Which formula describes the relationship between output and input speed in a pulley system?

The formula that describes the relationship between output and input speed in a pulley system is based on the concept of velocity ratio, which relates the speeds of the input and output components of the system. In a pulley system, the speed of the output is determined by dividing the speed of the input by the velocity ratio, which essentially accounts for the mechanical advantage provided by the system.

This relationship holds because the velocity ratio quantifies how much the input speed is altered to produce the output speed. For instance, if you have a pulley system where the input speed is greater and the velocity ratio reflects the mechanical advantage gained, the output speed will consequently be less. This illustrates the trade-off between speed and torque in mechanical systems, allowing for a clearer understanding of how pulleys can change motion parameters.

In contrast, the other choices do not accurately reflect the mechanics of a pulley system as defined in physics and engineering principles.