A particle is an idealized point mass with no size, used to simplify the study of motion.

A rigid body is an object with a definite shape in which the distances between its particles do not change under force.

Translational motion occurs when all parts of an object move together in the same direction and distance.

Rotational motion occurs when an object rotates around an axis, with different parts moving in circular paths.

Angular displacement (θ) = Arc length (s) / Radius (r).

The axis of rotation is the line around which a rigid body rotates; each particle moves in a circle about this axis.

A particle located on the axis of rotation does not move and remains stationary while the body rotates.

Precession is the phenomenon where the axis of a spinning object, like a top, moves in a circular motion around a vertical.

Rolling motion combines translational motion and rotational motion, exemplified by a wheel moving down an incline.

In pure translational motion, all particles move at the same velocity, while in rolling motion, particles have different velocities based on their distance from the axis.

Torque is a measure of the rotational force applied to an object, calculated as Torque (τ) = Force (F) x Distance (r) from the pivot.

A ceiling fan rotates around a fixed axis, with blades moving in circular paths while the pivot point remains stationary.

Linear velocity (v) of a point on a rotating body can be calculated as v = r × ω, where r is the radius and ω is the angular velocity.

Students often overlook that no real body is perfectly rigid, as they can deform under force, but can be approximated as rigid in many cases.

A fixed axis of rotation does not move, while a moving axis changes position, e.g., a fan oscillating horizontally.

Angular velocity (ω) is defined as ω = Δθ / Δt, where Δθ is the change in angular displacement over time Δt.

An example is a book sliding across a table, where all parts move uniformly in one direction.

External forces can create torque, changing the rotational motion and angular momentum of a rigid body.