Reference frame for analyzing ball rolling down incline

[dsdsuster]

Hi all,

I have a question about how to analyze the problem of a ball rolling down an incline plane. Assuming there is friction, at each instant the ball swivels about a pivot point on the incline that is stationary due to static friction. We then would analyze the torques about this point and find the rate of change of angular momentum.

However, at every instant, aren't we switching to a pivot point at a different location along the incline. Angular momentum is dependent on the choice of the coordinate origin and so is torque.
Am I understanding the way we are analyzing this problem correctly? or am I over complicating things?

So if we are analyzing the system each instant and at a different pivot point, and a different coordinate origin, how can we piece together all the information so the speak and describe how the ball is moving to a single stationary observer?

 

[Dale]

Problems like this are best solved through conservation of energy rather than through forces and torques. Don't worry about the forces or the pivot points, just calculate the KE as a function of velocity down the plane, and that is equal to the change in gravitational PE.

 

[WannabeNewton]

So if we are analyzing the system each instant and at a different pivot point, and a different coordinate origin, how can we piece together all the information so the speak and describe how the ball is moving to a single stationary observer?

The thing is that we do the calculation at an arbitrary instant of time, within the time interval we are interested in. Since the result of the calculation is shown to hold true for an arbitrary instant of time within the interval, we can conclude that the result holds for all instants of time in question.