Classical Mechanics-Rigid Body Dynamics - Moment of Inertia Tensor (CSIR Physical Sciences): Questions 4 - 5 of 5

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Question number: 4

» Classical Mechanics » Rigid Body Dynamics - Moment of Inertia Tensor

Appeared in Year: 2011

MCQ▾

Question

An annulus of mass M made of a material of uniform density has inner and outer radii ‘a’ and ‘b’ respectively. Its principal moment of inertia along the axis of symmetry perpendicular to the plane of the annulus is: (December)

Choices

Choice (4) Response

a.

12M(b2a2)

b.

12Mπ(b2a2)

c.

12Mb4+a2b2a2

d.

12M(b2+a2)

Passage

In the absence of an applied torque a rigid body with three distances principal moments of inertia given by I1,I2andI3 is rotating freely about a fixed point inside the body. The Euler equations for the components of its angular velocity (ω1,ω2,ω3) are

ω˙1=I2I1I1ω2ω3,ω˙2=(I3I1)I2ω1ω3,ω˙3=I1I2I3ω1ω2 (June)

Question number: 5 (1 of 1 Based on Passage) Show Passage

» Classical Mechanics » Rigid Body Dynamics - Moment of Inertia Tensor

Appeared in Year: 2011

MCQ▾

Question

The constant of motion are –

Choices

Choice (4) Response

a.

I1ω12+I2ω22+I3ω32andω1+ω2+ω3

b.

I1ω12+I2ω22+I3ω32andI12ω12+I22ω22+I32ω32

c.

ω12+ω22+ω32andI1ω1+I2ω2+I3ω3

d.

ω12+ω22+ω32andI12ω12+I22ω22+I32ω32

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