RPM, or, revolutions per minute, is a measure of angular velocity, ω. If I was feeling a little snarky today, I would tell you that the equation for RPM was revolutions/minutes.

Alas, angular velocity is defined by the equation P=τω and ω=v/r, where P is power in watts, τ is torque in newton-meters, v is velocity in meters per second, and r is radius of the rotating body in meters. As you can see in the τω expression, torque is inversely proportional to angular velocity, when considering a system sustained with a constant power P. With a little bit of algebra, you can also note that P=τv/r, which implies that as radius increases, the torque must as well for the same unit of power and linear velocity.

The implications of the inverse relationship between ω and τ are found pretty often in vex with gears. As you increase the radius of one input gear relative to its meshed, driven partner, the angular velocity of the output *increases* by the ratio of the sizes of the gears- while the torque *decreases* by that same factor.

So, simply put, the formula for rpm in vex is i can’t do this anymore

rpm = revolutions/minutes you’re welcome