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 find the angular acceleration of a particle moving in a circular path with constant angular speed, we can follow these steps:

### Step 1: Understand the Given Information
We are given:
- Radius of the circular path, \( R = 25 \) m
- Constant angular speed, \( \omega = 12 \) revolutions per minute (rev/min)

### Step 2: Convert Angular Speed to Radians per Second
Since angular acceleration is typically expressed in radians per second squared, we need to convert the angular speed from revolutions per minute to radians per second.

1 revolution = \( 2\pi \) radians
1 minute = 60 seconds

Thus, we can convert:
\[ \omega = 12 \text{ rev/min} \times \frac{2\pi \text{ radians}}{1 \text{ rev}} \times \frac{1 \text{ min}}{60 \text{ s}} = \frac{12 \times 2\pi}{60} = \frac{24\pi}{60} = \frac{2\pi}{5} \text{ radians/s} \]

### Step 3: Determine Angular Acceleration
Angular acceleration (\( \alpha \)) is defined as the rate of change of angular velocity with respect to time:
\[ \alpha = \frac{d\omega}{dt} \]

Since the problem states that the particle is moving with a constant angular speed, this means that there is no change in angular velocity over time. Therefore:
\[ \alpha = 0 \text{ radians/s}^2 \]

### Conclusion
The angular acceleration of the particle is \( 0 \text{ radians/s}^2 \).

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