I have doubt regarding when an object ( sphere , ring , cylinder etc ) rolls down a FRICTIONLESS inclined plane.
Let us suppose the angle of inclination of inclined plane is θ.
Now the forces acting on it will be weight force (mg) and normal reaction. A component of mg perpendicular to incline mgcosθ will be balanced by the normal reaction. There will be another component of mg along the incline mgsinθ which will give the object acceleration gsinθ. There is no friction.
Now, acceleration, a = radius ( r ) x angular acceleration (α) Now as there is, a = gsinθ so there must be nonzero value of α.
But force mg and normal reaction are forces whose line of action passes through the centre of the object ( ring etc ) ( passes through centre of mass). So net torque about centre should be zero and there should be no angular acceleration.
Also, will the angular momentum be conserved when it reaches the bottom of incline?
I'm confused please help me.