Understanding Forces on a Toppling Bicycle Wheel

AI Thread Summary
A stationary bicycle wheel on rough ground topples over, prompting a discussion on the forces acting on it at various angles. Initially, when the angle (theta) is small, the normal force is approximately equal to the gravitational force (mg), but as the wheel begins to topple, the friction force increases while the normal force decreases. Participants emphasize the need to understand why these forces change direction and magnitude during the toppling process. The conversation suggests drawing additional diagrams to illustrate the forces at different stages of the toppling, particularly when the wheel is nearly flat on the ground. Understanding these dynamics is crucial for accurately representing the forces involved in the toppling motion.
Vatsal
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Homework Statement


A stationary bicycle wheel is placed on its rim on rough ground. It topples over. Sketch a free body diagram for the wheel when it is at an arbitrary angle to the vertical and label the forces. Explain qualitatively what happens to the direction and magnitude of each of the forces during the toppling process.
What I don't get is how the forces change direction and magnitude.

Homework Equations

The Attempt at a Solution


What i did was draw the forces like in the picture. Not really sure how they change. I'm thinking at first when theta is small Normal ~ mg. Then friction increases and the normal force decreases.
Any help greatly appreciated.
 

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Are you sure there is friction? Maybe the normal force changes direction
 
Re thought and the centre of mass is accelerating to the right so there must be friction
 
Vatsal said:
<Q>... Explain qualitatively what happens to the direction and magnitude of each of the forces during the toppling process.</Q>
... how the forces change direction and magnitude.
... I'm thinking at first when theta is small Normal ~ mg. Then friction increases and the normal force decreases.
You seem to be well on the way with this. But try to give reasons for your statements.
Why is the friction force increasing?
Why is the normal force decreasing?
Then looking at your diagram, why have you shown friction acting in the direction you have? (I agree with you, but you can explain why.)

As for the direction of the forces, which can change?

Although they only ask for one diagram, perhaps it would be interesting to draw another when the wheel has toppled much further?
 
Merlin3189 said:
Although they only ask for one diagram, perhaps it would be interesting to draw another when the wheel has toppled much further?
I feel we can make that hint a bit stronger. @Vatsal , think about when the wheel is almost flat to the ground. What is the direction of its acceleration, assuming it is still not slipping?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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