# Torque - Work done and Power transmitted

## Work done and power transmitted by constant torque

Sponsored Links

### Work done

Work done is force multiplied with the distance moved by the force and can be expressed as

W = F s (1)

where

W = work done (J, Nm)

F = force (N)

s = distance moved by force (s)

For an angular motion

the work done can be expressed as

W = F θ r

= T θ (2)

where

W = work (Joules)

θ = angle (radians)

r = radius (m)

T = torque or moment (Nm)

### Power transmitted

Power is the ratio between work done and time taken and can be expressed as

P = W / dt

= T θ / dt

= T ω

= 2 π n T (3)

where

P = power (Watts)

dt = time taken (s)

ω = θ / dt = 2 π n = angular velocity (rad/s)

n = speed (rev/s)

**Note!** - a machine must rotate to produce power!

A machine with no rotation can deliver torque - like an electric motor - but since no distance is moved by force no power is produced. As soon as the machine starts to rotate power is produced.

### Example - Required Power

A machine rotating with speed *3000 rev/min (rpm)* consumes *5 kW*. The torque at the shaft can be calculated by modifying (3) to

T = P / 2 π n

= (5 kW) (1000 W/kW) / 2 π (3000 rev/min) / (60 sek/min)

= 15.9 Nm

Sponsored Links

Sponsored Links

## Related Topics

## Related Documents

## Tag Search

- en: torque power work force radians angle distance moved
- es: distancia ángulo de apriete de potencia fuerza de trabajo radianes trasladó
- de: Drehmoment Leistung Arbeitskräfte Radiant Winkelabstand bewegt