A particle moves with constant angular velocity in a circle. During the motion its

Options

A. energy is conserved
B. momentum is conserved
C. energy and momentum both are conserved
D. None of the above

Answer

To solve the question, we need to analyze the motion of a particle moving with constant angular velocity in a circle and determine the conservation of energy and momentum.

### Step-by-Step Solution:

1. **Understanding Circular Motion**:
- A particle moving in a circle with constant angular velocity means that it travels along a circular path at a constant rate of rotation. The angular velocity (ω) remains constant.

2. **Analyzing Energy Conservation**:
- In circular motion, if there are no external forces acting on the particle (like friction or air resistance), the mechanical energy of the system remains constant. This is because the kinetic energy (KE) of the particle is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the particle and \( v \) is its linear velocity. Since the speed (magnitude of velocity) remains constant, the kinetic energy is also constant. Therefore, energy is conserved.

3. **Analyzing Momentum Conservation**:
- Momentum (p) is defined as:
\[ p = mv \]
In circular motion, although the speed of the particle remains constant, the direction of the velocity vector changes continuously as the particle moves along the circular path. Since momentum is a vector quantity, the change in direction of the velocity means that the momentum is also changing. Thus, momentum is not conserved in this scenario.

4. **Conclusion**:
- From the analysis, we conclude that while energy is conserved in the motion of the particle, momentum is not conserved due to the continuous change in direction of the velocity. Therefore, the correct answer is:
- **Option A: Energy is conserved**.

### Final Answer:
The correct option is A: Energy is conserved.