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 can't produce power without rotation - no distance moved by force.

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

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