Скачать или смотреть A solid sphere of mass m and radius R has Moment of Inertia about an axis passing through the centre

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Rotational Kinematics
In rotational kinematics, we will investigate the relation between kinematical parameters of rotation. We shall now revisit angular equivalents of the linear quantities: position, displacement, velocity and acceleration which we have already dealt in a circular motion.
Axis of Rotation
A rigid body of an arbitrary shape in rotation about a fixed axis (axis that does not move) called axis of rotation or rotation axis
Types of Motion involving Rotation
Rotation about a fixed axis (Pure rotation)
Rotation about an axis of rotation (Combined translational and rotational motion)
Rotation about an axis in the rotation (rotating axis – out of the scope of JEE)
Rotation About a Fixed Axis
Rotation of a ceiling fan, opening and closing of the door, rotation of our planet, rotation of hour and minute hands in analogue clocks are few examples of this type.
Rotation about an axis of rotation
Rolling is an example of this category. Arguably, the most important application of rotational physics is in the rolling of wheels and wheels like objects as our world now is filled with automobiles and other rolling vehicles.

Rolling Motion of a body is a combination of both translational and rotational motion of a round-shaped body placed on a surface. When a body is set in a rolling motion, every particle of the body has two velocities – one due to its rotational motion and the other due to its translational motion (of the centre of mass), and the resulting effect is the vector sum of both velocities at all particles
Kinetic Energy of Rotation
The rapidly rotating blades of a table saw machine and the blades of a fan certainly have kinetic energy due to the rotation. If we apply the familiar equation to the saw machine as a whole, it would give us kinetic energy of its centre of mass only, which is zero.
What is Torque
Torque is a rotational analogue of force and expresses the tendency of a force applied to an object that causes the object to rotate about a given point.
Rotational Equilibrium
The centre of mass of a body remains in equilibrium if the total external force acting on the body is zero. This follows from the equation F = Ma.

Similarly, a body remains in rotational equilibrium if the total external torque acting on the body is zero.Therefore a body in rotational equilibrium must either be in rest or rotation with constant angular velocity.

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What is Moment of Inertia?
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. Or in more simple terms, it can be described as a quantity that decides the amount of torque needed for a specific angular acceleration in a rotational axis. Moment of Inertia is also known as the angular mass or rotational inertia. The SI unit of moment of inertia is kg m2.
Moment of Inertia Formula
What are the Factors on which Moment of Inertia Depends?
Moment of Inertia of a System of Particles
Moment of Inertia of Rigid Bodies
Moment of Inertia of a Rectangular Plate about a Line Parallel to an Edge and Passing through the Centre
Moment of Inertia of a Uniform Circular Plate about its Axis
Moment of Inertia of thin Spherical Shell or Uniform Hollow Sphere
Moment of Inertia of a uniform solid sphere
Parallel Axis Theorem
The moment of inertia of an object about an axis through its centre of mass is the minimum moment of inertia for an axis in that direction in space.
Radius of Gyration
Moment Of Inertia Of Cylinder Moment Of Inertia Of A Solid Cylinder
Moment Of Inertia Of A Hollow Cylinder Moment Of Inertia Of Rectangular Section
Moment Of Inertia Of Rectangular Plate Moment Of Inertia Of A Disc
Moment Of Inertia Of Annular Disc Moment Of Inertia Of A Sphere
Moment Of Inertia Of A Hollow Sphere Moment Of Inertia Of A Rod
Moment Of Inertia Of A Triangle Moment Of Inertia Of Ellipse
Moment Of Inertia Of A Cone Moment Of Inertia Of Solid Cone
Moment Of Inertia Of Hollow Cone Moment Of Inertia Of A Square
Moment Of Inertia Of A Circle Moment Of Inertia Of A Quarter Circle
Moment Of Inertia Of Semicircle Moment Of Inertia Of A Ring
Moment Of Inertia Of A Cube Moment Of Inertia Of Flywheel