## Dynamics of Rotational Motion – Class 11 | Chapter – 7 | Physics Short Notes Series PDF for NEET & JEE

Dynamics of Rotational Motion: Dynamics of rotational motion is a branch of mechanics that deals with the study of the forces, torques, and motions of objects that rotate about an axis. It involves the application of Newton’s laws of motion to rotating objects, as well as the concepts of torque, moment of inertia, and angular momentum. The dynamics of rotational motion is important in a wide range of fields, including physics, engineering, and astronomy, and is used in the design and analysis of rotating machinery, such as engines, turbines, and motors.

## Dynamics of Rotational Motion

Dynamics of rotational motion refers to the study of the forces and torques that cause objects to rotate about an axis, and the resulting motion of those objects. The basic quantities used to describe the dynamics of rotational motion are:

• Torque: Torque is the rotational equivalent of force. It is the product of the force applied to an object and the perpendicular distance from the axis of rotation to the point where the force is applied. Torque is usually measured in newton-meters (Nm).
• Moment of inertia: Moment of inertia is a measure of an object’s resistance to rotational motion. It depends on the mass and distribution of mass of the object and the axis of rotation. Moment of inertia is usually measured in kilogram-meters squared (kg·m2).

Using these quantities, we can derive the following equations for the dynamics of rotational motion:

Newton’s second law for rotational motion:

τ = Iα

Where,

• τ is the torque applied to an object
• I is the moment of inertia of the object
• α is the resulting angular acceleration of the object.

Kinetic energy of rotational motion:

Krot = ½Iω2

Where,

• Krot is the kinetic energy of the rotating object
• I is the moment of inertia of the object
• ω is the angular velocity of the object.

Work-energy theorem for rotational motion:

τθ = ΔKrot

Where,

• τ is the torque applied to the object
• θ is the angular displacement of the object
• ΔKrot is the change in kinetic energy of the object.

Conservation of angular momentum:

Iω = constant

Where,

• I is the moment of inertia of the object
• ω is the angular velocity of the object.

If there are no external torques acting on the object, then the angular momentum of the object is conserved.

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