Engineering Questions with Answers - Multiple Choice Questions

# Machine Dynamics MCQ – Effect of Inertia of the Constraint on Torsional Vibrations

1 - Question

A flywheel is mounted on a vertical shaft. The both ends of a shaft are fixed and its diameter is 50 mm. The flywheel has a mass of 500 kg, the modulus of rigidity for the shaft material is 80 GN/m2 and its radius of gyration is 0.5 m. Find the natural frequency of torsional vibrations.
a) 5.32
b) 5.86
c) 5.65
d) 6.66

Explanation: We know that J = πd4/32 = 0.6×10-6 m4
q1 = 56×103
q2 = 84×103
q = 140×103
therefore using the formula for fn
we get fn = 5.32 Hz.

2 - Question

If a mass whose moment of inertia is Ic/3 is placed at the free end and the constraint is assumed to be of negligible mass, then the kinetic energy is ______
a) 1/6 Icω2
b) 1/2Icω2
c) 1/3Icω2
d) 1/12Icω2

Explanation: Kinetic energy is given by the equation
0.5Iω2
inserting Ic/3 in place of I will give kinetic energy as
1/6 Icω2.

3 - Question

If Ic = 125 Kg-m2 and ω= 20 rad/s, calculate the kinetic of the constraint.
a) 8333 J
b) 7333 J
c) 6333 J
d) 9333 J

Explanation: The kinetic energy of the constraint is given by the equation:
K.E = 1/6 Icω2
substituting the value we get
K.E = 8333J.

4 - Question

If Ic = 500 Kg-m2 and ω = 10 rad/s, calculate the kinetic of the constraint.
a) 8333 J
b) 7363 J
c) 4578 J
d) 9333 J

Explanation: The kinetic energy of the constraint is given by the equation:
K.E = 1/6 Icω2
substituting the value we get
K.E = 8333J.

5 - Question

If the mass of the constraint is negligible then what is the kinetic energy of the system?
a) 0
b) Half the value
c) Double the value
d) Infinite

Explanation: If the mass of the constraint is negligible, then the mass moment of inertia will be 0. As a result the expression of the kinetic energy will become 0.

6 - Question

If the mass of the constraint is negligible and a mass is attached at the end of the rod having following values: Ic = 500 Kg-m2 and ω= 10 rad/s, then calculate the kinetic of the constraint system.
a) 8333 J
b) 7363 J
c) 4578 J
d) 9333 J

Explanation: The kinetic energy of the constraint system in the absence of mass of constrant is given by the equation:
K.E = 1/6 Icω2
substituting the value we get
K.E = 8333J.

7 - Question

Free torsional vibrations will occur in a two rotor system only if both rotors have same frequency.
a) True
b) False

Explanation: In a two rotor system the free torsional vibration will occur only if both the rotors have the same frequency of vibration, it follows the following relation between length and mass moment of inertia: L(A)I(A) = L(B)I(B).

8 - Question

Increasing which of the following factor would result in increase of free torsional vibration?