Identify the correct statement for the rotational motion of...

Identify the correct statement for the rotational motion of a rigid body $\{A\}$ Individual particles of the body do not undergo accelerated motion \{B \} The centre of mass of the body remains unchanged. \{C\} The centre of mass of the body moves uniformly in a circular path \{D\} Individual particle and centre of mass of the body undergo an accelerated motion.

Identify the correct statement for the rotational motion of a rigid body
$\{A\}$ Individual particles of the body do not undergo accelerated motion
\{B \} The centre of mass of the body remains unchanged.
\{C\} The centre of mass of the body moves uniformly in a
circular path
\{D\} Individual particle and centre of mass of the body
undergo an accelerated motion.

Key Concepts

Rotational Motion

Rotational motion refers to the movement of a body where all particles follow concentric circular paths about a fixed axis. In this type of motion, even if the speed of the particles remains constant, their velocity changes due to the continual change in the direction of the motion, resulting in centripetal (radial) acceleration.

Rigid Body Dynamics

A rigid body is defined as an object in which the distances between any two constituent particles remain constant over time, meaning it does not deform. This property simplifies the analysis of both translational and rotational motion, as the internal constraints allow the body to be treated as a single entity with its mass concentrated at the center of mass for translational motion, while rotation is considered about a fixed axis.

Center of Mass Motion

The center of mass is the weighted average position of all the mass in a body and is the point at which external forces can be considered to act for the purpose of translational motion. In rotational dynamics, the motion of the center of mass, whether at rest or moving uniformly, is an important consideration, as it affects how the overall motion of the body is analyzed in combination with its rotation.

Accelerated Motion in Rotational Dynamics

Even when a rigid body rotates at a constant angular speed, the individual particles undergo accelerated motion due to centripetal acceleration. This acceleration is directed towards the axis of rotation and is essential in maintaining the circular paths of the particles. Additionally, any translation of the body’s center of mass may involve acceleration if forces are applied.

Transcript

Please give Ace some feedback