Explanation: The radius of gyration of a body about an axis is a distance such that its square multiplied by the area gives moment of inertia of the area about the given axis The formula of radius of gyration is given as k2 = I/A

hollow cylinder

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

Radius of gyration or gyradius of a body about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body’s actual distribution of mass, if the total mass of the body were concentrated there

No, radius of gyration of a body depends on axis of rotation and also on distribution of mass of the body this axis

It is not zero, but only a minimum when axis is passing through CM This is because there are particles of physical mass that are away from the mathematically defined line axis through CM, as ∫r2dm=k2m

The smallest value of the radius of gyration is used for structural calculations as this is the plane in which the member is most likely to buckle Square or circular shapes are ideal choices for columns as there is no smallest radius of gyration They have the same value because the radius is constant

We can define the radius of gyration as the imaginary distance from the centroid at which the area of cross-section is imagined to be focused at a point in order to obtain the same moment of inertia It is denoted by k

Radius of gyration is generally defined as the distance from the axis of rotation to a point where total mass of any body is supposed to be concentrated, so that the moment of inertia about the axis may remain same Simply, gyration is the distribution of the components of an object

Answer No, Radius of gyration is not a vector quantity Its a scalar quantity

So finally, the dimensional formula of the radius of gyration will be written as: [M0LT0] The power of zero on the dimension of the mass and time shows that the mass and the time dimensions are zero for the radius of gyration So, the correct answer is “Option C”

Physical significance: The radius of gyration is less if I is less ie, if the mass is distributed close to the axis ; and it is more if I is more , ie, if the mass is distributed away from the axis Thus, it gives an idea about the distribution of mass about the axis of rotation

meter

Moment of inertia is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation Moment of Inertia is also known as the angular mass or rotational inertia

Explanation: The modulus of section may be defined as the ratio of moment of inertia to the distance to the extreme fibre It is denoted by Z Z= I/y ; For rectangular section, I = bd3/12 & y = d/2

One radian is the measure of a central angle subtended by an arc that is equal in length to the radius of the circle When no symbol is used, radians are assumed When degrees are the unit of angular measure, the symbol “°” is written Note that the radian is a derived unit in the International System of Units (SI)

Well if an entire circle is 2π⋅r half will be only π⋅r but half a circle corresponds to 180° ok Perfect Your arc length, for half circle, we saw that was π⋅r dividing by r you get π radians!!!!!!

Angles measured in radians are considered to be dimensionless because the radian measure of angles is defined as the ratio of two lengths θ=sr (where s is some arc measuring s-units in length, and r is the radius) however the degree measure is not defined in this way and it is said to be dimensionless too

A radian is a unit of measurement for angles defined by the ratio of the length of the arc of a circle to the radius of that circle One radian is the angle at which that ratio equals one (see the first diagram)

Calculus is always done in radian measure Degree (a right angle is 90 degrees) and gradian measure (a right angle is 100 grads) have their uses Radians make it possible to relate a linear measure and an angle measure A unit circle is a circle whose radius is one unit

or, equivalently, 180∘=π radians So one radian is equal to 180π degrees, which is approximately 573∘ Since many angles in degrees can be expressed as simple fractions of 180, we use π as a basic unit in radians and often express angles as fractions of πSolution

Radians are often used instead of degrees when measuring angles In degrees a complete revolution of a circle is 360◦, however in radians it is 2π If an arc of a circle is drawn such that the radius is the same length as the arc, the angle created is 1 Radian (as shown below)

Answers (To Check Your Work): (a) pi/6 or 052 Radians