The discussion focuses on the mechanics of a ring with two attached masses (m and 2m) rolling on a rough surface. Participants analyze the center of mass (com) of the ring, which is calculated to be at R/5, and explore the implications for angular acceleration, frictional force, and normal reaction. Key equations such as torque (τ = Iα) and the parallel axis theorem are emphasized for solving the problem. The conversation highlights the importance of drawing free body diagrams (FBD) to visualize forces acting on the system.
PREREQUISITESStudents and educators in physics, particularly those focusing on mechanics, as well as engineers and anyone involved in analyzing dynamic systems involving rotational motion.
I have a question: if I look at ANY point on the ring relative to some other point, will it be in circular motion? Or is this true only relative to the geometric center of the ring and IAOR?Lnewqban said:
Wrong. The center of the ring follows a straight line because it is always at distance ##R## above ground. The distance of the CM above ground varies from ##R+\frac{1}{5}R## at its highest to ##R-\frac{1}{5}R## at its lowest.palaphys said:
I meant in a general case, not this case. Here the center of mass follows a circular path relative to the geometric center?kuruman said:
Is there a moment arm of ##f## about the instantaneous center of rotation?palaphys said:
No, but there is a moment arm about the center of the ring right.. the IAOR is always at rest momentarily?erobz said:
Mark the center of mass on a diagram. Next let system it roll without slipping to the point where the ##2m## mass is directly below the center of the ring and the ##m## mass directly above it. Can you conclude whether the center of mass has changed position?palaphys said:
Yes I can. It is going in circular motion right.. with radius r÷5 if u see from center of ringerobz said:
Well how did it change position if it didn't accelerate?palaphys said:
You said this. It makes me believe that you believe the center of mass is not accelerating to the right initially as well?palaphys said:
I wanted to say that the geometric center of the wheel is just accelerating in a straight line sorry for confusionerobz said:
Please tell me how the tendency to slip is towards the left.. I still can't believe it.. pleaseerobz said:
Well, I'm trying to get you to see that if the center of mass (not explicitly the center of the wheel) there must be a force acting on the body ( via Newton's Second) that accelerates the center of mass as it moves in this case.palaphys said:
I see that .. just can't predict what direction friction is going to be. It seems intuitive that it would be towards right, but I want a physics proof why it is so.erobz said:
In this case the wheel is initially pushing on the ground to the left, and the ground is pushing the wheel to the right...via friction. This thing is just a pendulum whose pivot moves back and forth. The wheel will have some oscillatory motion, first it goes to the right then it turns back and heads to the left. friction flips with acceleration. Its observer to be "accelerationally" dependent. If you assume it, and correctly carry out the mathematics, the math will tell you. Here its observationally obvious, in other problems it might be challenging to get it out of the gate.palaphys said:
All points of the ring instantaneously rotate about the instantaneous ring-surface point of contact, which is constantly disappearing while another contact point, located just a little further, is constantly assuming the function of a new instantaneous pivot, around which all the points of the ring rotate again, and so on.palaphys said:
I don't understand this part please make it simpleLnewqban said:
I am extremely confused with friction in this case. What i was taught was that friction opposes relative tendency of motion. Here all of you are saying something else. Generally how I found direction of friction in rolling type of questions was by assuming none at all, and observing tendency of slipping. Please explain in simpler way plserobz said:
You are confusing kinetic friction with static friction. Kinetic friction is molecules sliding past each other, breaking structure permanently - converting mechanical energy to internal energy, and static friction is armwrestling with a wall...you might be warping it a bit, but it's springing back. Thats as far as I can see in plain terms.palaphys said:
It is correct.palaphys said:
That's not my confusion. I know that it's static friction here. The direction of friction is spoiling my day. I'm not able to figure it out.erobz said:
You don't need a proof, just logic. For the CM to accelerate to the right there must be a horizontal force acting on it. How many forces are there that act in the horizontal direction on any of the masses here?palaphys said:
How is the CM accelerating to the right? You said it was a cycloid path right? Also check the screenshot I posted.how can I conclude that it is horizontal?kuruman said:
But you are confused about it. You said you were taught friction always opposes motion. It doesn't, I'm trying to clarify that concept for you. There are two distinct names, two concepts to grapple with. One of them (static friction) is a fickle mistress.palaphys said:
friction does not oppose relative motion?erobz said:
