Friction on a flat rotating surface

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Discussion Overview

The discussion revolves around the effects of friction on a flat rotating surface, specifically focusing on a wooden cylinder being pushed and rotated on a table. Participants explore the relationship between friction, surface area, and energy required for both linear and rotational motion.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant asserts that the frictional force and energy required to push a cylinder along a table is independent of the surface area in contact with the table, following the equation Friction = μ N.
  • Another participant suggests that when the cylinder is rotated about its center of mass, the friction and energy required may depend on the surface area in contact with the table, although the mathematics would be more complex.
  • A participant provides a mathematical approach to calculate the torque exerted by frictional forces on a rotating cylinder, indicating that the torque varies with radius and results in a specific angular acceleration.
  • There is a discussion about the complexities involved when the cylinder is both rotating and sliding linearly, with a reference to the sport of curling as an example of such dynamics.
  • One participant notes that a wider cylinder has a greater moment of inertia (MOI) and thus slows less after being spun up, emphasizing that this is not due to reduced friction but rather increased frictional torque requiring more energy to maintain constant angular speed.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between surface area and friction in the context of rotation, with some agreeing on the complexities of the mathematics involved while others emphasize different aspects of the physics, indicating that multiple competing views remain.

Contextual Notes

The discussion includes unresolved mathematical steps and assumptions regarding the behavior of friction in both linear and rotational contexts, particularly when considering varying surface areas and their effects on torque and energy requirements.

waverider
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If I push an object such as a cylinder of wood along a flat table (flat face of cylinder in contact with the table) through it's center of mass, the friction or energy required is not dependent of the surface area the block makes with the table, Friction = μ N, correct? And the energy required = friction force x distance.

However, if I now rotate the cylinder about the center of mass (axis of rotation normal to the table) then does the friction (and energy required to rotate the block) depend on the surface area of the block in contact with the table (block weight and coefficient of friction are constant)?
Obviously the mathematics is going to be a lot more complicated for the rotating block but I suspect the diameter of the block will affect the friction and energy require to turn the block one revolution. Correct?
 
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waverider said:
the mathematics is going to be a lot more complicated for the rotating block
If rotating on the spot it is easy. Consider a small area dA of a cylinder radius R, mass M. The normal force is proportional to dA, so the frictional force is too: μgM.dA/(πR2). All the frictional forces are tangential. The torque they exert varies as radius. So total torque is μgM∫r2.drdθ/(πR2) = μMg(2πR3/3)/(πR2) = 2μMgR/3.
Since the MoI is MR2/2, the angular acceleration is 4μg/(3R).

If rotating and sliding linearly it becomes extremely nasty. I believe it would not follow a straight line. Ever watched the Scots/Irish/Canadian/NZ sport of curling?
 
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Great! thanks for the confirmation and equations.

Yeah, I have seen the sports curling...fun to watch, and I agree the math could get very nasty.
 
waverider said:
Great! thanks for the confirmation and equations.
Note that the wider cylinder slows less after being spun up, because it has a greater MOI, not because it has less friction. The frictional torque is greater for the wider base, so takes more energy to turn it against friction, at constant angular speed.
 
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A.T. said:
Note that the wider cylinder slows less after being spun up, because it has a greater MOI, not because it has less friction. The frictional torque is greater for the wider base, so takes more energy to turn it against friction, at constant angular speed.
Yes, a good point to bring up - I have recently seen some people on YT make this very mistake.
 

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