Engineering Mechanics

Chapter 31 : Kinetics of Motion of Rotation „„„„„ 629

Fig. 31.7. Flywheel.

Similarly, moment of the force for particles of mass m 2

=m 2 r 22 α

∴ Total moment for all the particles (i.e. torque)

T=Σ m 1 r 12 α = α Σ m 1 r 12

But Σm 1 r 12 is the* mass moment of inertia (if r is taken as the radius of gyration). Therefore

T=Iα

31.16.RELATION BETWEEN KINETICS OF LINEAR MOTION AND KINETICS
OF MOTION OF ROTATION
Following are the relations between the kinetics of linear motion and kinetics of motion of
rotation :

S.No. Linear motion Motion of relation

1. Mass (M) Moment of inertia (I)


2. Force (P) Torque (T)


3. Force equation (P = Mα) Torque equation (T = Iα)


4. Linear motion (v) Angular motion (ω)


5. Linear momentum (Mv) Angular momentum (Iω)


6. Linear kinetic energy Rotational kinetic energy
   2

2

Mv

E

⎛⎞

⎜⎟⎜⎟=

⎝⎠

2

2

I

E

⎛⎞ω

⎜⎟⎜⎟=

⎝⎠

7. Distance traversed (s) Angular displacement (θ)


8. Work done (W) = Ps Work done (W) = T × θ

31.17.FLYWHEEL

It is a circular heavy wheel, generally, fitted to a rotating engine shaft to control variation
in its speed during each cycle. Strictly speaking, it serves as a reservoir
to store and restore energy by virtue of its inertia. Or in other words, it
shares its energy during the period, when the supply of energy is more
than the requirement; and releases it during the period when the supply
of energy is less than the requirement.

It will be interesting to know that in all types of steam engines
and I.C. engines, the power generated and supplied to the shaft is vari-
able. As a matter of fact, the flywheel speed increases when it absorbs
energy and decreases when it releases energy. Thus a flywheel is de-
signed to keep the engine speed within the prescribed limits during each
cycle.

The difference between the maximum and minimum speeds of an engine during a cycle is
called the fluctuation of speeds. And the ratio of fluctuation of speed, to the mean engine speed, is
called coefficient of fluctuation of speed.

Let M = Mass of the flywheel,

I = Mass moment of inertia of the flywheel,

N 1 = Maximum speed of flywheel during a cycle,