How Do You Calculate Power from Torque and Angular Velocity?

[Pablo]

Homework Statement

Motor runs at a rate of four revolutions/sec has a torque of 20. What is it's power.

Homework Equations

T = (2π) / w
f = w / (2π)
w = 2πf

P = T * w
Power = Torque * angular velocity

The Attempt at a Solution

[/B]
T = 20 Nm
f = 4 * 2π = 8π
w = 2π * (8π) = 16π^2

P = 20 * (16π^2) = 3158 Watts

My answer is too big, and I am not sure what I am doing wrong.

 

[gneill]

f = 4 * 2π = 8π
w = 2π * (8π) = 16π^2

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.

 

[Pablo]

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.

Ah okay, so when they say the frequency they mean the angular velocity right. So it'd be 500 watts.

 

[gneill]

Ah okay, so when they say the frequency they mean the angular velocity right. So it'd be 500 watts.

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.

Yes, 500 watts looks good.