Angular speed of a uniformly circulating body with time period T is

Options

A. ` 2piT`
B. `(2pi)/T`
C. `piT`
D. `pi/T`

Answer

To find the angular speed of a uniformly circulating body with a time period \( T \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Angular Speed**:
Angular speed (\( \omega \)) is defined as the rate of change of angular displacement with respect to time. Mathematically, it can be expressed as:
\[ \omega = \frac{\theta}{t} \]
where \( \theta \) is the angular displacement and \( t \) is the time taken.

2. **Identify the Angular Displacement for One Revolution**:
For one complete revolution, the angular displacement (\( \theta \)) is \( 2\pi \) radians.

3. **Relate Time Period to Time**:
The time period \( T \) is the time taken for one complete revolution. Therefore, for one revolution, the time \( t \) is equal to \( T \).

4. **Substitute Values into the Angular Speed Formula**:
Now, substituting \( \theta = 2\pi \) and \( t = T \) into the angular speed formula, we get:
\[ \omega = \frac{2\pi}{T} \]

5. **Conclusion**:
Thus, the angular speed of a uniformly circulating body with time period \( T \) is:
\[ \omega = \frac{2\pi}{T} \]

### Final Answer:
The angular speed of a uniformly circulating body with time period \( T \) is \( \frac{2\pi}{T} \).