A particle is revoiving in a circular path of radius 25 m with constant angular speed 12 rev/min. then the angular acceleration of particle is

Options

A. `2pi^(2)` rad/`s^(2)`
B. `4pi^(2) "rad"//s^(2)`
C. `pi^(2) " rad"//s^(2)`
D. zero

Answer

To solve the problem, we need to determine the angular acceleration of a particle moving in a circular path with constant angular speed.

### Step-by-Step Solution:

1. **Understanding Angular Speed**:
The particle is revolving with a constant angular speed of 12 revolutions per minute (rev/min). This means that the angular velocity (ω) is constant.

2. **Convert Angular Speed to Radians per Second**:
To work with standard units, we convert revolutions per minute to radians per second.
- 1 revolution = 2π radians
- 1 minute = 60 seconds
- Therefore,
\[ \omega = 12 \, \text{rev/min} \times \frac{2\pi \, \text{radians}}{1 \, \text{rev}} \times \frac{1 \, \text{min}}{60 \, \text{s}} = \frac{12 \times 2\pi}{60} = \frac{24\pi}{60} = \frac{2\pi}{5} \, \text{rad/s} \]

3. **Determine Angular Acceleration**:
Angular acceleration (α) is defined as the rate of change of angular velocity (ω) over time. Since the problem states that the angular speed is constant, we can conclude:
\[ \alpha = \frac{d\omega}{dt} = 0 \, \text{rad/s}^2 \]

4. **Conclusion**:
Since the angular velocity is constant, the angular acceleration of the particle is zero. Thus, the answer is:
\[ \text{Angular acceleration} = 0 \, \text{rad/s}^2 \]

### Final Answer:
The angular acceleration of the particle is **0 rad/s²**.

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