ROTATIONAL EQUILIBRIUM AND ROTATIONAL DYNAMICS

Moment of Inertia

The resistance a body exhibits to changes in its rotational speed about an axis when torque is applied. It depends on the body's mass, axis of rotation, and shape and size.

Torque

A measure of the force that causes an object to rotate about an axis. It is a vector quantity whose direction depends on the force's direction relative to the axis. Torque causes angular acceleration in an object.

Static Torque

The force applied to a stationary object that is required to initiate rotation.

Dynamic Torque

The force applied to a rotating object to change its rotational speed.

Angular Acceleration

The rate at which an object's angular velocity changes over time. It becomes harder to achieve when an object has a large moment of inertia.

Rotational Equilibrium

A state in which all torques acting on an object cancel out, resulting in no change in its rotational motion.

Static Equilibrium

A state in which an object remains at rest and experiences no net force or torque.

Role of Torque in Rotational Kinematics

Torque in rotational kinematics is analogous to force in linear kinematics. It is related to angular acceleration through the formula (\tau = I\alpha), where (\tau) is torque, (I) is rotational inertia, and (\alpha) is angular acceleration.