Which will reach the bottom first?

  • Context: Undergrad 
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Discussion Overview

The discussion centers around the dynamics of two cylindrical rods of different diameters rolling down an inclined plane without friction. Participants explore the effects of diameter on the motion of the rods, including torque, angular velocity, and energy conservation principles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that calculations involving torque and angular velocity are necessary to determine which rod reaches the bottom first.
  • Others question the premise of rolling without friction, arguing that without friction, the rods would not roll at all.
  • There is a discussion about the role of static contact friction in enabling the rods to roll, while some participants assert that rolling friction does not dissipate energy.
  • One participant proposes that the larger mass may have a lower velocity due to differences in potential energy, while others challenge this assumption, stating that the change in height is the same for both cylinders.
  • Some participants discuss the relationship between rotational kinetic energy and linear kinetic energy, emphasizing the importance of moment of inertia and angular velocity in the context of the problem.
  • There is a mention of the need to consider both rotational and linear kinetic energy when analyzing the motion of the rods.

Areas of Agreement / Disagreement

Participants do not reach a consensus on which rod will reach the bottom first. There are multiple competing views regarding the effects of diameter, mass, and energy conservation on the motion of the rods.

Contextual Notes

Participants express uncertainty regarding the assumptions made about friction and the calculations needed to analyze the motion. The discussion includes various interpretations of free body diagrams and the forces acting on the rods.

  • #31
You will have to use multiple equations, yes, but what I am saying is there's multiple ways to go about solving the problem. Kinematics and energy conservation.
 
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  • #32
A.T. said:
Do you mean there is static contact friction that makes it roll, but no rolling resistance that dissipates energy? If that's the case, then you can use energy conservation to find the speeds.
I just read this and your answer. Ignore my other post. I think energy conservation would be a lot easier to solve the problem with. But I could be wrong. I suggested the ##\Delta t## after reading the problem statement as that would be the time it takes for the cylinder to reach the bottom of the ramp from Top. Are you confused about how to use the math, physics, or the process, or all of the above?
 
  • #33
Shinaolord said:
I think energy conservation would be a lot easier to solve the problem with.
Yes, and I think jbriggs444 already did that in post #25.
 

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