# Understanding Forces on a Toppling Bicycle Wheel

• Vatsal
In summary, the question asks to sketch a free body diagram for a stationary bicycle wheel placed on its rim on rough ground and explain how the forces change during the toppling process. The forces involved include normal force, friction force, and weight. As the wheel topples, the direction and magnitude of the forces change due to the wheel's acceleration and change in angle. Initially, when the wheel is at a small angle, the normal force is approximately equal to the weight. As the wheel topples further, the friction force increases and the normal force decreases, causing the wheel to gain acceleration to the right. When the wheel is almost flat to the ground, the direction of its acceleration is towards the ground, causing the normal force to change direction
Vatsal

## 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.

## 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.

#### Attachments

• WIN_20160424_18_53_43_Pro.jpg
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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?

## 1. What is the force that causes a wheel to topple over?

The force that causes a wheel to topple over is known as torque. Torque is the rotational force that is applied to an object, in this case the wheel, causing it to rotate and eventually topple over.

## 2. How does the weight of the wheel affect its stability?

The weight of the wheel plays a significant role in its stability. A heavier wheel will have a lower center of mass, making it more stable and less likely to topple over. On the other hand, a lighter wheel will have a higher center of mass, making it more prone to toppling over.

## 3. Can the shape of a wheel affect its stability?

Yes, the shape of a wheel can greatly affect its stability. A wider wheel will have a larger base and therefore be more stable, while a narrower wheel will have a smaller base and be less stable. The distribution of weight within the wheel also plays a role in its stability.

## 4. How does the surface on which the wheel is rolling affect its stability?

The surface on which the wheel is rolling can have a significant impact on its stability. A rough or uneven surface can cause the wheel to lose traction and topple over, while a smooth and even surface will provide more stability.

## 5. Are there any other factors that can influence the stability of a toppling wheel?

Yes, there are many other factors that can influence the stability of a toppling wheel. These include the speed at which the wheel is rotating, the angle at which it is being pushed or pulled, and external forces such as wind or friction. Additionally, the design and construction of the wheel itself can also affect its stability.

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