The Law of gearing describes the relationship between the rotational speeds of two gears in mesh. According to this law, the gear with the greater rotationa...
The Law of gearing describes the relationship between the rotational speeds of two gears in mesh. According to this law, the gear with the greater rotational inertia will exert a greater torque on the gear with the smaller rotational inertia. This means that the slower gear will have to overcome a greater torque to rotate at the same rotational speed as the faster gear.
The law can be mathematically expressed as follows:
where:
is the rotational speed of gear 1
is the torque applied to gear 1
is the rotational speed of gear 2
is the torque applied to gear 2
The law of gearing also tells us that the ratio of the rotational inertias of the gears is equal to the ratio of the applied torques. This means that if we increase the torque applied to one gear, we must decrease the torque applied to the other gear in order to maintain a constant rotational speed.
Here are some examples of how the law of gearing works:
If you increase the torque applied to a gear, its rotational speed will increase.
If you decrease the torque applied to a gear, its rotational speed will decrease.
If you increase the rotational inertia of a gear, its rotational speed will decrease.
If you decrease the rotational inertia of a gear, its rotational speed will increase