Problem understanding rolling motion

AI Thread Summary
In the discussion on rolling motion, participants explore the relationship between the movement of a pen and the hand rolling over it. The initial claim suggested that the pen moves the same distance as the length of the hand during this motion, which was challenged by others who pointed out that the hand should move twice as far as the pen due to the mechanics of rolling. Clarifications revealed that the misunderstanding stemmed from measuring the distance incorrectly, specifically to the end of the palm rather than the fingertips. Ultimately, the conversation highlighted the importance of understanding the dynamics of rolling motion and the distances involved. The resolution emphasized the correct interpretation of the distances traveled by both the hand and the pen.
Phyman1109
Messages
14
Reaction score
0
we know that in rolling motion the top of drum has linear velocity 2v if the centre of mass has linear velocity v. thus if a board moves over a drum without slipping it wil roll 2vt=2L if the center of mass moves vt=L in time t, and this result is independent of size of the drum. but when i do this with a pen or pencil rolling by my hand i always find that the pen moves the distance equal to length of my hand. do it yourself and please comment on this.
 
Physics news on Phys.org
Phyman1109 said:
we know that in rolling motion the top of drum has linear velocity 2v if the centre of mass has linear velocity v. thus if a board moves over a drum without slipping it wil roll 2vt=2L if the center of mass moves vt=L in time t, and this result is independent of size of the drum. but when i do this with a pen or pencil rolling by my hand i always find that the pen moves the distance equal to length of my hand. do it yourself and please comment on this.
So you are claiming that when you roll your hand over a pen, that the pen moves at the same rate as your hand? So if you start with the pen at your fingertips, the pen remains at your fingertips as your hand moves? I don't see how that is possible.

Better try that again!
 
Doc Al said:
So you are claiming that when you roll your hand over a pen, that the pen moves at the same rate as your hand? So if you start with the pen at your fingertips, the pen remains at your fingertips as your hand moves? I don't see how that is possible.

Better try that again!
i am saying that when i roll the pen under my hand from fingertips to end of palm without letting my hand slip over the pen, the pen traverse the same distance as the length of my palm which it should cover only half of the length.
 
Phyman1109 said:
i am saying that when i roll the pen under my hand from fingertips to end of palm without letting my hand slip over the pen, the pen traverse the same distance as the length of my palm which it should cover only half of the length.
Compare the distance your hand moves with respect to the table with the distance the pen moves. Your hand moves twice as far.

Thus your hand moves with respect to the pen (which is moving) the same distance that the pen moves with respect to the table. This is what you are describing, which makes perfect sense.
 
Doc Al said:
Compare the distance your hand moves with respect to the table with the distance the pen moves. Your hand moves twice as far.
oops..i got it..i was making a mistake: i was measuring distance to end of the palm. Thanks.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
Back
Top