Rotation between meter stick and a can

[Smartguy94]

Homework Statement

The tip of a meterstick rests on the can. The stick is pushed horizontally so that the can rolls on the table, with no slipping between the can and the table or the can or the can and the meterstick. The push continues until the can makes one complete rotation. During the roll, the displacement of the meterstick is equal to

The Attempt at a Solution

since there is no slipping between the can and the table and the meter stick, wouldn't the answer just be the can's circumference? because one rotational of the can is equal to the circumference of the can? therefore the meterstick displacement is equal to the circumference of the can?

but I got it wrong. can anybody help and explain?

 

[Spinnor]

Does the can's center move as fast as the stick?

Do the experiment, get a beer bottle, rubber bands, and a ruler. Wrap the rubber bands around the bottle, the ruler does not slip on the rubber bands as it does on the glass, and move the bottle one revolution with the ruler.

 

[Smartguy94]

Does the can's center move as fast as the stick?

Do the experiment, get a beer bottle, rubber bands, and a ruler. Wrap the rubber bands around the bottle, the ruler does not slip on the rubber bands as it does on the glass, and move the bottle one revolution with the ruler.

i did it with a battery and a ruler, the battery's diameter is 1.4cm and so the circumference is 1.4∏ = which is 4.39822cm

and then i roled the batery with my ruler and got 4.4cm for one revolution. so it is the circumference of the battery.. but apparently that's not the answer.

 

[Spinnor]

The ruler should move about twice as far as the can.

 

[Smartguy94]

The ruler should move about twice as far as the can.

could you please explain why and how do you get this?

 

[Spinnor]

See,

http://www.google.com/imgres?q=rota...rt=18&ndsp=10&ved=1t:429,r:5,s:18&tx=59&ty=27

and

http://www.google.com/imgres?q=rota...48&tbnw=157&start=0&ndsp=8&ved=1t:429,r:1,s:0

Roll something slowly and observe, the "top" moves the fastest while the point of contact has zero velocity.

 

[NascentOxygen]

i did it with a battery and a ruler, the battery's diameter is 1.4cm and so the circumference is 1.4Pi = which is 4.39822cm

and then i roled the batery with my ruler and got 4.4cm for one revolution. so it is the circumference of the battery.. but apparently that's not the answer.

Try it again. Have one end of the ruler on the battery, but allow the other end of the ruler to drag along the table. It is this dragging end of the ruler that you focus on. Mark the start and finish points of that dragging end, then measure their distance apart.