Final answer:
Gearing systems increase motor torque at the expense of speed by creating a mechanical advantage. This allows for more work to be done at lower speeds but care must be taken to avoid overheating of the motor due to increased current flow.
Step-by-step explanation:
Gearing can be used to increase motor torque at the expense of speed. When a gear system is implemented, it often trades angular velocity for increased force, which translates to an increase in torque. This relationship is due to the mechanical advantage created by the gearing system. By decreasing the size of the lever arm to which the existing force is applied, the force exerted by the motor is amplified but at a reduced speed.
In a motor, when there is an increase in the mechanical load, such as an electric wheelchair climbing a hill, the motor slows down. This slower speed results in a decrease in the back electromotive force (emf), leading to more current flowing through the motor, which in turn increases the torque. The motor can do more work with increased torque, but it is important to ensure that it does not run too slowly to prevent overheating from resistive power loss, characterized by the equation P = I²R. A gearing mechanism again helps to optimize the trade-off between torque and speed to achieve the desired performance without damaging the motor.