The angular velocity of a rigid body about any point of that body is same :

Options

A. only in magnitude
B. only in direction
C. both in magnitude and direction necessarily
D. both in magnitude and direction about some points but not about all points.

Explanation

To solve the question regarding the angular velocity of a rigid body about any point of that body, we can follow these steps:

### Step 1: Understand the Concept of Angular Velocity
Angular velocity (\( \omega \)) is a vector quantity that represents the rate of rotation of an object around an axis. It has both magnitude (how fast the object is rotating) and direction (the axis about which the object is rotating).

### Step 2: Consider the Rigid Body
A rigid body is an object with a fixed shape that does not deform under the influence of forces. When a rigid body rotates, every point in the body moves in a circular path around the axis of rotation.

### Step 3: Analyze Angular Velocity for Points in the Rigid Body
For any point in a rigid body, the angular velocity is the same in both magnitude and direction. This means that if the body is rotating, every point in that body experiences the same angular velocity vector.

### Step 4: Evaluate the Options
Now, let's evaluate the options given in the question:
1. **Only in magnitude** - This is incorrect because angular velocity is the same in both magnitude and direction.
2. **Only in direction** - This is also incorrect for the same reason.
3. **Both in magnitude and direction necessarily** - This is correct. The angular velocity is the same for all points in the rigid body.
4. **Both in magnitude and direction about some points but not about all points** - This is incorrect because it applies to all points in the rigid body.

### Conclusion
The correct answer is that the angular velocity of a rigid body about any point of that body is the same in both magnitude and direction necessarily.

### Final Answer
**The correct option is: Both in magnitude and direction necessarily.**

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