Torque - Work done and Power transmitted

Work done and power transmitted by constant torque

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

force torque moment work power

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 

Related Topics

  • Mechanics - Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects

Related Documents

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