Rotational Kinetic Energy and Moment of Inertia Quiz

The radius of gyration of a body about its given axis is defined as the distance between the axis of rotation and a point at which the whole mass of the body is supposed to be concentrated, so as to possess the same moment of inertia as that of body about the same axis.

The physical significance of the radius of gyration is that it represents the point at which the entire mass of the body can be concentrated to have the same effect on moment of inertia as the actual body about the given axis of rotation.

Rotational kinetic energy of the object is the sum of individual translational kinetic energies.

<p>The moment of inertia depends upon the mass of the object and how that mass is distributed from or around the given axis of rotation.</p> Signup and view all the answers

<p>If K is the radius of gyration for an object, I = MK² is the moment of inertia of that object.</p> Signup and view all the answers

<p>Rotational kinetic energy = 1/2Iω², where I is the moment of inertia and ω is the angular speed.</p> Signup and view all the answers

<p>Moment of inertia of a rigid body is the sum of the product of the mass of each particle and the square of its perpendicular distance from the axis of rotation.</p> Signup and view all the answers

<p>SI unit: kgm², Dimensions: [M L² T⁻²].</p> Signup and view all the answers

<p>The kinetic energy of a body rotating with a uniform angular speed is given by the sum of the translational kinetic energies of all the particles in the body.</p> Signup and view all the answers

<p>The translational kinetic energy of a particle in a rotating body is given by (1/2)mv², where m is the mass of the particle and v is its linear speed.</p> Signup and view all the answers

<p>Angular speed is the rate of change of angular displacement with respect to time. Radius of gyration is the distance from the axis of rotation at which the total mass of the body is considered to be concentrated to calculate moment of inertia.</p> Signup and view all the answers

<p>Rotational kinetic energy is the energy possessed by a rotating body due to its rotational motion. It is given by the sum of the rotational kinetic energies of all the particles in the body.</p> Signup and view all the answers

<p>The moment of inertia of an object about any axis is the sum of its moment of inertia about an axis parallel to the given axis, and passing through the centre of mass, and the product of the mass of the object and the square of the distance between the two axes.</p> Signup and view all the answers

<p>I = I₁ + Mh²</p> Signup and view all the answers

<p>Moment of inertia can be calculated as the sum of the moment of inertia about an axis parallel to the given axis and passing through the centre of mass, and the product of mass and the square of the distance between the two axes.</p> Signup and view all the answers

<p>The proof involves considering an object of mass M, with an axis MOP being any axis passing through point O, and another axis ACB passing through the centre of mass C of the object, parallel to the axis MOP, and at a distance h from it.</p> Signup and view all the answers

<p>The perpendicular axes theorem provides a mathematical tool to calculate the moment of inertia of an object about any axis by using the known moment of inertia about an axis passing through the centre of mass and parallel to it.</p> Signup and view all the answers