The discussion focuses on calculating power from torque and angular velocity using the formula P = T * ω. The motor operates at four revolutions per second with a torque of 20 Nm. The correct interpretation of frequency as angular velocity is crucial; thus, the angular velocity is calculated as ω = 4 * 2π, leading to a power output of 500 watts. Miscalculations arose from incorrectly applying the conversion of revolutions to radians.
PREREQUISITESStudents in physics, mechanical engineers, and anyone involved in the design or analysis of rotating machinery will benefit from this discussion.
I think you're confusing frequency and angular frequency. You've ended up multiplying the given revolutions per second by 2π twice.Pablo said:f = 4 * 2π = 8π
w = 2π * (8π) = 16π^2
Ah okay, so when they say the frequency they mean the angular velocity right. So it'd be 500 watts.gneill said:I think you're confusing frequency and angular frequency. You've ended up multiplying the given revolutions per second by 2π twice.
One revolution is 2π radians of angular displacement. So 4 revolutions per second is 4 x 2π radians per second and is the angular velocity, ω.
When they say "frequency" they mean "events per unit time". If the "events" in question happen to be rotations then you can interpret them as 2π radian angular displacements. From there you can calculate the angular velocity by multiplying the frequency by 2π.Pablo said:Ah okay, so when they say the frequency they mean the angular velocity right. So it'd be 500 watts.