A plank that rests on top of two identical cylinders.

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Homework Help Overview

The discussion revolves around a plank resting on two identical cylindrical rollers, focusing on the motion of the rollers in relation to the plank. The original poster questions why the center of each roller moves forward only half as far as the plank, suggesting a connection to the mechanics of rolling without slipping.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the motion of the plank and the rollers, with some referencing the mechanics of a car wheel to illustrate their points. Questions arise regarding the implications of rolling without slipping and the speeds of different points on the rollers.

Discussion Status

The discussion is ongoing, with participants sharing insights and clarifying their understanding of the mechanics involved. There is recognition of the complexities in the motion of the rollers and the plank, but no consensus has been reached yet.

Contextual Notes

Participants are navigating assumptions about the motion of the rollers and the plank, particularly in relation to the concept of rolling without slipping. The original poster's reference to the book's statement indicates a reliance on external sources for understanding the problem.

Warlic
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Homework Statement



Dont need to read the problem, just copied it on for the figure:
upload_2015-12-2_20-14-8.png


So a plank rests on top of two identical cylindrical rollers - rolling without slipping both between cylinders and plank, and cylinders and surface.
My book says that center of each roller moves forward only half as far as the plank - why is this?
Is it because there are two rollers? Because doesn't a point R away from center of rollers move as far as the center does when we have rolling without slipping? [/B]

Homework Equations


rω=v

The Attempt at a Solution

 

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Consider the wheel on a car. The axle travels at the speed of the car. The bottom of the wheel where it touches the ground is stationary. The top of the wheel moves at twice the speed of the car.
 
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CWatters said:
Consider the wheel on a car. The axle travels at the speed of the car. The bottom of the wheel where it touches the ground is
CWatters said:
Consider the wheel on a car. The axle travels at the speed of the car. The bottom of the wheel where it touches the ground is stationary. The top of the wheel moves at twice the speed of the car.
Thank you, lol, seems ridiculous now, but I was thinking why isn't the car moving twice the speed of the center of mass of the wheels - didn't realize the car was only moving with the same speed as the axle and not the top of the wheels.
 

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Warlic said:
didn't realize the car was only moving with the same speed as the axle and not the top of the wheels.
Of course, the car would go twice as fast that way, but as the ancient Egyptians discovered someone has to keep collecting the wheels as they fall out behind the car and put them back in front.
 
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