HC Verma for Class 11 Physics Chapter 10:Rotational Mechanics

In the chapter "Rotational mechanics", various concepts like Kinematics, Rotational Dynamics, Angular Momentum, Angular Impulse, Moment of Inertia have been discussed. Initially, the rotation of a rigid body about a given fixed line and axis of rotation have been explained briefly.

Next, the concept of kinematics has been detailed. Relation between the Linear Motion of a Particle of a Rigid Body and its Rotation is provided. Finally, the concept of Angular momentum, the principle of conservation of angular momentum and angular impulse, has been discussed. The chapter also discusses how the kinetic energy of a rigid body rotating about a given axis can be calculated. The power delivered and work done by the torque and the formula for the Moment of inertia of a system has been stated.

In the section titled "Moment of Inertia of Continuous Mass Distributions", Moment of inertia of the uniform rod about a perpendicular bisector, Moment of inertia of a rectangular plate about a line parallel to an edge and passing through the centre, Moment of inertia of a circular ring about its axis (the line perpendicular to the plane of the ring through its centre), Moment of inertia of a uniform circular plate about its Axis, Moment of inertia of a hollow cylinder about its Axis, Moment of inertia of a uniform solid cylinder about its Axis, Moment of inertia of a uniform hollow sphere about a diameter and Moment of inertia of a uniform solid sphere about a diameter have been explained in a detailed manner.

Two important theorems on the Moment of inertia are the Theorem of Parallel Axes and the Theorem of Perpendicular Axes. It is worth noting that these theorems are only applicable to plane bodies. Then the theorem states that I_z = I_x + I_y.

The radius of gyration k of a body about a given line is defined by the equation I = Mk² where I is its Moment of inertia about the given line and M is its total mass. Further, Combined rotation and translation, the body's kinetic energy and angular momentum in combined rotation and translation have been discussed.

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