A circular disc is rotating about its own axis at an angular velocity `omega`. If P is exact midpoint of dise between axis and rim of disc then angular velocity of Pis

Options

A. `(omega)/(2)`
B. `omega`
C. `sqrt(2)omega`
D. `2omega`

Answer

To solve the problem, we need to understand the concept of angular velocity in the context of a rotating circular disc. Here's a step-by-step breakdown of the solution:

### Step 1: Understand the Setup
We have a circular disc rotating about its own axis with an angular velocity denoted as `ω`. The disc has a center (axis of rotation) and a rim (outer edge).

**Hint:** Visualize the disc and identify the axis of rotation and the points of interest.

### Step 2: Identify Point P
Point P is defined as the exact midpoint between the axis of the disc and the rim. If we denote the radius of the disc as `r`, then point P is located at a distance of `r/2` from the center (axis of rotation).

**Hint:** Mark the location of point P on the disc, which is halfway to the rim.

### Step 3: Angular Velocity Concept
Angular velocity (ω) is the same for all points on a rigid body that is rotating about an axis. This means that every point on the disc, including point P, rotates with the same angular velocity `ω`.

**Hint:** Remember that angular velocity is uniform across the entire disc as it rotates.

### Step 4: Conclusion
Since point P is on the disc and the disc rotates uniformly, the angular velocity of point P is the same as the angular velocity of the entire disc, which is `ω`.

**Hint:** Conclude that the angular velocity does not change with the position on the disc.

### Final Answer
The angular velocity of point P is `ω`.

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