The difference in velocity between two gears is determined by the gear ratio, which is the ratio of the number of teeth on the driving gear to the number of teeth on the driven gear.
When two gears mesh together, their teeth engage and transfer rotational motion from one gear to the other. The relationship between the rotational velocities (or angular velocities) of the gears is inversely proportional to their gear ratio.
Let's denote the angular velocity of the driving gear as ω₁ and the angular velocity of the driven gear as ω₂. The gear ratio (GR) is given by:
GR = ω₁ / ω₂
From this equation, we can rearrange it to solve for the difference in velocity:
Difference in velocity = |ω₁ - ω₂|
If the gear ratio is greater than 1, the driven gear will rotate at a slower angular velocity than the driving gear, resulting in a positive difference in velocity. If the gear ratio is less than 1, the driven gear will rotate at a faster angular velocity, resulting in a negative difference in velocity.
It's important to note that the velocity referred to here is angular velocity, measured in radians per unit of time (e.g., radians per second). The linear velocity at any point on a gear's circumference can be determined by multiplying the angular velocity by the radius of that point.