- #1
JProffitt71
- 8
- 0
Okay, so I am somewhat new to physics (finishing up my first Mechanics/EM course), and I often get stuck on concepts until they make sense to me intuitively. Everything to do with translational motion made sense instantaneously, and I have powered through EM, but I have always struggled with rotational motion, and the physics behind any object rolling down a ramp without slipping has been eluding me all year. I understand mathematically that the sum of the forces upon the ball along the ramp is equal to mgsin(theta) minus some frictional force, and I can solve for that frictional force with the non-slipping relations between translational and rotational motion. However, I have yet to figure out what the hell that force is and what it does to the ball's motion, conceptually.
I do know that it resists the gravitational force, and varies directly with the coefficient of its rotational inertia, which makes sense. I know also that it is what rolls the ball, being a force displaced from its center of mass, otherwise I couldn't solve for it. However, I run into a problem when I consider how exactly the ball is moving down the ramp. Gravity is acting on the entire ball, pulling it down the ramp and friction seems to be resisting, but friction makes the ball roll, making it go down the ramp if there's no slippage.
This becomes a problem when I ask myself what happens when the coefficient of friction on the ramp is increased. Does the ball roll down slower due to the extra resistance, or faster with the extra torque, or neither? What happens when I change other things and why, without using equations? I can solve for all of this given enough time, but if that is limited and I don't have a feel for what that ball (or any rotating object) should do, things could get quite stressful.
It all makes sense on a very strictly mathematical level, but I cannot picture it happening in my head like I can nearly everything else. So, if you have any insights on any part of how rolling objects accelerate the way they do down ramps, I would greatly appreciate it. And if not, that's okay too, my approach is kinda weird and sometimes math will be the only way (I can think of it as rotational KE and translational KE, but that doesn't help me visualize it very well)
I do know that it resists the gravitational force, and varies directly with the coefficient of its rotational inertia, which makes sense. I know also that it is what rolls the ball, being a force displaced from its center of mass, otherwise I couldn't solve for it. However, I run into a problem when I consider how exactly the ball is moving down the ramp. Gravity is acting on the entire ball, pulling it down the ramp and friction seems to be resisting, but friction makes the ball roll, making it go down the ramp if there's no slippage.
This becomes a problem when I ask myself what happens when the coefficient of friction on the ramp is increased. Does the ball roll down slower due to the extra resistance, or faster with the extra torque, or neither? What happens when I change other things and why, without using equations? I can solve for all of this given enough time, but if that is limited and I don't have a feel for what that ball (or any rotating object) should do, things could get quite stressful.
It all makes sense on a very strictly mathematical level, but I cannot picture it happening in my head like I can nearly everything else. So, if you have any insights on any part of how rolling objects accelerate the way they do down ramps, I would greatly appreciate it. And if not, that's okay too, my approach is kinda weird and sometimes math will be the only way (I can think of it as rotational KE and translational KE, but that doesn't help me visualize it very well)
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