What is the physical meaning of radius of gyration?
Radius of gyration is defined as the distance from the axis of rotation to a point where total mass of the body is supposed to be concentrated. 1. It the particles of body are distributed lose to axis of rotation,the radius gyration is less.
What is the unit of mass moment of inertia *?
The unit of moment of inertia is a composite unit of measure. In the International System (SI), m is expressed in kilograms and r in metres, with I (moment of inertia) having the dimension kilogram-metre square.
What is unit of product of inertia?
The amount of torque needed to cause any given angular acceleration (the rate of change in angular velocity) is proportional to the moment of inertia of the body. Moment of inertia may be expressed in units of kilogram metre squared (kg. · m2) in SI units and pound-foot-second squared (lbf.
Is product of inertia always positive?
Values for center of gravity can be either positive or negative, and in fact their polarity depends on the choice of reference axis location. Values for moment of inertia can only be positive, just as mass can only be positive.
What is product of inertia used for?
The concept of the product of inertia plays an important role in the study of the rotational motion of bodies. The magnitudes of the pressure forces on the bearings on which the axial shaft of a body rotates depend on the values of the products of inertia.
Can a product of inertia be negative?
Product of inertia can be positive or negative value as oppose the moment of inertia. The calculation of the product of inertia isn’t different much for the calculation of the moment of inertia.
What is cross product of inertia?
In Eq.(B.14) above, the mass moment of inertia was expressed in terms of orthogonal projection as , where . In terms of the vector cross product, we can now express it as. where is the distance from the rotation axis out to the point (which equals the length of the vector ).
How do you add moment of inertia?
Moments of inertia for the parts of the body can only be added when they are taken about the same axis. The moments of inertia in the table are generally listed relative to that shape’s centroid though. Because each part has its own individual centroid coordinate, we cannot simply add these numbers.
What is the sum of moments?
Moments of components (Varignon’s Theorem) In equilibrium, the sum of moments about any point is zero. “The moment caused by the resultant force (of some system of forces) about some arbitrary point is equal to the sum of the moments due to all of the component forces of the system.”