Physics Puzzle: A Trick with a Yo-yo
July 4th, 2009
| Categories: Mechanics, Physics Puzzles
Level of Difficulty: Undergraduate
A yo-yo lies on the floor. It’s made out of an inner disc of radius r and an outer disc of radius R. Its mass is m. There’s a (massless) string wound around its inner disc. You pull the string with force F and angle θ with respect to the horizontal direction. What is the acceleration of yo-yo? Assume the yo-yo rolls with slipping.
(If you’ve never done this before, try it before answering the question and see which direction the yo-yo rolls.)
Since torque is the cross product of force and radius, and the direction of the force here is tangential to the inner circle, torque should be Fr. The torque can be used to find the force on the outer circle. This force should equal Fr/R. NSL: Fnet=MA. So, A = Fnet/M. Substituting for Fnet, A= Fr/MR.
I might have done something wrong, since I didn’t use theta.
If the yo yo rolls with slipping then the answer is a= Fcos theta/m
But is it that it rolls without slipping. Then only we can make use of R and r. Check the question
This force should equal Fr/R. NSL: Fnet=MA. So, A = Fnet/M. If the yo yo rolls with slipping then the answer is a= Fcos theta/m
But is it that it rolls without slipping.
One thing I think you are forgetting is the addition of friction. If the coefficient is low, I would think it would go in the direction of the applied force. However, if it was high, the torque would cause it to roll in the opposite direction. Or am I just crazy?
I understand the roll with or without slipping, but I think there is a specific coefficient that is related to all of the variables and not just 0 or 1.
Don’t think it can roll at all without slipping. The force of the string (F.cos(theta)) is trying to pull the yo-yo to the right (which would result in a clockwise rotation.) However, the torque (Fr) is trying to force the yo yo to rotate in a counter-clockwise direction.
When the force is great enough to overcome friction, the yo yo gets dragged along the ground without rotating (otherwise it just sits there). When the force stops, the yo yo should start to roll forward (continuing the rightward velocity).
if yo-yo is slipping then its acceleration a = Fcos theta/m