Torque - Work done and Power Transmitted
The work done and power transmitted by a constant torque.
Work done
Work done is the 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 the work done and the time taken and can be expressed as
P = W / dt
= T θ / dt
= T ω
= 2 π n T
= 2 π (nrpm / 60) T
= 0.105 nrpm T (3)
where
P = power (Watts)
dt = time taken (s)
ω = θ / dt = 2 π n = angular velocity (rad/s)
n = speed (rev/s)
nrpm = speed (rev/min, rpm)
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 Torque to produce Power
A machine rotates with speed 3000 rev/min (rpm) and 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 sec/min)
= 15.9 Nm
Related Topics
-
Mechanics
Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
Related Documents
-
Belt Transmissions - Speed and Length of Belts
Calculate length and speed of belt and belt gearing. -
Belts - Power Transmission and Efficiency
Calculate belts power transmission and efficiency -
Conn-Rod Mechanism
The connecting rod mechanism. -
Distance Traveled vs. Speed and Time - Calculator and Chart
Velocity plotted in time used diagram. -
Electric Motors - IEC and NEMA Standard Torques
IEC and NEMA torque classifications of electrical motors. -
Electric Motors - Torque vs. Power and Speed
Electric motor output power and torque vs. rotation speed. -
Electrical Induction Motors - Torque vs. Speed
Full load operating torque vs. break down, pull up and locked rotor torque. -
Elevators - Force and Power
Required force and power to lift an elevator. -
Improvised Torque Wrench
Improvise a torque wrench with a luggage scale. -
Mass Moment of Inertia
The Mass Moment of Inertia vs. mass of object, it's shape and relative point of rotation - the Radius of Gyration. -
Power
Power is the rate at which work is done or energy converted. -
Rotating Shafts - Torque
Torsional moments acting on rotating shafts. -
Shafts Torsion
The torsion of solid or hollow shafts - Polar Moment of Inertia of Area. -
Torque or Moment of Force - Online Converter
Torque or moment - the tendency of a force to rotate an object. -
Work done by Force
Work done by a force acting on an object.
