A plank that rests on top of two identical cylinders.

[Warlic]

Homework Statement

Dont need to read the problem, just copied it on for the figure:

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

 

[CWatters]

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.

 

[Warlic]

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

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.

 

[haruspex]

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.