A body is executing circular motion in the vertical plane containing directions. If the direction of velocity `(oversetrightarrow(v))` at the top most point is towards west, what is the direction of angular velocity `(oversetrightarrow(omega))? `

Options

A. east
B. west
C. north
D. south

Answer

To determine the direction of the angular velocity vector \((\oversetrightarrow{\omega})\) when a body is executing circular motion in a vertical plane, we can follow these steps:

### Step 1: Understand the Circular Motion
The body is moving in a circular path in a vertical plane. At the topmost point of the circular path, the velocity vector \((\oversetrightarrow{v})\) is directed towards the west.

### Step 2: Visualize the Directions
Let's visualize the directions:
- At the topmost point, if we denote north, south, east, and west, we can set:
- North = Upward
- South = Downward
- East = Right
- West = Left

### Step 3: Determine the Sense of Rotation
Since the velocity vector \((\oversetrightarrow{v})\) at the topmost point is directed towards the west, we need to determine the sense of rotation. The body is moving in a circular path, and at the topmost point, the direction of motion is horizontal towards the west.

### Step 4: Apply the Right-Hand Rule
To find the direction of the angular velocity vector \((\oversetrightarrow{\omega})\), we can use the right-hand rule:
- Curl the fingers of your right hand in the direction of the circular motion (which is counterclockwise when viewed from above).
- Your thumb will point in the direction of the angular velocity vector \((\oversetrightarrow{\omega})\).

### Step 5: Identify the Direction of \((\oversetrightarrow{\omega})\)
Since the body is moving counterclockwise at the topmost point and the velocity is directed towards the west, the thumb of your right hand will point downward (towards the south). Therefore, the direction of the angular velocity vector \((\oversetrightarrow{\omega})\) is towards the south.

### Conclusion
Thus, the direction of the angular velocity vector \((\oversetrightarrow{\omega})\) is towards the south.

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