Derive the slope of a track where a sphere having frictional coefficient u maintains constant velocity v.
Assuming the sphere rolls without slipping, this looks good.Gamma said:If I use Torque = I * alpha and Newtons second law, I end up with the following for acceleration.
a = mg sin(theta) * r^2 /(I + mr^2) where I is w.r.t. the center of the rolling object.
Not sure what you did here. Realize that as long as the sphere rolls without slipping, the friction does no work.If I use the energy relation (i.e Change in Energy = work done by the force), I get
a = g[2 sin (theta) + u cos(theta)] / ( 1 + I/mr^2)