What is the radius of gyration of a thin uniform rod having a length L about a perpendicular axis passing through its centre?

The radius of gyration of a uniform rod of length L about an axis passing through its centre of mass is. K=√Im=√(mL2/12)m=L2√3.

What is the radius of gyration of a thin rod?

In other words, the radius of gyration is calculated as the perpendicular distance noted from the rotational axis to the point mass. The actual radial distance between the rotational axis and the point where the body mass is joined to it keeps the inertia of a rotating object fixed.

What will be the radius of gyration of a thin uniform disc of radius 4 cm about its diameter?

Correct Answer is: (c) 2 cm or k = r/2 = 4 cm/2 = 2 cm.

How do you find the radius of gyration of a rod?

Initially, calculate the moment of inertia using its formula and then substitute it in the formula for radius of gyration. This obtained value will be the radius of gyration of the rod of mass m and length 2l. Hence, the radius of gyration of the rod is 2l√3.

What is the radius of gyration of a rod of length L?

The radius of gyration of a uniform rod of length l, about an axis passing through a point 1/4 away from the centre of rod, and perpendicular to it, is: (A) √748l. So, to find the radius of gyration, we can use the direct formula for the radius of gyration which is dependent on the moment of inertia and mass of the rod …

What is parallel axis theorem and perpendicular axis theorem?

The parallel axis theorem states that, the moment of inertia of a body about any axis is equal to the moment of inertia about parallel axis through its center of mass plus the product of the mass of the body and the square of the perpendicular distance between the two parallel axes. This is the parallel axis theorem.

What is the formula of radius of gyration K?

Mechanics: Here radius of gyration about an axis of rotation is calculated using mass moment of inertia and its formula is given by relation, k=√IM(1) (1) k = I M This equation (1) is the radius of gyration formula for mass moment of inertia.

What do you mean by radius of gyration K?

radius of gyration. noun. a length that represents the distance in a rotating system between the point about which it is rotating and the point to or from which a transfer of energy has the maximum effect. Symbol: k or r . In a system with a moment of inertia I and mass m, k ² = I / m.

What is the radius of gradation of uniform rod whose length is L and passes through the Centre of mass?

The radius of gyration of an uniform rod of length L about an axis passing through its centre of mass and perpendicular to its length is. (a) K=√IM=√ML2/12M=L√12.

What is the moment of inertia of a thin rod of mass m and length L about an axis perpendicular to the rod at a distance L 4 from one end?

The moment of inertia of a thin uniform rod of mass M and length L about an axis perpendicular to its length is gML2​.

Why is it useful to define radius of gyration?

The physical significance of defining the radius of gyration is as follow, The mass and radius of gyration of the body about a given axis of rotation gives the value of its moment of inertia about the same axis, even if we do not know the actual shape of the body.