The discussion revolves around determining the acceleration due to gravity (little g) using an inclined plane and analyzing the relationship between potential energy and kinetic energy in the context of rotational motion. Participants explore the implications of different shapes and moments of inertia on the experimental outcomes.
The conversation includes confirmations of theoretical principles and hypothetical considerations regarding the effects of air resistance and other potential errors on the measurement of g. Participants are actively questioning and clarifying assumptions without reaching a definitive conclusion.
There are discussions about the appropriateness of using different shapes with specific moments of inertia, such as a hoop or a uniform disc, and the implications of these choices on the accuracy of the results. The impact of external factors like air resistance and timing errors is also noted as a potential source of discrepancies in measurements.
Not quite. What is I in this case?Ahmed Mutaz said:mgh=0.5mv^2+0.5Iw^2 gives v^2=gh
I=mr^2haruspex said:Not quite. What is I in this case?
Ah, sorry, didn't notice you specified that. But you would never quite achieve it. Better to specify a uniform disc.Ahmed Mutaz said:I=mr^2
I meant a hoop/wheel thing idk how to describe it but it has a moment of inertia of I=mr^2. So assuming that is true, would you be able to obtain a value close to 9.8 for g?haruspex said:Ah, sorry, didn't notice you specified that. But you would never quite achieve it. Better to specify a uniform disc.
I understand, but to be literally mr2 it would have to be very thin radially, so could easily get bent out of round. I'm just saying it would be easier to arrange for a uniform disc.Ahmed Mutaz said:I meant a hoop/wheel thing idk how to describe it but it has a moment of inertia of I=mr^2. So assuming that is true, would you be able to obtain a value close to 9.8 for g?
I figured as much; I’m only saying that assuming we have a shape that can be approximated to mr^2 does plotting v^2 against h give a decent value of g? I don’t really see any other problems besides the mr^2 approximation so forget about it for now. Also, I believe it is possible to get really thin hoops.haruspex said:I understand, but to be literally mr2 it would have to be very thin radially, so could easily get bent out of round. I'm just saying it would be easier to arrange for a uniform disc.
Yes, the principle is fine.Ahmed Mutaz said:I figured as much; I’m only saying that assuming we have a shape that can be approximated to mr^2 does plotting v^2 against h give a decent value of g? I don’t really see any other problems besides the mr^2 approximation so forget about it for now. Also, I believe it is possible to get really thin hoops.
haruspex said:Yes, the principle is fine.
Yes, air resistance and rolling resistance will lead to underestimates. Other errors, like timing offset and granularity, could go either way.Ahmed Mutaz said:Thanks for confirming the theory. Now another hypothetical, last question lol, because of air resistance wouldn’t you get an under approximation of g? Or do you think there are other sources of error that may cause it to be an overestimation?