Solving the Spinning Wheel Problem - Jonathan

[zarcon]

Hi All! This is my first real post here.

I have a pretty basic question regarding rotating objects and the manner in which the rotation becomes a translation.

If I drop a bicycle wheel against the ground, it bounces back toward my hand. But if the wheel is spinning as it falls, it will move forward after it bounces.

I know (think) this is because of the opposing friction from the contact of the spinning wheel and the ground, but a diagram of the forces would show a frictional force perpendicular to the wheel's center of mass. Shouldn't this then be a completely rotational force?

If the wheel is floating perfectly still in space and a force is applied perpendicular to the wheel's center of mass, it will cause the object to spin without any linear translation, like a basketball on the end of somebody's finger, or a plate on a stick, right?

So a perpendicular force applied opposite to the direction an object is rotating will cause it to move in the direction of the force? Is that right? How would that be calculated?

Thanks! Hope I made my question understandable. Anything to point me in the right direction would be really appreciated.

Jonathan

 

[shadow12345]

This is something that takes a bit getting used to, but there's no such thing as 'only a rotational force'. I know, it's completely counter-intuitive, but if you apply a force so that it hits the center of mass, then it produces a translation but no rotation. However, if you apply this same force at a different point such that it induces a torque and a rotation, it will still product the same translation!

This is NOT a violation of any laws. You may be thinking "but isn't there also an increase in kinetic energy, due to the fact that the object is rotation AND translating". That would be a true statement. However, when you apply a force away from the center of mass, the force is applied over a greater distance as the object rotates, and subsequently the increase in kinetic energy comes from the fact that you really did increase the amount of work you did on the object.

 

[GSXR750]

Hi Jonathan, welcome to the community and thanks for your question! You are correct in your understanding that the spinning wheel problem is due to the opposing friction between the wheel and the ground. This is known as the gyroscopic effect, where a spinning object resists changes in its orientation.

To answer your question about the perpendicular force causing linear translation, it depends on the point of application of the force. If the force is applied at the center of mass of the spinning object, it will only cause rotation without any linear translation. However, if the force is applied at a point other than the center of mass, it will cause both rotation and linear translation.

In terms of calculation, this can be done using the principles of torque and angular momentum. The torque, or rotational force, is equal to the product of the force and the distance from the point of application to the center of mass. The angular momentum, or rotational motion, is equal to the product of the moment of inertia (a measure of an object's resistance to rotation) and the angular velocity.

I hope this helps clarify your understanding of the spinning wheel problem. Keep exploring and asking questions!