be found using Newton's second law. The force of friction acting on the sphere can be determined by analyzing the free-body diagram.
For the linear acceleration, we can use the following equation:
a = g*sin(θ)/(1 + I/mr^2)
Where 'g' is the acceleration due to gravity, 'θ' is the angle of inclination, 'I' is the moment of inertia of the sphere, 'r' is the radius of the sphere, and 'm' is the mass of the sphere.
The force of friction can be determined using the equation:
f = μ*N
Where 'μ' is the coefficient of static friction and 'N' is the normal force.
To support pure rolling without slipping, the minimum coefficient of static friction should be equal to the ratio of the linear acceleration to the acceleration due to gravity:
μ ≥ a/g