166 MECHANICAL ENGINEERING PRINCIPLES

But

∑

mr^2 =I

Therefore,

kinetic energy (in rotation)=^12 Iω^2 (J)

whereI=the mass moment of inertia about the
point of rotation
and ω=angular velocity.

Problem 28. Calculate the kinetic energy of

a solid flat disc of diameter 0.5 m and of a

uniform thickness of 0.1 m, rotating about its

centre at 40 rpm. Take the density of the

material as 7860 kg/m^3.

Angular velocity,

ω= 2 π

rad

rev

× 40

rev

min

×

1 min

60 s

= 4 .189 rad/s

From Table 13.1, page 150,

I=ρ×πR^2 ×t×

R^2

2

= 7860

kg

m^3

×π× 0. 252 m^2

× 0 .1m×^0.^25

(^2) m 2
2
i.e. I= 4 .823 kg m^2
Hence,kinetic energy

1
2
Iω^2 =
1
2
× 4 .823 kg m^2 ×( 4. 189 )^2
1
s^2
= 42 .32 J.
Now try the following exercises
Exercise 72 Further problems on kinetic
energy in rotation

1. Calculate the kinetic energy of a solid flat
   disc of diameter 0.6 m and of uniform
   thickness of 0.1 m rotating about its cen-
   tre at 50 rpm. Take the density of the disc
   material as 7860 kg/m^3. [137.1 J]
   2. If the disc of Problem 1 had a hole in its
   centre of 0.2 m diameter, what would be
   its kinetic energy? [135.4 J]
   3. If an annulus of external diameter 0.4 m
   and internal diameter 0.2 m were rotated
   about its centre at 100 rpm, what would
   be its kinetic energy? Assume the uniform
   thickness of the annulus is 0.08 m and the
   density of the material is 7860 kg/m^3.
   [81.2 J]

Exercise 73 Short answer questions on

work, energy and power

1. Define work in terms of force applied
   and distance moved.


2. Define energy, and state its unit.


3. Define the joule.


4. The area under a force/distance graph
   represents......


5. Name five forms of energy.


6. State the principle of conservation of
   energy.


7. Give two examples of conversion of heat
   energy to other forms of energy.


8. Give two examples of conversion of
   electrical energy to other forms of
   energy.


9. Give two examples of conversion of
   chemical energy to other forms of
   energy.


10. Give two examples of conversion of
    mechanical energy to other forms of
    energy.


11. (a) Define efficiency in terms of energy
    input and energy output.
    (b) State the symbol used for
    efficiency.


12. Define power and state its unit.


13. Define potential energy.


14. The change in potential energy of a
    body of massmkg when lifted verti-
    cally upwards to a heighthmisgiven
    by......


15. What is kinetic energy?