Q.When a disc rotates with uniform angular velocity, which of the following is not true?

The key idea here is the definition of uniform angular velocity.

Angular velocity, denoted by $\vec{\omega}$, is a vector quantity. When a disc rotates with uniform angular velocity, it means that both the magnitude (angular speed) and the direction of the angular velocity vector remain constant over time.

1. A constant direction of $\vec{\omega}$ implies that the sense of rotation (e.g., clockwise or anticlockwise) and the orientation of the axis of rotation remain unchanged.
2. A constant magnitude of $\vec{\omega}$ implies that the speed of rotation is constant and, for rotation to occur, non-zero. …

When a disc rotates with uniform angular velocity, it means that its angular velocity vector, $\vec{\omega}$, is constant. This is a crucial distinction: "uniform angular velocity" refers to the vector quantity, not just its magnitude. For a vector to be constant, both its magnitude and its direction must remain unchanged over time.

Let's break down what this implies for the rotation:

1. Understanding Angular Velocity ($\vec{\omega}$):

   Angular velocity is a vector quantity that describes both the speed and the axis of rotation.

   • The magnitude of $\vec{\omega}$, denoted as $|\vec{\omega}|$ or $\omega$, represents the angular speed (how fast the disc is rotating).
   • The direction of $\vec{\omega}$ points along the axis of rotation, determined by the right-hand rule (if you curl the fingers of your right hand in the direction of rotation, your thumb points in the direction of $\vec{\omega}$).
   Important

   "Uniform angular velocity" means that the angular velocity vector $\vec{\omega}$ is constant. This implies:

   1. The magnitude of $\vec{\omega}$ (angular speed) is constant.
   2. The direction of $\vec{\omega}$ (orientation of the axis of rotation and sense of rotation) is constant.

2. Analyzing Option (A): The sense of rotation remains same.

   The sense of rotation (clockwise or anticlockwise) is directly determined by the direction of the angular velocity vector $\vec{\omega}$. Since uniform angular velocity means the direction of $\vec{\omega}$ is constant, the sense of rotation must also remain the same.

   Therefore, statement (A) is true.

3. Analyzing Option (B): The orientation of the axis of rotation remains same.

   The axis of rotation is defined by the direction of the angular velocity vector $\vec{\omega}$. If $\vec{\omega}$ is constant, its direction is constant, which means the orientation of the axis of rotation in space does not change.

   Therefore, statement (B) is true.

4. Analyzing Option (C): The speed of rotation is non-zero and remains same. …

Concept: Uniform Angular Velocity is a Constant Vector

Step 1: What "uniform angular velocity" means

$\vec\omega$ constant in both magnitude and direction.

Step 2: Evaluate each option

• (a) Sense of rotation is fixed by the direction of $\vec\omega$ — true.
• (b) Axis orientation is fixed by the direction of $\vec\omega$ — true.
• (c) Speed of rotation is the magnitude of $\vec\omega$, constant and non-zero — true. …