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# Machine Dynamics MCQ– Effect of Gyroscopic Couple on a Disc Fixed Rigidly at a Certain Angle to a Rotating Shaft

In the figure given below, the moment of inertia about polar axis OP is _______

a) mr^{2}/2

b) mr^{2}

c) 2mr^{2}

d) 4mr^{2}

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Answer: a

Explanation: In the figure given above, if m is the mass of the disk and r is the radius, then the moment of inertia about the axis OP is given by mr2/2.

When seen from the top, the gyroscopic couple acting on the disc will act in the clockwise direction.

a) True

b) False

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Answer: b

Explanation: When seen from the top, the gyroscopic couple acting on the disc will act in the anti-clockwise direction.

In the figure given below, the moment of inertia about diametral axis is _______

a) m(l^{2}/12 + r^{2}/4)

b) m(l^{2}/6 + r^{2}/4)

c) m(l^{2}/12 + r^{2}/2)

d) m(l^{2}/12 + r^{2})

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Answer: a

Explanation: If m is the mass, l is the length and r is the radius of the disc, then the moment of inertia about the diametral axis is given by m(l^{2}/12 + r^{2}/4).

If the length of the disc is negligible, then what will be the moment of inertia about the diametral axis?

a) mr^{2}/4

b) mr^{2}

c) mr^{2}/2

d) 2mr^{2}

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Answer: a

Explanation: If m is the mass, l is the length and r is the radius of the disc, then the moment of inertia about the diametral axis is given by m (l^{2}/12 + r^{2}/4), if l is negligible then the expression becomes

mr^{2}/4.

If the length and radius of the disc is same them moment of inertia is more about which axis?

a) Polar

b) Diametral

c) Shaft

d) Center

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Answer: a

Explanation: If the length and radius are same then the moment of inertia will be more about the polar axis. Mr^{2}/2 as compared to mr^{2}/3.

From the following data calculate the gyroscopic couple on the bearing in N-m.

Mass of disc = 30 Kg, diameter = 60 cm

Rotation speed = 1200 rpm

Angle between disc and a plane 90 degree to the axis of shaft = 1°

a) 180

b) 186

c) 190

d) 196

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Answer: b

Explanation: ω = 125.7 rad/s

Couple acting on the bearings

= mω^{2}r^{2}/8 sin2θ

substituting the values we get

C = 186 N-m.

If the rotation speed of the disc is increased to 2 times and the mass is reduced to half, overall the Couple acting on bearings will increase.

a) True

b) False

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Answer: a

Explanation: If the rotation speed of the disc is increased to 2 times and the mass is reduced to half, overall the Couple acting on bearings will increase as couple on bearing depends on the relation

mω^{2}r^{2}/8 sin2θ, hence it will increase by two times.