ABSTRACT
The unit of torque is the newton metre, N m When a force F newtons is applied at a radius r metres from the axis of, say, a nut to be turned by a spanner,
At the end of this chapter you should be able to: • define a couple • define a torque and state its unit • calculate torque given force and radius • calculate work done, given torque and angle turned through • calculate power, given torque and angle turned through
• appreciate kinetic energy = ωI 2
where I is the moment of inertia
• appreciate that torque T = Iα where α is the angular acceleration • calculate torque given I and α • calculate kinetic energy given I and ω • understand power transmission by means of belt and pulley • perform calculations involving torque, power and efficiency of belt drives
When two equal forces act on a body as shown in Figure 11.1, they cause the body to rotate, and the system of forces is called a couple. The turning moment of a couple is called a torque, T. In Figure 11.1, torque = magnitude of either force × perpendicular distance between the forces,
i.e. T = Fd
Why it is important to understand: Torque This chapter commences by defining a couple and a torque. It then shows how the energy and work done can be calculated from these terms. It then derives the expression which relates torque to the product of mass moment of inertia and the angular acceleration. The expression for kinetic energy due to rotation is also derived. These expressions are then used for calculating the power transmitted from one shaft to another, via a belt. This work is very important for calculating the power transmitted in rotating shafts and other similar artefacts in many branches of engineering. For example, torque is important when designing propeller shafts for ships and automobiles, and also for helicopters, etc.
