The mass moment of inertia I of a homogeneous sphere about its diameter is I = (2/5)m R², where m and R are its mass and radius, respectively. Find the dimension of I in terms of the base dimensions of (a) a gravitational [FLT] system and (b) an absolute [MLT] system.

The mass moment of inertia I of a homogeneous sphere about its diameter is I = (2/5)m R², where m and R are its mass and radius, respectively. Find the dimension of I in terms of the base dimensions of (a) a gravitational [FLT] system and (b) an absolute [MLT] system.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.40P

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Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.

Question

The mass moment of inertia I of a homogeneous sphere about its diameter
is I = (2/5)m R², where m and R are its mass and radius, respectively. Find the
dimension of I in terms of the base dimensions of (a) a gravitational [FLT] system
and (b) an absolute [MLT] system.

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