Mechanical Engineering Principles

9

Torque

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=

Iω^2

2

whereI

is the moment of inertia

• appreciate that torqueT=Iαwhereαis
  the angular acceleration


• calculate torque givenIandα


• calculate kinetic energy givenIandω


• understand power transmission by means
  of belt and pulley


• perform calculations involving torque,
  power and efficiency of belt drives

9.1 Couple and torque

When two equal forces act on a body as shown in
Figure 9.1, they cause the body to rotate, and the
system of forces is called acouple.

F

F d

Figure 9.1

The turning moment of a couple is called a

torque,T. In Figure 9.1, torque =magnitude of

either force×perpendicular distance between the

forces

i.e. T=Fd

The unit of torque is thenewton metre, N m

When a forceF newtons is applied at a radiusr

metres from the axis of, say, a nut to be turned

by a spanner, as shown in Figure 9.2, the torqueT

applied to the nut is given by:T=FrNm

Turning radius, r

Force, F

Moment,M

P

Figure 9.2

Problem 1. Determine the torque when a

pulley wheel of diameter 300 mm has a

force of 80 N applied at the rim.

TorqueT=Fr, where forceF=80 N and radius

r=

300

2

=150 mm= 0 .15 m.

Hence,torque,T=( 80 )( 0. 15 )=12 N m

Problem 2. Determine the force applied

tangentially to a bar of a screw jack at a

radius of 800 mm, if the torque required is

600 N m

Torque,T=force×radius,from which

force=

torque

radius

=

600 N m

800 × 10 −^3 m

=750 N