1.explain how a cyclist maintain his stability when riding a bicycle

2.explain why it's easier to loosen a nut with a long spanner than a short one.
3. explain why the handle of a door is usually placed as far as possible from the hinges

A moving bicycle is already stable and thus the cyclist remains upright.

The last two are related to leverage. The first has to do with the gyro effect. I will be happy to critique your thinking.

As the rider is cycling he maintains the stability by riding upright.

1. A cyclist maintains stability on a bicycle by following a few key principles. Firstly, there is the gyroscopic effect of the spinning wheels. As the wheels rotate, they create a gyroscopic force that helps to keep the bicycle upright. Secondly, a cyclist maintains balance by making constant small adjustments with their body and steering. By shifting their weight, leaning into turns, and making steering corrections, they can keep the bicycle balanced. Additionally, using the handlebars to steer and the pedals to control speed and direction allows the cyclist to maintain stability. Lastly, a bicycle frame is designed with a geometry that promotes stability. The angles of the frame and the relationship between the front and rear wheels contribute to the overall stability of the bike.

2. When trying to loosen a nut, using a long spanner is generally easier than using a short one due to the principles of leverage. Leverage is the concept of using a lever or a tool to amplify the force applied to an object. The longer the spanner, the greater the leverage. When you apply force to the end of a long spanner, the force is spread out over a greater distance. This means that the same amount of force is more effective in turning the nut. With a short spanner, a smaller amount of force is applied over a shorter distance, making it more difficult to loosen the nut.

3. The handle of a door is usually placed as far as possible from the hinges to maximize the leverage and mechanical advantage when opening or closing the door. When you apply force to the handle, it creates a moment of force or torque around the axis of rotation, which is the hinges in this case. By placing the handle farther from the hinges, the length of the lever arm increases, which magnifies the force applied to the door. This makes it easier to open or close the door with less effort. If the handle were located closer to the hinges, the lever arm would be shorter, meaning you would need to apply more force to achieve the same result.