(^588) A Textbook of Engineering Mechanics
Example 29.1. A body A of mass 10 kg, with its c.g. 250 mm from the axis of rotation, is to
be balanced by another body B of mass 4 kg. Find the radius at which the centre of gravity of mass
B should be placed.
Solution. Given : Mass of body A (m 1 ) = 10 kg ; Radius of rotating body A (r 1 ) = 250 mm
and mass of body B (m 2 ) = 4 kg
Let r 2 = Radius at which the c.g. of mass B should be placed.
We know that m 1 r 1 = m 2 r 2
∴
11
2
2
10 250
625 mm
4
mr
r
m
×
== = Ans.
29.6.BALANCING OF A SINGLE ROTATING MASS BY TWO MASSES IN
DIFFERENT PLANES
In the previous article, we have discussed the method of balancing of a single rotating body by
another mass in the same plane. But sometimes, it is not possible to introduce one balancing mass in
the same plane of rotation. In such a case, two balancing masses are provided in two different planes
(one on either side of the body to be balanced). In such a case, the following two conditions should be
satisfied in order to balance the body completely :
- The resultant of all the centrifugal forces (or assumed forces) must be equal to zero.
- The resultant of moments of all the centrifugal forces (or assumed forces) must be equal
to zero. Or in other words, the c.g. of the balancing bodies should lie on the line of action
of the body to be balanced.
Fig. 29.2.
Now consider the body A, attached to a rotating shaft. In order to balance it, let us attach
two bodies B and C as shown in Fig. 29.2 (a) and (b).
Let m 1 = Mass of the rotating body A,
r 1 = Radius of the rotating body (i.e. distance between the centre
of the mass A and the axis of rotation).
m 2 , r 2 = Corresponding values for the balancing body B.