SECTION 3 - ROTATIONAL EFFECTS OF FORCES
3.1 MOMENT OF A FORCE - so far we have looked at forces which tend, or try, to move bodies in
a straight line in the direction of application of the force. Now a force may also tend to ROTATE a
body about an AXIS and this rotational tendency is known as the MOMENT (M) OF THE FORCE.
NOTE – moment is also referred to as TORQUE.
Moment of = Size of x Perpendicular distance from axis of
Force Force rotation to line of action of force ()
M = Fxd ( often called the MOMENT ARM)
Units: newtons x Metres = N m
EXAMPLE 10 – a force of 500 newtons is applied at the end of a spanner. Determine the turning
moment in each of the four situations shown.
NOTE – for a constant force the turning moment decreases as the moment arm decreases.
– it can be concluded from (d) in the above example that there is no turning effect if
the line of action of the force passes through the axis of rotation.
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, PROBLEM 12 – a torque wrench is to be used to tighten a nut and bolt to a torque level of 225
Nm. The torque wrench is 450 mm long and is being used as shown in diagram (a) in example 10.
Determine the force F that must be applied at the end of the wrench. (Answer: 500 N)
PROBLEM 13 – a spanner 250 mm long is used to tighten a nut and bolt in the same way as
shown in diagram (b) in example 10. If a torque level of 180 Nm is required determine the length of
the moment arm d in mm and the magnitude of the force F in Newtons.
(Answer: d = 216.51 mm and F = 831 N)
PROBLEM 14 – a spanner is used to tighten a nut and bolt in the same way as shown in diagram
(a) in example 10. Friction between the nut and bolt creates a friction torque of 18 N m. If the
spanner is 270 mm long determine the minimum force (F) required to overcome this resistance.
(Answer: 67 N)
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3.1 MOMENT OF A FORCE - so far we have looked at forces which tend, or try, to move bodies in
a straight line in the direction of application of the force. Now a force may also tend to ROTATE a
body about an AXIS and this rotational tendency is known as the MOMENT (M) OF THE FORCE.
NOTE – moment is also referred to as TORQUE.
Moment of = Size of x Perpendicular distance from axis of
Force Force rotation to line of action of force ()
M = Fxd ( often called the MOMENT ARM)
Units: newtons x Metres = N m
EXAMPLE 10 – a force of 500 newtons is applied at the end of a spanner. Determine the turning
moment in each of the four situations shown.
NOTE – for a constant force the turning moment decreases as the moment arm decreases.
– it can be concluded from (d) in the above example that there is no turning effect if
the line of action of the force passes through the axis of rotation.
24
, PROBLEM 12 – a torque wrench is to be used to tighten a nut and bolt to a torque level of 225
Nm. The torque wrench is 450 mm long and is being used as shown in diagram (a) in example 10.
Determine the force F that must be applied at the end of the wrench. (Answer: 500 N)
PROBLEM 13 – a spanner 250 mm long is used to tighten a nut and bolt in the same way as
shown in diagram (b) in example 10. If a torque level of 180 Nm is required determine the length of
the moment arm d in mm and the magnitude of the force F in Newtons.
(Answer: d = 216.51 mm and F = 831 N)
PROBLEM 14 – a spanner is used to tighten a nut and bolt in the same way as shown in diagram
(a) in example 10. Friction between the nut and bolt creates a friction torque of 18 N m. If the
spanner is 270 mm long determine the minimum force (F) required to overcome this resistance.
(Answer: 67 N)
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